Prognostic Factors for Survival in Noncastrate Metastatic Prostate Cancer: Validation of the Glass Model and Development of a Novel Simplified Prognostic Model

2.1. The GETUG-15 trial

The GETUG-15 study included 385 patients between October 2004 and December 2008 [9] . Randomization was centralized using a 1:1 ratio to androgen deprivation therapy (ADT) with docetaxel (D) or ADT alone. In the D + ADT arm, patients received D 75 mg/m²on day 1 of a 21-d cycle, for up to nine cycles. ADT consisted of orchiectomy or luteinizing hormone-releasing hormone agonists, alone or combined with nonsteroidal antiandrogens. Patients older than 18 yr were eligible if they had histologically confirmed adenocarcinoma of the prostate and radiologically proven metastatic disease, a Karnofsky score ≥70%, and life expectancy ≥3 months, with adequate hepatic, hematologic and renal function.

2.2. Prognostic factors

The following prognostic factors were recorded at baseline: age, Eastern Cooperative Oncology Group (ECOG) performance score (PS), Gleason score, hemoglobin (Hb; normal vs abnormal), PSA, alkaline phosphatase (ALP; normal vs abnormal), lactate dehydrogenase (LDH; normal vs abnormal), bone metastases (yes vs no), visceral disease (yes vs no), metastases at diagnosis versus after local treatment failure, and body mass index (BMI). LDH, ALP, and Hb were defined as abnormal for values above the upper limit or below the lower limit of the normal range for the laboratory in which the assay was performed. Pain was assessed using the European Organization for Research and Treatment of Cancer (EORTC) 30-item quality-of-life (QLQC-30) self-administered questionnaire. Item responses were recorded as not at all; a little; quite a bit; or very much. The categorical raw scores were then linearly transformed to a 100-point scale according to the EORTC guidelines [10] , with higher scores representing a higher level of pain.

2.3. Data

The Glass model was validated using the full GETUG-15 study population (n = 385). To develop a new prognostic model, the data were randomly split into two independent data sets, with two-thirds of the population assigned to the learning set (n = 257) and one-third to the validation set (n = 128). Allocation was balanced for the randomized treatment arm and the number of events (deaths) observed.

2.4. Statistical analysis

The primary endpoint of the GETUG-15 trial was overall survival (OS), defined as the time from randomization to death. Patients known to be alive or lost to follow-up on the date of last contact were censored. Baseline characteristics were summarized using descriptive statistics (median and range for continuous variables, number and percentage for categorical variables). A proportional hazards regression model was used to assess the prognostic significance of the Glass risk groups. The performance of the model was measured using the concordance index (C-index). All baseline characteristics were further tested for univariate association with OS. Before univariate analysis, all baseline characteristics (categorical or continuous) were grouped or categorized using predefined cutoffs (PS 0 vs 1–2; Gleason score 2–7 vs 8–10; age ≤63 vs >63 yr; PSA ≤65 vs >65 ng/ml; BMI ≤30 vs >30 kg/m²; pain raw score not at all vs other scores). Continuous variables were analyzed in both continuous and categorical forms. Following Glass and colleagues [7] , a recursive partitioning-tree method was used on the learning set to classify patients into distinct prognostic risk groups. Null martingale residuals were first derived from censored survival data and used as the input into a standard classification and regression tree (CART) algorithm, implemented in the R packagerpart. CART evaluates all possible dichotomous splits on candidate factors or regression covariates, and selects the best variable and split variable. The process was continued until a minimum of 20 observations in any terminal leaf was reached. Only baseline characteristics significantly associated with OS at the 0.15 level were considered as candidate split variables, and tenfold cross-validation was used to prune possible tree overgrowth. The prognostic significance and C-index of the final prognostic model were assessed in the validation set using a Cox regression model considering the terminal groups as categorical factors. To further compare the performance of our model strategy with that of more state-of-the-art methods keeping all continuous variables in continuous form, we carried out stepwise proportional hazards regression with backward elimination and evaluated its discriminatory ability. The level of significance for retaining variables in the model was set to 0.15.

Survival curves were estimated using the Kaplan-Meier method. The 5-yr survival rate and median times are presented. All statistical tests were two-tailed with a nominal statistical significance level of 0.05, and bilateral confidence intervals were all estimated with 95% coverage probability. All statistical analyses were performed in the R 3.0.0 environment.

3.1. Patient characteristics

Data were analyzed for 385 patients ( Table 2 ). Most patients had metastases at the time of prostate cancer diagnosis (72%). The most common metastatic site was bone (81%); only 13% of the patients had visceral metastases (10% lung and 3% liver). The remaining 6% had lymph node metastases only. The median pain intensity was 16.7 (range 0–100).

3.2. Overall survival

The median follow-up was 58.3 mo (50.5–68.6 mo), during which 176 patients died; median follow-up for the 209 survivors was 48.0 mo (45.4–49.4 mo). Median OS did not significantly differ between the treatment groups, at 58.9 mo (95% CI 50.8–69.1) for the ADT + T arm and 54.2 mo (95% CI 42.2 to not reached [NR]) for the ADT arm (hazard ratio [HR] 1.01, 95% CI 0.75–1.36).

3.3. Validation of Glass risk groups

Regardless of treatment group, OS was significantly longer in the good-prognosis subgroup (median 69.1 mo, 95% CI 60.9 mo to NR) than in the intermediate-prognosis (46.5 mo, 95% CI 37.7 mo to NR) and poor-prognosis (36.6 mo, 95% CI 28.5–58.9 mo) subgroups (p = 0.001), with no difference between the latter two ( Fig. 1 ). In a multivariate Cox model including Glass risk categories and treatment arm, Glass risk group was found to be significant. The HR was 1.6 (1.1–2.3;p = 0.007) for intermediate versus low risk, 2.1 (1.5–3.1;p < 0.0010 for high versus low risk, and 1.3 (0.9–1.9;p = 0.17) for high versus intermediate risk. However, the discriminatory value of the model was low, with a C-index of 0.59 (95% CI 0.54–0.63).

Fig. 1 Kaplan Meier overall survival curves by Glass risk groups.

3.4. Univariate analysis and predictive accuracy of patient characteristics

We explored the prognostic significance of each categorical and continuous variable ( Table 3 ). Visceral metastases, bone metastases, PS (0 vs 1–2), Hb, ALP, LDH, PSA (≤65 vs >65 ng/ml), metastases (at diagnosis vs onset after local treatment failure), and pain intensity (≤16.7 vs 16.7 or continuous) were significant univariate predictors of OS (p ≤ 0.05). Gleason score and log(PSA) were of borderline significance (p ≤ 0.15), whereas age and BMI were not significant. We quantified the predictive accuracy of each variable using the C-index measure derived from univariate Cox regression analysis. The variables with the greatest discriminatory power were ALP (C-index 0.65, 95% CI 0.61–0.68), pain intensity (C-index 0.61, 95% CI 0.57–0.68), Hb (C-index 0.59, 95% CI 0.55–0.62), LDH (C-index 0.57, 95% CI 0.54–0.61), and bone metastases (C-index 0.57, 95% CI 0.-0.59).

3.5. Identification of new prognostic risk groups using recursive partitioning

All covariates of significance or borderline significance at the 0.15 level were included in the recursive partitioning algorithm (RPART): visceral metastases, bone metastases, metastases at diagnosis, Hb (normal vs abnormal), ALP (normal vs abnormal), LDH (normal vs abnormal), PSA (continuous), Gleason score, and pain intensity (0–100 points). In the learning set, unpruned recursive tree partitioning identified ALP, Gleason score, and pain intensity as variables with the greatest degree of discrimination ( Fig. 2 ). Cross-validation results identified ALP as the first split variable and the strongest predictor of OS. In the learning set, median OS was 69.1 mo (95% CI 66.1 mo to NR) for patients with normal ALP and 33.6 mo (95% CI 28.0–39.0 mo) for patients with abnormal ALP, with 5-yr survival estimates of 62.1% (95% CI 53.3–72.4%) and 23.2% (95% CI 14.3–37.6%), respectively. Kaplan-Meier survival estimates for the prognosis groups, identified by recursive partitioning until a minimum of 20 patients was reached, are plotted in Figure 3 A for the learning set and Figure 3 B for the validation set.

Fig. 2 Unpruned recursive partitioning tree for overall survival (OS) endpoint. HR = hazard ratio.

Fig. 3 Kaplan Meier overall survival curves for the unpruned tree in (A) the learning set and (B) the validation set. Group 1: normal alkaline phosphatase (ALP), Gleason ≤8, and pain score ≤25; group 2: normal ALP, Gleason ≤8, and pain score >25; group 3: normal ALP, Gleason ≥9; group 4: abnormal ALP, Gleason score ≥8; group 5: abnormal ALP, Gleason ≤7.

3.6. Validation of abnormal versus normal ALP predictive value

In the validation set, median OS was 75.0 mo (95% CI 62.5–NR) in patients with normal ALP (good prognosis) and 33.5 mo (95% CI 22.9–54.2 mo) in patients with abnormal ALP (poor prognosis), with 5-yr survival estimates of 67.3% (95% CI 56.8–80.8%) and 20.9% (95% CI 9.4–46.3%), respectively. Figure 3 A shows OS curves for the prognosis groups, defined by ALP and Gleason score. The HR for ALP was 3.11 (95% CI 2.14–4.52) and 3.13 (95% CI 1.82–5.37) for the learning and validation sets, respectively. By comparison, HR for the intermediate and poor Glass prognostic risk groups was respectively 1.56 (95% CI: 1.0-2.42) and 2.20 (95% CI 1.42–3.38) in the learning set, and 1.77 (95% CI: 0.98-3.18) and 1.87 (95% CI: 0.94-3.74) in the validation set. The Cox model using the single independent factor ALP was found to be superior to the Glass model with regards to predictive accuracy: C-index = 0.64 (0.58-0.71) vs 0.59 (0.52-0.66). The upper bound of the 95% bootstrap confidence interval for the difference between C-indexes indicates statistically significant difference (95% CI: >0.001-0.13). Survival curves according to ALP in the whole population are displayed in Figure 4 (p < 0.001).

Fig. 4 Survival according to alkaline phosphatase (normal vs abnormal) in the whole population.

3.7. Discrimination ability of different models

A secondary analysis involved stepwise proportional hazards regression, keeping all continuous variables in a continuous form. Starting with all baseline characteristics significant at the 0.15 level, the final variables retained in the multivariable model after backward elimination were PS (0 vs 1–2), ALP (normal vs abnormal), LDH (normal vs abnormal), and pain intensity (scale 0–100). We determined the discrimination ability of four different models in the learning and validation sets ( Table 4 ): a stepwise selection model with backward elimination; models defining two to four risk categories using percentiles for the linear predictor of the Cox regression model; normal/abnormal ALP model; and the original Glass model. Only patients with no missing data were included, because those with missing data were excluded from Cox regression analyses. The performance of the different models did not improve the discrimination ability of the simple risk model with ALP as a single regression variable.

2.1. The GETUG-15 trial

The GETUG-15 study included 385 patients between October 2004 and December 2008 [9] . Randomization was centralized using a 1:1 ratio to androgen deprivation therapy (ADT) with docetaxel (D) or ADT alone. In the D + ADT arm, patients received D 75 mg/m²on day 1 of a 21-d cycle, for up to nine cycles. ADT consisted of orchiectomy or luteinizing hormone-releasing hormone agonists, alone or combined with nonsteroidal antiandrogens. Patients older than 18 yr were eligible if they had histologically confirmed adenocarcinoma of the prostate and radiologically proven metastatic disease, a Karnofsky score ≥70%, and life expectancy ≥3 months, with adequate hepatic, hematologic and renal function.

2.2. Prognostic factors

The following prognostic factors were recorded at baseline: age, Eastern Cooperative Oncology Group (ECOG) performance score (PS), Gleason score, hemoglobin (Hb; normal vs abnormal), PSA, alkaline phosphatase (ALP; normal vs abnormal), lactate dehydrogenase (LDH; normal vs abnormal), bone metastases (yes vs no), visceral disease (yes vs no), metastases at diagnosis versus after local treatment failure, and body mass index (BMI). LDH, ALP, and Hb were defined as abnormal for values above the upper limit or below the lower limit of the normal range for the laboratory in which the assay was performed. Pain was assessed using the European Organization for Research and Treatment of Cancer (EORTC) 30-item quality-of-life (QLQC-30) self-administered questionnaire. Item responses were recorded as not at all; a little; quite a bit; or very much. The categorical raw scores were then linearly transformed to a 100-point scale according to the EORTC guidelines [10] , with higher scores representing a higher level of pain.

2.3. Data

The Glass model was validated using the full GETUG-15 study population (n = 385). To develop a new prognostic model, the data were randomly split into two independent data sets, with two-thirds of the population assigned to the learning set (n = 257) and one-third to the validation set (n = 128). Allocation was balanced for the randomized treatment arm and the number of events (deaths) observed.

2.4. Statistical analysis

The primary endpoint of the GETUG-15 trial was overall survival (OS), defined as the time from randomization to death. Patients known to be alive or lost to follow-up on the date of last contact were censored. Baseline characteristics were summarized using descriptive statistics (median and range for continuous variables, number and percentage for categorical variables). A proportional hazards regression model was used to assess the prognostic significance of the Glass risk groups. The performance of the model was measured using the concordance index (C-index). All baseline characteristics were further tested for univariate association with OS. Before univariate analysis, all baseline characteristics (categorical or continuous) were grouped or categorized using predefined cutoffs (PS 0 vs 1–2; Gleason score 2–7 vs 8–10; age ≤63 vs >63 yr; PSA ≤65 vs >65 ng/ml; BMI ≤30 vs >30 kg/m²; pain raw score not at all vs other scores). Continuous variables were analyzed in both continuous and categorical forms. Following Glass and colleagues [7] , a recursive partitioning-tree method was used on the learning set to classify patients into distinct prognostic risk groups. Null martingale residuals were first derived from censored survival data and used as the input into a standard classification and regression tree (CART) algorithm, implemented in the R packagerpart. CART evaluates all possible dichotomous splits on candidate factors or regression covariates, and selects the best variable and split variable. The process was continued until a minimum of 20 observations in any terminal leaf was reached. Only baseline characteristics significantly associated with OS at the 0.15 level were considered as candidate split variables, and tenfold cross-validation was used to prune possible tree overgrowth. The prognostic significance and C-index of the final prognostic model were assessed in the validation set using a Cox regression model considering the terminal groups as categorical factors. To further compare the performance of our model strategy with that of more state-of-the-art methods keeping all continuous variables in continuous form, we carried out stepwise proportional hazards regression with backward elimination and evaluated its discriminatory ability. The level of significance for retaining variables in the model was set to 0.15.

Survival curves were estimated using the Kaplan-Meier method. The 5-yr survival rate and median times are presented. All statistical tests were two-tailed with a nominal statistical significance level of 0.05, and bilateral confidence intervals were all estimated with 95% coverage probability. All statistical analyses were performed in the R 3.0.0 environment.

3.1. Patient characteristics

Data were analyzed for 385 patients ( Table 2 ). Most patients had metastases at the time of prostate cancer diagnosis (72%). The most common metastatic site was bone (81%); only 13% of the patients had visceral metastases (10% lung and 3% liver). The remaining 6% had lymph node metastases only. The median pain intensity was 16.7 (range 0–100).

3.2. Overall survival

The median follow-up was 58.3 mo (50.5–68.6 mo), during which 176 patients died; median follow-up for the 209 survivors was 48.0 mo (45.4–49.4 mo). Median OS did not significantly differ between the treatment groups, at 58.9 mo (95% CI 50.8–69.1) for the ADT + T arm and 54.2 mo (95% CI 42.2 to not reached [NR]) for the ADT arm (hazard ratio [HR] 1.01, 95% CI 0.75–1.36).

3.3. Validation of Glass risk groups

Regardless of treatment group, OS was significantly longer in the good-prognosis subgroup (median 69.1 mo, 95% CI 60.9 mo to NR) than in the intermediate-prognosis (46.5 mo, 95% CI 37.7 mo to NR) and poor-prognosis (36.6 mo, 95% CI 28.5–58.9 mo) subgroups (p = 0.001), with no difference between the latter two ( Fig. 1 ). In a multivariate Cox model including Glass risk categories and treatment arm, Glass risk group was found to be significant. The HR was 1.6 (1.1–2.3;p = 0.007) for intermediate versus low risk, 2.1 (1.5–3.1;p < 0.0010 for high versus low risk, and 1.3 (0.9–1.9;p = 0.17) for high versus intermediate risk. However, the discriminatory value of the model was low, with a C-index of 0.59 (95% CI 0.54–0.63).

Fig. 1 Kaplan Meier overall survival curves by Glass risk groups.

3.4. Univariate analysis and predictive accuracy of patient characteristics

We explored the prognostic significance of each categorical and continuous variable ( Table 3 ). Visceral metastases, bone metastases, PS (0 vs 1–2), Hb, ALP, LDH, PSA (≤65 vs >65 ng/ml), metastases (at diagnosis vs onset after local treatment failure), and pain intensity (≤16.7 vs 16.7 or continuous) were significant univariate predictors of OS (p ≤ 0.05). Gleason score and log(PSA) were of borderline significance (p ≤ 0.15), whereas age and BMI were not significant. We quantified the predictive accuracy of each variable using the C-index measure derived from univariate Cox regression analysis. The variables with the greatest discriminatory power were ALP (C-index 0.65, 95% CI 0.61–0.68), pain intensity (C-index 0.61, 95% CI 0.57–0.68), Hb (C-index 0.59, 95% CI 0.55–0.62), LDH (C-index 0.57, 95% CI 0.54–0.61), and bone metastases (C-index 0.57, 95% CI 0.-0.59).

3.5. Identification of new prognostic risk groups using recursive partitioning

All covariates of significance or borderline significance at the 0.15 level were included in the recursive partitioning algorithm (RPART): visceral metastases, bone metastases, metastases at diagnosis, Hb (normal vs abnormal), ALP (normal vs abnormal), LDH (normal vs abnormal), PSA (continuous), Gleason score, and pain intensity (0–100 points). In the learning set, unpruned recursive tree partitioning identified ALP, Gleason score, and pain intensity as variables with the greatest degree of discrimination ( Fig. 2 ). Cross-validation results identified ALP as the first split variable and the strongest predictor of OS. In the learning set, median OS was 69.1 mo (95% CI 66.1 mo to NR) for patients with normal ALP and 33.6 mo (95% CI 28.0–39.0 mo) for patients with abnormal ALP, with 5-yr survival estimates of 62.1% (95% CI 53.3–72.4%) and 23.2% (95% CI 14.3–37.6%), respectively. Kaplan-Meier survival estimates for the prognosis groups, identified by recursive partitioning until a minimum of 20 patients was reached, are plotted in Figure 3 A for the learning set and Figure 3 B for the validation set.

Fig. 2 Unpruned recursive partitioning tree for overall survival (OS) endpoint. HR = hazard ratio.

Fig. 3 Kaplan Meier overall survival curves for the unpruned tree in (A) the learning set and (B) the validation set. Group 1: normal alkaline phosphatase (ALP), Gleason ≤8, and pain score ≤25; group 2: normal ALP, Gleason ≤8, and pain score >25; group 3: normal ALP, Gleason ≥9; group 4: abnormal ALP, Gleason score ≥8; group 5: abnormal ALP, Gleason ≤7.

3.6. Validation of abnormal versus normal ALP predictive value

In the validation set, median OS was 75.0 mo (95% CI 62.5–NR) in patients with normal ALP (good prognosis) and 33.5 mo (95% CI 22.9–54.2 mo) in patients with abnormal ALP (poor prognosis), with 5-yr survival estimates of 67.3% (95% CI 56.8–80.8%) and 20.9% (95% CI 9.4–46.3%), respectively. Figure 3 A shows OS curves for the prognosis groups, defined by ALP and Gleason score. The HR for ALP was 3.11 (95% CI 2.14–4.52) and 3.13 (95% CI 1.82–5.37) for the learning and validation sets, respectively. By comparison, HR for the intermediate and poor Glass prognostic risk groups was respectively 1.56 (95% CI: 1.0-2.42) and 2.20 (95% CI 1.42–3.38) in the learning set, and 1.77 (95% CI: 0.98-3.18) and 1.87 (95% CI: 0.94-3.74) in the validation set. The Cox model using the single independent factor ALP was found to be superior to the Glass model with regards to predictive accuracy: C-index = 0.64 (0.58-0.71) vs 0.59 (0.52-0.66). The upper bound of the 95% bootstrap confidence interval for the difference between C-indexes indicates statistically significant difference (95% CI: >0.001-0.13). Survival curves according to ALP in the whole population are displayed in Figure 4 (p < 0.001).

Fig. 4 Survival according to alkaline phosphatase (normal vs abnormal) in the whole population.

3.7. Discrimination ability of different models

A secondary analysis involved stepwise proportional hazards regression, keeping all continuous variables in a continuous form. Starting with all baseline characteristics significant at the 0.15 level, the final variables retained in the multivariable model after backward elimination were PS (0 vs 1–2), ALP (normal vs abnormal), LDH (normal vs abnormal), and pain intensity (scale 0–100). We determined the discrimination ability of four different models in the learning and validation sets ( Table 4 ): a stepwise selection model with backward elimination; models defining two to four risk categories using percentiles for the linear predictor of the Cox regression model; normal/abnormal ALP model; and the original Glass model. Only patients with no missing data were included, because those with missing data were excluded from Cox regression analyses. The performance of the different models did not improve the discrimination ability of the simple risk model with ALP as a single regression variable.

2.1. The GETUG-15 trial

The GETUG-15 study included 385 patients between October 2004 and December 2008 [9] . Randomization was centralized using a 1:1 ratio to androgen deprivation therapy (ADT) with docetaxel (D) or ADT alone. In the D + ADT arm, patients received D 75 mg/m²on day 1 of a 21-d cycle, for up to nine cycles. ADT consisted of orchiectomy or luteinizing hormone-releasing hormone agonists, alone or combined with nonsteroidal antiandrogens. Patients older than 18 yr were eligible if they had histologically confirmed adenocarcinoma of the prostate and radiologically proven metastatic disease, a Karnofsky score ≥70%, and life expectancy ≥3 months, with adequate hepatic, hematologic and renal function.

2.2. Prognostic factors

The following prognostic factors were recorded at baseline: age, Eastern Cooperative Oncology Group (ECOG) performance score (PS), Gleason score, hemoglobin (Hb; normal vs abnormal), PSA, alkaline phosphatase (ALP; normal vs abnormal), lactate dehydrogenase (LDH; normal vs abnormal), bone metastases (yes vs no), visceral disease (yes vs no), metastases at diagnosis versus after local treatment failure, and body mass index (BMI). LDH, ALP, and Hb were defined as abnormal for values above the upper limit or below the lower limit of the normal range for the laboratory in which the assay was performed. Pain was assessed using the European Organization for Research and Treatment of Cancer (EORTC) 30-item quality-of-life (QLQC-30) self-administered questionnaire. Item responses were recorded as not at all; a little; quite a bit; or very much. The categorical raw scores were then linearly transformed to a 100-point scale according to the EORTC guidelines [10] , with higher scores representing a higher level of pain.

2.3. Data

The Glass model was validated using the full GETUG-15 study population (n = 385). To develop a new prognostic model, the data were randomly split into two independent data sets, with two-thirds of the population assigned to the learning set (n = 257) and one-third to the validation set (n = 128). Allocation was balanced for the randomized treatment arm and the number of events (deaths) observed.

2.4. Statistical analysis

The primary endpoint of the GETUG-15 trial was overall survival (OS), defined as the time from randomization to death. Patients known to be alive or lost to follow-up on the date of last contact were censored. Baseline characteristics were summarized using descriptive statistics (median and range for continuous variables, number and percentage for categorical variables). A proportional hazards regression model was used to assess the prognostic significance of the Glass risk groups. The performance of the model was measured using the concordance index (C-index). All baseline characteristics were further tested for univariate association with OS. Before univariate analysis, all baseline characteristics (categorical or continuous) were grouped or categorized using predefined cutoffs (PS 0 vs 1–2; Gleason score 2–7 vs 8–10; age ≤63 vs >63 yr; PSA ≤65 vs >65 ng/ml; BMI ≤30 vs >30 kg/m²; pain raw score not at all vs other scores). Continuous variables were analyzed in both continuous and categorical forms. Following Glass and colleagues [7] , a recursive partitioning-tree method was used on the learning set to classify patients into distinct prognostic risk groups. Null martingale residuals were first derived from censored survival data and used as the input into a standard classification and regression tree (CART) algorithm, implemented in the R packagerpart. CART evaluates all possible dichotomous splits on candidate factors or regression covariates, and selects the best variable and split variable. The process was continued until a minimum of 20 observations in any terminal leaf was reached. Only baseline characteristics significantly associated with OS at the 0.15 level were considered as candidate split variables, and tenfold cross-validation was used to prune possible tree overgrowth. The prognostic significance and C-index of the final prognostic model were assessed in the validation set using a Cox regression model considering the terminal groups as categorical factors. To further compare the performance of our model strategy with that of more state-of-the-art methods keeping all continuous variables in continuous form, we carried out stepwise proportional hazards regression with backward elimination and evaluated its discriminatory ability. The level of significance for retaining variables in the model was set to 0.15.

Survival curves were estimated using the Kaplan-Meier method. The 5-yr survival rate and median times are presented. All statistical tests were two-tailed with a nominal statistical significance level of 0.05, and bilateral confidence intervals were all estimated with 95% coverage probability. All statistical analyses were performed in the R 3.0.0 environment.

3.1. Patient characteristics

Data were analyzed for 385 patients ( Table 2 ). Most patients had metastases at the time of prostate cancer diagnosis (72%). The most common metastatic site was bone (81%); only 13% of the patients had visceral metastases (10% lung and 3% liver). The remaining 6% had lymph node metastases only. The median pain intensity was 16.7 (range 0–100).

3.2. Overall survival

The median follow-up was 58.3 mo (50.5–68.6 mo), during which 176 patients died; median follow-up for the 209 survivors was 48.0 mo (45.4–49.4 mo). Median OS did not significantly differ between the treatment groups, at 58.9 mo (95% CI 50.8–69.1) for the ADT + T arm and 54.2 mo (95% CI 42.2 to not reached [NR]) for the ADT arm (hazard ratio [HR] 1.01, 95% CI 0.75–1.36).

3.3. Validation of Glass risk groups

Regardless of treatment group, OS was significantly longer in the good-prognosis subgroup (median 69.1 mo, 95% CI 60.9 mo to NR) than in the intermediate-prognosis (46.5 mo, 95% CI 37.7 mo to NR) and poor-prognosis (36.6 mo, 95% CI 28.5–58.9 mo) subgroups (p = 0.001), with no difference between the latter two ( Fig. 1 ). In a multivariate Cox model including Glass risk categories and treatment arm, Glass risk group was found to be significant. The HR was 1.6 (1.1–2.3;p = 0.007) for intermediate versus low risk, 2.1 (1.5–3.1;p < 0.0010 for high versus low risk, and 1.3 (0.9–1.9;p = 0.17) for high versus intermediate risk. However, the discriminatory value of the model was low, with a C-index of 0.59 (95% CI 0.54–0.63).

Fig. 1 Kaplan Meier overall survival curves by Glass risk groups.

3.4. Univariate analysis and predictive accuracy of patient characteristics

We explored the prognostic significance of each categorical and continuous variable ( Table 3 ). Visceral metastases, bone metastases, PS (0 vs 1–2), Hb, ALP, LDH, PSA (≤65 vs >65 ng/ml), metastases (at diagnosis vs onset after local treatment failure), and pain intensity (≤16.7 vs 16.7 or continuous) were significant univariate predictors of OS (p ≤ 0.05). Gleason score and log(PSA) were of borderline significance (p ≤ 0.15), whereas age and BMI were not significant. We quantified the predictive accuracy of each variable using the C-index measure derived from univariate Cox regression analysis. The variables with the greatest discriminatory power were ALP (C-index 0.65, 95% CI 0.61–0.68), pain intensity (C-index 0.61, 95% CI 0.57–0.68), Hb (C-index 0.59, 95% CI 0.55–0.62), LDH (C-index 0.57, 95% CI 0.54–0.61), and bone metastases (C-index 0.57, 95% CI 0.-0.59).

3.5. Identification of new prognostic risk groups using recursive partitioning

All covariates of significance or borderline significance at the 0.15 level were included in the recursive partitioning algorithm (RPART): visceral metastases, bone metastases, metastases at diagnosis, Hb (normal vs abnormal), ALP (normal vs abnormal), LDH (normal vs abnormal), PSA (continuous), Gleason score, and pain intensity (0–100 points). In the learning set, unpruned recursive tree partitioning identified ALP, Gleason score, and pain intensity as variables with the greatest degree of discrimination ( Fig. 2 ). Cross-validation results identified ALP as the first split variable and the strongest predictor of OS. In the learning set, median OS was 69.1 mo (95% CI 66.1 mo to NR) for patients with normal ALP and 33.6 mo (95% CI 28.0–39.0 mo) for patients with abnormal ALP, with 5-yr survival estimates of 62.1% (95% CI 53.3–72.4%) and 23.2% (95% CI 14.3–37.6%), respectively. Kaplan-Meier survival estimates for the prognosis groups, identified by recursive partitioning until a minimum of 20 patients was reached, are plotted in Figure 3 A for the learning set and Figure 3 B for the validation set.

Fig. 2 Unpruned recursive partitioning tree for overall survival (OS) endpoint. HR = hazard ratio.

Fig. 3 Kaplan Meier overall survival curves for the unpruned tree in (A) the learning set and (B) the validation set. Group 1: normal alkaline phosphatase (ALP), Gleason ≤8, and pain score ≤25; group 2: normal ALP, Gleason ≤8, and pain score >25; group 3: normal ALP, Gleason ≥9; group 4: abnormal ALP, Gleason score ≥8; group 5: abnormal ALP, Gleason ≤7.

3.6. Validation of abnormal versus normal ALP predictive value

In the validation set, median OS was 75.0 mo (95% CI 62.5–NR) in patients with normal ALP (good prognosis) and 33.5 mo (95% CI 22.9–54.2 mo) in patients with abnormal ALP (poor prognosis), with 5-yr survival estimates of 67.3% (95% CI 56.8–80.8%) and 20.9% (95% CI 9.4–46.3%), respectively. Figure 3 A shows OS curves for the prognosis groups, defined by ALP and Gleason score. The HR for ALP was 3.11 (95% CI 2.14–4.52) and 3.13 (95% CI 1.82–5.37) for the learning and validation sets, respectively. By comparison, HR for the intermediate and poor Glass prognostic risk groups was respectively 1.56 (95% CI: 1.0-2.42) and 2.20 (95% CI 1.42–3.38) in the learning set, and 1.77 (95% CI: 0.98-3.18) and 1.87 (95% CI: 0.94-3.74) in the validation set. The Cox model using the single independent factor ALP was found to be superior to the Glass model with regards to predictive accuracy: C-index = 0.64 (0.58-0.71) vs 0.59 (0.52-0.66). The upper bound of the 95% bootstrap confidence interval for the difference between C-indexes indicates statistically significant difference (95% CI: >0.001-0.13). Survival curves according to ALP in the whole population are displayed in Figure 4 (p < 0.001).

Fig. 4 Survival according to alkaline phosphatase (normal vs abnormal) in the whole population.

3.7. Discrimination ability of different models

A secondary analysis involved stepwise proportional hazards regression, keeping all continuous variables in a continuous form. Starting with all baseline characteristics significant at the 0.15 level, the final variables retained in the multivariable model after backward elimination were PS (0 vs 1–2), ALP (normal vs abnormal), LDH (normal vs abnormal), and pain intensity (scale 0–100). We determined the discrimination ability of four different models in the learning and validation sets ( Table 4 ): a stepwise selection model with backward elimination; models defining two to four risk categories using percentiles for the linear predictor of the Cox regression model; normal/abnormal ALP model; and the original Glass model. Only patients with no missing data were included, because those with missing data were excluded from Cox regression analyses. The performance of the different models did not improve the discrimination ability of the simple risk model with ALP as a single regression variable.

2.1. The GETUG-15 trial

The GETUG-15 study included 385 patients between October 2004 and December 2008 [9] . Randomization was centralized using a 1:1 ratio to androgen deprivation therapy (ADT) with docetaxel (D) or ADT alone. In the D + ADT arm, patients received D 75 mg/m²on day 1 of a 21-d cycle, for up to nine cycles. ADT consisted of orchiectomy or luteinizing hormone-releasing hormone agonists, alone or combined with nonsteroidal antiandrogens. Patients older than 18 yr were eligible if they had histologically confirmed adenocarcinoma of the prostate and radiologically proven metastatic disease, a Karnofsky score ≥70%, and life expectancy ≥3 months, with adequate hepatic, hematologic and renal function.

2.2. Prognostic factors

The following prognostic factors were recorded at baseline: age, Eastern Cooperative Oncology Group (ECOG) performance score (PS), Gleason score, hemoglobin (Hb; normal vs abnormal), PSA, alkaline phosphatase (ALP; normal vs abnormal), lactate dehydrogenase (LDH; normal vs abnormal), bone metastases (yes vs no), visceral disease (yes vs no), metastases at diagnosis versus after local treatment failure, and body mass index (BMI). LDH, ALP, and Hb were defined as abnormal for values above the upper limit or below the lower limit of the normal range for the laboratory in which the assay was performed. Pain was assessed using the European Organization for Research and Treatment of Cancer (EORTC) 30-item quality-of-life (QLQC-30) self-administered questionnaire. Item responses were recorded as not at all; a little; quite a bit; or very much. The categorical raw scores were then linearly transformed to a 100-point scale according to the EORTC guidelines [10] , with higher scores representing a higher level of pain.

2.3. Data

The Glass model was validated using the full GETUG-15 study population (n = 385). To develop a new prognostic model, the data were randomly split into two independent data sets, with two-thirds of the population assigned to the learning set (n = 257) and one-third to the validation set (n = 128). Allocation was balanced for the randomized treatment arm and the number of events (deaths) observed.

2.4. Statistical analysis

The primary endpoint of the GETUG-15 trial was overall survival (OS), defined as the time from randomization to death. Patients known to be alive or lost to follow-up on the date of last contact were censored. Baseline characteristics were summarized using descriptive statistics (median and range for continuous variables, number and percentage for categorical variables). A proportional hazards regression model was used to assess the prognostic significance of the Glass risk groups. The performance of the model was measured using the concordance index (C-index). All baseline characteristics were further tested for univariate association with OS. Before univariate analysis, all baseline characteristics (categorical or continuous) were grouped or categorized using predefined cutoffs (PS 0 vs 1–2; Gleason score 2–7 vs 8–10; age ≤63 vs >63 yr; PSA ≤65 vs >65 ng/ml; BMI ≤30 vs >30 kg/m²; pain raw score not at all vs other scores). Continuous variables were analyzed in both continuous and categorical forms. Following Glass and colleagues [7] , a recursive partitioning-tree method was used on the learning set to classify patients into distinct prognostic risk groups. Null martingale residuals were first derived from censored survival data and used as the input into a standard classification and regression tree (CART) algorithm, implemented in the R packagerpart. CART evaluates all possible dichotomous splits on candidate factors or regression covariates, and selects the best variable and split variable. The process was continued until a minimum of 20 observations in any terminal leaf was reached. Only baseline characteristics significantly associated with OS at the 0.15 level were considered as candidate split variables, and tenfold cross-validation was used to prune possible tree overgrowth. The prognostic significance and C-index of the final prognostic model were assessed in the validation set using a Cox regression model considering the terminal groups as categorical factors. To further compare the performance of our model strategy with that of more state-of-the-art methods keeping all continuous variables in continuous form, we carried out stepwise proportional hazards regression with backward elimination and evaluated its discriminatory ability. The level of significance for retaining variables in the model was set to 0.15.

Survival curves were estimated using the Kaplan-Meier method. The 5-yr survival rate and median times are presented. All statistical tests were two-tailed with a nominal statistical significance level of 0.05, and bilateral confidence intervals were all estimated with 95% coverage probability. All statistical analyses were performed in the R 3.0.0 environment.

3.1. Patient characteristics

Data were analyzed for 385 patients ( Table 2 ). Most patients had metastases at the time of prostate cancer diagnosis (72%). The most common metastatic site was bone (81%); only 13% of the patients had visceral metastases (10% lung and 3% liver). The remaining 6% had lymph node metastases only. The median pain intensity was 16.7 (range 0–100).

3.2. Overall survival

The median follow-up was 58.3 mo (50.5–68.6 mo), during which 176 patients died; median follow-up for the 209 survivors was 48.0 mo (45.4–49.4 mo). Median OS did not significantly differ between the treatment groups, at 58.9 mo (95% CI 50.8–69.1) for the ADT + T arm and 54.2 mo (95% CI 42.2 to not reached [NR]) for the ADT arm (hazard ratio [HR] 1.01, 95% CI 0.75–1.36).

3.3. Validation of Glass risk groups

Regardless of treatment group, OS was significantly longer in the good-prognosis subgroup (median 69.1 mo, 95% CI 60.9 mo to NR) than in the intermediate-prognosis (46.5 mo, 95% CI 37.7 mo to NR) and poor-prognosis (36.6 mo, 95% CI 28.5–58.9 mo) subgroups (p = 0.001), with no difference between the latter two ( Fig. 1 ). In a multivariate Cox model including Glass risk categories and treatment arm, Glass risk group was found to be significant. The HR was 1.6 (1.1–2.3;p = 0.007) for intermediate versus low risk, 2.1 (1.5–3.1;p < 0.0010 for high versus low risk, and 1.3 (0.9–1.9;p = 0.17) for high versus intermediate risk. However, the discriminatory value of the model was low, with a C-index of 0.59 (95% CI 0.54–0.63).

Fig. 1 Kaplan Meier overall survival curves by Glass risk groups.

3.4. Univariate analysis and predictive accuracy of patient characteristics

We explored the prognostic significance of each categorical and continuous variable ( Table 3 ). Visceral metastases, bone metastases, PS (0 vs 1–2), Hb, ALP, LDH, PSA (≤65 vs >65 ng/ml), metastases (at diagnosis vs onset after local treatment failure), and pain intensity (≤16.7 vs 16.7 or continuous) were significant univariate predictors of OS (p ≤ 0.05). Gleason score and log(PSA) were of borderline significance (p ≤ 0.15), whereas age and BMI were not significant. We quantified the predictive accuracy of each variable using the C-index measure derived from univariate Cox regression analysis. The variables with the greatest discriminatory power were ALP (C-index 0.65, 95% CI 0.61–0.68), pain intensity (C-index 0.61, 95% CI 0.57–0.68), Hb (C-index 0.59, 95% CI 0.55–0.62), LDH (C-index 0.57, 95% CI 0.54–0.61), and bone metastases (C-index 0.57, 95% CI 0.-0.59).

3.5. Identification of new prognostic risk groups using recursive partitioning

All covariates of significance or borderline significance at the 0.15 level were included in the recursive partitioning algorithm (RPART): visceral metastases, bone metastases, metastases at diagnosis, Hb (normal vs abnormal), ALP (normal vs abnormal), LDH (normal vs abnormal), PSA (continuous), Gleason score, and pain intensity (0–100 points). In the learning set, unpruned recursive tree partitioning identified ALP, Gleason score, and pain intensity as variables with the greatest degree of discrimination ( Fig. 2 ). Cross-validation results identified ALP as the first split variable and the strongest predictor of OS. In the learning set, median OS was 69.1 mo (95% CI 66.1 mo to NR) for patients with normal ALP and 33.6 mo (95% CI 28.0–39.0 mo) for patients with abnormal ALP, with 5-yr survival estimates of 62.1% (95% CI 53.3–72.4%) and 23.2% (95% CI 14.3–37.6%), respectively. Kaplan-Meier survival estimates for the prognosis groups, identified by recursive partitioning until a minimum of 20 patients was reached, are plotted in Figure 3 A for the learning set and Figure 3 B for the validation set.

Fig. 2 Unpruned recursive partitioning tree for overall survival (OS) endpoint. HR = hazard ratio.

Fig. 3 Kaplan Meier overall survival curves for the unpruned tree in (A) the learning set and (B) the validation set. Group 1: normal alkaline phosphatase (ALP), Gleason ≤8, and pain score ≤25; group 2: normal ALP, Gleason ≤8, and pain score >25; group 3: normal ALP, Gleason ≥9; group 4: abnormal ALP, Gleason score ≥8; group 5: abnormal ALP, Gleason ≤7.

3.6. Validation of abnormal versus normal ALP predictive value

In the validation set, median OS was 75.0 mo (95% CI 62.5–NR) in patients with normal ALP (good prognosis) and 33.5 mo (95% CI 22.9–54.2 mo) in patients with abnormal ALP (poor prognosis), with 5-yr survival estimates of 67.3% (95% CI 56.8–80.8%) and 20.9% (95% CI 9.4–46.3%), respectively. Figure 3 A shows OS curves for the prognosis groups, defined by ALP and Gleason score. The HR for ALP was 3.11 (95% CI 2.14–4.52) and 3.13 (95% CI 1.82–5.37) for the learning and validation sets, respectively. By comparison, HR for the intermediate and poor Glass prognostic risk groups was respectively 1.56 (95% CI: 1.0-2.42) and 2.20 (95% CI 1.42–3.38) in the learning set, and 1.77 (95% CI: 0.98-3.18) and 1.87 (95% CI: 0.94-3.74) in the validation set. The Cox model using the single independent factor ALP was found to be superior to the Glass model with regards to predictive accuracy: C-index = 0.64 (0.58-0.71) vs 0.59 (0.52-0.66). The upper bound of the 95% bootstrap confidence interval for the difference between C-indexes indicates statistically significant difference (95% CI: >0.001-0.13). Survival curves according to ALP in the whole population are displayed in Figure 4 (p < 0.001).

Fig. 4 Survival according to alkaline phosphatase (normal vs abnormal) in the whole population.

3.7. Discrimination ability of different models

A secondary analysis involved stepwise proportional hazards regression, keeping all continuous variables in a continuous form. Starting with all baseline characteristics significant at the 0.15 level, the final variables retained in the multivariable model after backward elimination were PS (0 vs 1–2), ALP (normal vs abnormal), LDH (normal vs abnormal), and pain intensity (scale 0–100). We determined the discrimination ability of four different models in the learning and validation sets ( Table 4 ): a stepwise selection model with backward elimination; models defining two to four risk categories using percentiles for the linear predictor of the Cox regression model; normal/abnormal ALP model; and the original Glass model. Only patients with no missing data were included, because those with missing data were excluded from Cox regression analyses. The performance of the different models did not improve the discrimination ability of the simple risk model with ALP as a single regression variable.

2.1. The GETUG-15 trial

The GETUG-15 study included 385 patients between October 2004 and December 2008 [9] . Randomization was centralized using a 1:1 ratio to androgen deprivation therapy (ADT) with docetaxel (D) or ADT alone. In the D + ADT arm, patients received D 75 mg/m²on day 1 of a 21-d cycle, for up to nine cycles. ADT consisted of orchiectomy or luteinizing hormone-releasing hormone agonists, alone or combined with nonsteroidal antiandrogens. Patients older than 18 yr were eligible if they had histologically confirmed adenocarcinoma of the prostate and radiologically proven metastatic disease, a Karnofsky score ≥70%, and life expectancy ≥3 months, with adequate hepatic, hematologic and renal function.

2.2. Prognostic factors

The following prognostic factors were recorded at baseline: age, Eastern Cooperative Oncology Group (ECOG) performance score (PS), Gleason score, hemoglobin (Hb; normal vs abnormal), PSA, alkaline phosphatase (ALP; normal vs abnormal), lactate dehydrogenase (LDH; normal vs abnormal), bone metastases (yes vs no), visceral disease (yes vs no), metastases at diagnosis versus after local treatment failure, and body mass index (BMI). LDH, ALP, and Hb were defined as abnormal for values above the upper limit or below the lower limit of the normal range for the laboratory in which the assay was performed. Pain was assessed using the European Organization for Research and Treatment of Cancer (EORTC) 30-item quality-of-life (QLQC-30) self-administered questionnaire. Item responses were recorded as not at all; a little; quite a bit; or very much. The categorical raw scores were then linearly transformed to a 100-point scale according to the EORTC guidelines [10] , with higher scores representing a higher level of pain.

2.3. Data

The Glass model was validated using the full GETUG-15 study population (n = 385). To develop a new prognostic model, the data were randomly split into two independent data sets, with two-thirds of the population assigned to the learning set (n = 257) and one-third to the validation set (n = 128). Allocation was balanced for the randomized treatment arm and the number of events (deaths) observed.

2.4. Statistical analysis

The primary endpoint of the GETUG-15 trial was overall survival (OS), defined as the time from randomization to death. Patients known to be alive or lost to follow-up on the date of last contact were censored. Baseline characteristics were summarized using descriptive statistics (median and range for continuous variables, number and percentage for categorical variables). A proportional hazards regression model was used to assess the prognostic significance of the Glass risk groups. The performance of the model was measured using the concordance index (C-index). All baseline characteristics were further tested for univariate association with OS. Before univariate analysis, all baseline characteristics (categorical or continuous) were grouped or categorized using predefined cutoffs (PS 0 vs 1–2; Gleason score 2–7 vs 8–10; age ≤63 vs >63 yr; PSA ≤65 vs >65 ng/ml; BMI ≤30 vs >30 kg/m²; pain raw score not at all vs other scores). Continuous variables were analyzed in both continuous and categorical forms. Following Glass and colleagues [7] , a recursive partitioning-tree method was used on the learning set to classify patients into distinct prognostic risk groups. Null martingale residuals were first derived from censored survival data and used as the input into a standard classification and regression tree (CART) algorithm, implemented in the R packagerpart. CART evaluates all possible dichotomous splits on candidate factors or regression covariates, and selects the best variable and split variable. The process was continued until a minimum of 20 observations in any terminal leaf was reached. Only baseline characteristics significantly associated with OS at the 0.15 level were considered as candidate split variables, and tenfold cross-validation was used to prune possible tree overgrowth. The prognostic significance and C-index of the final prognostic model were assessed in the validation set using a Cox regression model considering the terminal groups as categorical factors. To further compare the performance of our model strategy with that of more state-of-the-art methods keeping all continuous variables in continuous form, we carried out stepwise proportional hazards regression with backward elimination and evaluated its discriminatory ability. The level of significance for retaining variables in the model was set to 0.15.

Survival curves were estimated using the Kaplan-Meier method. The 5-yr survival rate and median times are presented. All statistical tests were two-tailed with a nominal statistical significance level of 0.05, and bilateral confidence intervals were all estimated with 95% coverage probability. All statistical analyses were performed in the R 3.0.0 environment.

3.1. Patient characteristics

Data were analyzed for 385 patients ( Table 2 ). Most patients had metastases at the time of prostate cancer diagnosis (72%). The most common metastatic site was bone (81%); only 13% of the patients had visceral metastases (10% lung and 3% liver). The remaining 6% had lymph node metastases only. The median pain intensity was 16.7 (range 0–100).

3.2. Overall survival

The median follow-up was 58.3 mo (50.5–68.6 mo), during which 176 patients died; median follow-up for the 209 survivors was 48.0 mo (45.4–49.4 mo). Median OS did not significantly differ between the treatment groups, at 58.9 mo (95% CI 50.8–69.1) for the ADT + T arm and 54.2 mo (95% CI 42.2 to not reached [NR]) for the ADT arm (hazard ratio [HR] 1.01, 95% CI 0.75–1.36).

3.3. Validation of Glass risk groups

Regardless of treatment group, OS was significantly longer in the good-prognosis subgroup (median 69.1 mo, 95% CI 60.9 mo to NR) than in the intermediate-prognosis (46.5 mo, 95% CI 37.7 mo to NR) and poor-prognosis (36.6 mo, 95% CI 28.5–58.9 mo) subgroups (p = 0.001), with no difference between the latter two ( Fig. 1 ). In a multivariate Cox model including Glass risk categories and treatment arm, Glass risk group was found to be significant. The HR was 1.6 (1.1–2.3;p = 0.007) for intermediate versus low risk, 2.1 (1.5–3.1;p < 0.0010 for high versus low risk, and 1.3 (0.9–1.9;p = 0.17) for high versus intermediate risk. However, the discriminatory value of the model was low, with a C-index of 0.59 (95% CI 0.54–0.63).

Fig. 1 Kaplan Meier overall survival curves by Glass risk groups.

3.4. Univariate analysis and predictive accuracy of patient characteristics

We explored the prognostic significance of each categorical and continuous variable ( Table 3 ). Visceral metastases, bone metastases, PS (0 vs 1–2), Hb, ALP, LDH, PSA (≤65 vs >65 ng/ml), metastases (at diagnosis vs onset after local treatment failure), and pain intensity (≤16.7 vs 16.7 or continuous) were significant univariate predictors of OS (p ≤ 0.05). Gleason score and log(PSA) were of borderline significance (p ≤ 0.15), whereas age and BMI were not significant. We quantified the predictive accuracy of each variable using the C-index measure derived from univariate Cox regression analysis. The variables with the greatest discriminatory power were ALP (C-index 0.65, 95% CI 0.61–0.68), pain intensity (C-index 0.61, 95% CI 0.57–0.68), Hb (C-index 0.59, 95% CI 0.55–0.62), LDH (C-index 0.57, 95% CI 0.54–0.61), and bone metastases (C-index 0.57, 95% CI 0.-0.59).

3.5. Identification of new prognostic risk groups using recursive partitioning

All covariates of significance or borderline significance at the 0.15 level were included in the recursive partitioning algorithm (RPART): visceral metastases, bone metastases, metastases at diagnosis, Hb (normal vs abnormal), ALP (normal vs abnormal), LDH (normal vs abnormal), PSA (continuous), Gleason score, and pain intensity (0–100 points). In the learning set, unpruned recursive tree partitioning identified ALP, Gleason score, and pain intensity as variables with the greatest degree of discrimination ( Fig. 2 ). Cross-validation results identified ALP as the first split variable and the strongest predictor of OS. In the learning set, median OS was 69.1 mo (95% CI 66.1 mo to NR) for patients with normal ALP and 33.6 mo (95% CI 28.0–39.0 mo) for patients with abnormal ALP, with 5-yr survival estimates of 62.1% (95% CI 53.3–72.4%) and 23.2% (95% CI 14.3–37.6%), respectively. Kaplan-Meier survival estimates for the prognosis groups, identified by recursive partitioning until a minimum of 20 patients was reached, are plotted in Figure 3 A for the learning set and Figure 3 B for the validation set.

Fig. 2 Unpruned recursive partitioning tree for overall survival (OS) endpoint. HR = hazard ratio.

Fig. 3 Kaplan Meier overall survival curves for the unpruned tree in (A) the learning set and (B) the validation set. Group 1: normal alkaline phosphatase (ALP), Gleason ≤8, and pain score ≤25; group 2: normal ALP, Gleason ≤8, and pain score >25; group 3: normal ALP, Gleason ≥9; group 4: abnormal ALP, Gleason score ≥8; group 5: abnormal ALP, Gleason ≤7.

3.6. Validation of abnormal versus normal ALP predictive value

In the validation set, median OS was 75.0 mo (95% CI 62.5–NR) in patients with normal ALP (good prognosis) and 33.5 mo (95% CI 22.9–54.2 mo) in patients with abnormal ALP (poor prognosis), with 5-yr survival estimates of 67.3% (95% CI 56.8–80.8%) and 20.9% (95% CI 9.4–46.3%), respectively. Figure 3 A shows OS curves for the prognosis groups, defined by ALP and Gleason score. The HR for ALP was 3.11 (95% CI 2.14–4.52) and 3.13 (95% CI 1.82–5.37) for the learning and validation sets, respectively. By comparison, HR for the intermediate and poor Glass prognostic risk groups was respectively 1.56 (95% CI: 1.0-2.42) and 2.20 (95% CI 1.42–3.38) in the learning set, and 1.77 (95% CI: 0.98-3.18) and 1.87 (95% CI: 0.94-3.74) in the validation set. The Cox model using the single independent factor ALP was found to be superior to the Glass model with regards to predictive accuracy: C-index = 0.64 (0.58-0.71) vs 0.59 (0.52-0.66). The upper bound of the 95% bootstrap confidence interval for the difference between C-indexes indicates statistically significant difference (95% CI: >0.001-0.13). Survival curves according to ALP in the whole population are displayed in Figure 4 (p < 0.001).

Fig. 4 Survival according to alkaline phosphatase (normal vs abnormal) in the whole population.

3.7. Discrimination ability of different models

A secondary analysis involved stepwise proportional hazards regression, keeping all continuous variables in a continuous form. Starting with all baseline characteristics significant at the 0.15 level, the final variables retained in the multivariable model after backward elimination were PS (0 vs 1–2), ALP (normal vs abnormal), LDH (normal vs abnormal), and pain intensity (scale 0–100). We determined the discrimination ability of four different models in the learning and validation sets ( Table 4 ): a stepwise selection model with backward elimination; models defining two to four risk categories using percentiles for the linear predictor of the Cox regression model; normal/abnormal ALP model; and the original Glass model. Only patients with no missing data were included, because those with missing data were excluded from Cox regression analyses. The performance of the different models did not improve the discrimination ability of the simple risk model with ALP as a single regression variable.

2.1. The GETUG-15 trial

The GETUG-15 study included 385 patients between October 2004 and December 2008 [9] . Randomization was centralized using a 1:1 ratio to androgen deprivation therapy (ADT) with docetaxel (D) or ADT alone. In the D + ADT arm, patients received D 75 mg/m²on day 1 of a 21-d cycle, for up to nine cycles. ADT consisted of orchiectomy or luteinizing hormone-releasing hormone agonists, alone or combined with nonsteroidal antiandrogens. Patients older than 18 yr were eligible if they had histologically confirmed adenocarcinoma of the prostate and radiologically proven metastatic disease, a Karnofsky score ≥70%, and life expectancy ≥3 months, with adequate hepatic, hematologic and renal function.

2.2. Prognostic factors

The following prognostic factors were recorded at baseline: age, Eastern Cooperative Oncology Group (ECOG) performance score (PS), Gleason score, hemoglobin (Hb; normal vs abnormal), PSA, alkaline phosphatase (ALP; normal vs abnormal), lactate dehydrogenase (LDH; normal vs abnormal), bone metastases (yes vs no), visceral disease (yes vs no), metastases at diagnosis versus after local treatment failure, and body mass index (BMI). LDH, ALP, and Hb were defined as abnormal for values above the upper limit or below the lower limit of the normal range for the laboratory in which the assay was performed. Pain was assessed using the European Organization for Research and Treatment of Cancer (EORTC) 30-item quality-of-life (QLQC-30) self-administered questionnaire. Item responses were recorded as not at all; a little; quite a bit; or very much. The categorical raw scores were then linearly transformed to a 100-point scale according to the EORTC guidelines [10] , with higher scores representing a higher level of pain.

2.3. Data

The Glass model was validated using the full GETUG-15 study population (n = 385). To develop a new prognostic model, the data were randomly split into two independent data sets, with two-thirds of the population assigned to the learning set (n = 257) and one-third to the validation set (n = 128). Allocation was balanced for the randomized treatment arm and the number of events (deaths) observed.

2.4. Statistical analysis

The primary endpoint of the GETUG-15 trial was overall survival (OS), defined as the time from randomization to death. Patients known to be alive or lost to follow-up on the date of last contact were censored. Baseline characteristics were summarized using descriptive statistics (median and range for continuous variables, number and percentage for categorical variables). A proportional hazards regression model was used to assess the prognostic significance of the Glass risk groups. The performance of the model was measured using the concordance index (C-index). All baseline characteristics were further tested for univariate association with OS. Before univariate analysis, all baseline characteristics (categorical or continuous) were grouped or categorized using predefined cutoffs (PS 0 vs 1–2; Gleason score 2–7 vs 8–10; age ≤63 vs >63 yr; PSA ≤65 vs >65 ng/ml; BMI ≤30 vs >30 kg/m²; pain raw score not at all vs other scores). Continuous variables were analyzed in both continuous and categorical forms. Following Glass and colleagues [7] , a recursive partitioning-tree method was used on the learning set to classify patients into distinct prognostic risk groups. Null martingale residuals were first derived from censored survival data and used as the input into a standard classification and regression tree (CART) algorithm, implemented in the R packagerpart. CART evaluates all possible dichotomous splits on candidate factors or regression covariates, and selects the best variable and split variable. The process was continued until a minimum of 20 observations in any terminal leaf was reached. Only baseline characteristics significantly associated with OS at the 0.15 level were considered as candidate split variables, and tenfold cross-validation was used to prune possible tree overgrowth. The prognostic significance and C-index of the final prognostic model were assessed in the validation set using a Cox regression model considering the terminal groups as categorical factors. To further compare the performance of our model strategy with that of more state-of-the-art methods keeping all continuous variables in continuous form, we carried out stepwise proportional hazards regression with backward elimination and evaluated its discriminatory ability. The level of significance for retaining variables in the model was set to 0.15.

Survival curves were estimated using the Kaplan-Meier method. The 5-yr survival rate and median times are presented. All statistical tests were two-tailed with a nominal statistical significance level of 0.05, and bilateral confidence intervals were all estimated with 95% coverage probability. All statistical analyses were performed in the R 3.0.0 environment.

3.1. Patient characteristics

Data were analyzed for 385 patients ( Table 2 ). Most patients had metastases at the time of prostate cancer diagnosis (72%). The most common metastatic site was bone (81%); only 13% of the patients had visceral metastases (10% lung and 3% liver). The remaining 6% had lymph node metastases only. The median pain intensity was 16.7 (range 0–100).

3.2. Overall survival

The median follow-up was 58.3 mo (50.5–68.6 mo), during which 176 patients died; median follow-up for the 209 survivors was 48.0 mo (45.4–49.4 mo). Median OS did not significantly differ between the treatment groups, at 58.9 mo (95% CI 50.8–69.1) for the ADT + T arm and 54.2 mo (95% CI 42.2 to not reached [NR]) for the ADT arm (hazard ratio [HR] 1.01, 95% CI 0.75–1.36).

3.3. Validation of Glass risk groups

Regardless of treatment group, OS was significantly longer in the good-prognosis subgroup (median 69.1 mo, 95% CI 60.9 mo to NR) than in the intermediate-prognosis (46.5 mo, 95% CI 37.7 mo to NR) and poor-prognosis (36.6 mo, 95% CI 28.5–58.9 mo) subgroups (p = 0.001), with no difference between the latter two ( Fig. 1 ). In a multivariate Cox model including Glass risk categories and treatment arm, Glass risk group was found to be significant. The HR was 1.6 (1.1–2.3;p = 0.007) for intermediate versus low risk, 2.1 (1.5–3.1;p < 0.0010 for high versus low risk, and 1.3 (0.9–1.9;p = 0.17) for high versus intermediate risk. However, the discriminatory value of the model was low, with a C-index of 0.59 (95% CI 0.54–0.63).

Fig. 1 Kaplan Meier overall survival curves by Glass risk groups.

3.4. Univariate analysis and predictive accuracy of patient characteristics

We explored the prognostic significance of each categorical and continuous variable ( Table 3 ). Visceral metastases, bone metastases, PS (0 vs 1–2), Hb, ALP, LDH, PSA (≤65 vs >65 ng/ml), metastases (at diagnosis vs onset after local treatment failure), and pain intensity (≤16.7 vs 16.7 or continuous) were significant univariate predictors of OS (p ≤ 0.05). Gleason score and log(PSA) were of borderline significance (p ≤ 0.15), whereas age and BMI were not significant. We quantified the predictive accuracy of each variable using the C-index measure derived from univariate Cox regression analysis. The variables with the greatest discriminatory power were ALP (C-index 0.65, 95% CI 0.61–0.68), pain intensity (C-index 0.61, 95% CI 0.57–0.68), Hb (C-index 0.59, 95% CI 0.55–0.62), LDH (C-index 0.57, 95% CI 0.54–0.61), and bone metastases (C-index 0.57, 95% CI 0.-0.59).

3.5. Identification of new prognostic risk groups using recursive partitioning

All covariates of significance or borderline significance at the 0.15 level were included in the recursive partitioning algorithm (RPART): visceral metastases, bone metastases, metastases at diagnosis, Hb (normal vs abnormal), ALP (normal vs abnormal), LDH (normal vs abnormal), PSA (continuous), Gleason score, and pain intensity (0–100 points). In the learning set, unpruned recursive tree partitioning identified ALP, Gleason score, and pain intensity as variables with the greatest degree of discrimination ( Fig. 2 ). Cross-validation results identified ALP as the first split variable and the strongest predictor of OS. In the learning set, median OS was 69.1 mo (95% CI 66.1 mo to NR) for patients with normal ALP and 33.6 mo (95% CI 28.0–39.0 mo) for patients with abnormal ALP, with 5-yr survival estimates of 62.1% (95% CI 53.3–72.4%) and 23.2% (95% CI 14.3–37.6%), respectively. Kaplan-Meier survival estimates for the prognosis groups, identified by recursive partitioning until a minimum of 20 patients was reached, are plotted in Figure 3 A for the learning set and Figure 3 B for the validation set.

Fig. 2 Unpruned recursive partitioning tree for overall survival (OS) endpoint. HR = hazard ratio.

Fig. 3 Kaplan Meier overall survival curves for the unpruned tree in (A) the learning set and (B) the validation set. Group 1: normal alkaline phosphatase (ALP), Gleason ≤8, and pain score ≤25; group 2: normal ALP, Gleason ≤8, and pain score >25; group 3: normal ALP, Gleason ≥9; group 4: abnormal ALP, Gleason score ≥8; group 5: abnormal ALP, Gleason ≤7.

3.6. Validation of abnormal versus normal ALP predictive value

In the validation set, median OS was 75.0 mo (95% CI 62.5–NR) in patients with normal ALP (good prognosis) and 33.5 mo (95% CI 22.9–54.2 mo) in patients with abnormal ALP (poor prognosis), with 5-yr survival estimates of 67.3% (95% CI 56.8–80.8%) and 20.9% (95% CI 9.4–46.3%), respectively. Figure 3 A shows OS curves for the prognosis groups, defined by ALP and Gleason score. The HR for ALP was 3.11 (95% CI 2.14–4.52) and 3.13 (95% CI 1.82–5.37) for the learning and validation sets, respectively. By comparison, HR for the intermediate and poor Glass prognostic risk groups was respectively 1.56 (95% CI: 1.0-2.42) and 2.20 (95% CI 1.42–3.38) in the learning set, and 1.77 (95% CI: 0.98-3.18) and 1.87 (95% CI: 0.94-3.74) in the validation set. The Cox model using the single independent factor ALP was found to be superior to the Glass model with regards to predictive accuracy: C-index = 0.64 (0.58-0.71) vs 0.59 (0.52-0.66). The upper bound of the 95% bootstrap confidence interval for the difference between C-indexes indicates statistically significant difference (95% CI: >0.001-0.13). Survival curves according to ALP in the whole population are displayed in Figure 4 (p < 0.001).

Fig. 4 Survival according to alkaline phosphatase (normal vs abnormal) in the whole population.

3.7. Discrimination ability of different models

A secondary analysis involved stepwise proportional hazards regression, keeping all continuous variables in a continuous form. Starting with all baseline characteristics significant at the 0.15 level, the final variables retained in the multivariable model after backward elimination were PS (0 vs 1–2), ALP (normal vs abnormal), LDH (normal vs abnormal), and pain intensity (scale 0–100). We determined the discrimination ability of four different models in the learning and validation sets ( Table 4 ): a stepwise selection model with backward elimination; models defining two to four risk categories using percentiles for the linear predictor of the Cox regression model; normal/abnormal ALP model; and the original Glass model. Only patients with no missing data were included, because those with missing data were excluded from Cox regression analyses. The performance of the different models did not improve the discrimination ability of the simple risk model with ALP as a single regression variable.

2.1. The GETUG-15 trial

The GETUG-15 study included 385 patients between October 2004 and December 2008 [9] . Randomization was centralized using a 1:1 ratio to androgen deprivation therapy (ADT) with docetaxel (D) or ADT alone. In the D + ADT arm, patients received D 75 mg/m²on day 1 of a 21-d cycle, for up to nine cycles. ADT consisted of orchiectomy or luteinizing hormone-releasing hormone agonists, alone or combined with nonsteroidal antiandrogens. Patients older than 18 yr were eligible if they had histologically confirmed adenocarcinoma of the prostate and radiologically proven metastatic disease, a Karnofsky score ≥70%, and life expectancy ≥3 months, with adequate hepatic, hematologic and renal function.

2.2. Prognostic factors

The following prognostic factors were recorded at baseline: age, Eastern Cooperative Oncology Group (ECOG) performance score (PS), Gleason score, hemoglobin (Hb; normal vs abnormal), PSA, alkaline phosphatase (ALP; normal vs abnormal), lactate dehydrogenase (LDH; normal vs abnormal), bone metastases (yes vs no), visceral disease (yes vs no), metastases at diagnosis versus after local treatment failure, and body mass index (BMI). LDH, ALP, and Hb were defined as abnormal for values above the upper limit or below the lower limit of the normal range for the laboratory in which the assay was performed. Pain was assessed using the European Organization for Research and Treatment of Cancer (EORTC) 30-item quality-of-life (QLQC-30) self-administered questionnaire. Item responses were recorded as not at all; a little; quite a bit; or very much. The categorical raw scores were then linearly transformed to a 100-point scale according to the EORTC guidelines [10] , with higher scores representing a higher level of pain.

2.3. Data

The Glass model was validated using the full GETUG-15 study population (n = 385). To develop a new prognostic model, the data were randomly split into two independent data sets, with two-thirds of the population assigned to the learning set (n = 257) and one-third to the validation set (n = 128). Allocation was balanced for the randomized treatment arm and the number of events (deaths) observed.

2.4. Statistical analysis

The primary endpoint of the GETUG-15 trial was overall survival (OS), defined as the time from randomization to death. Patients known to be alive or lost to follow-up on the date of last contact were censored. Baseline characteristics were summarized using descriptive statistics (median and range for continuous variables, number and percentage for categorical variables). A proportional hazards regression model was used to assess the prognostic significance of the Glass risk groups. The performance of the model was measured using the concordance index (C-index). All baseline characteristics were further tested for univariate association with OS. Before univariate analysis, all baseline characteristics (categorical or continuous) were grouped or categorized using predefined cutoffs (PS 0 vs 1–2; Gleason score 2–7 vs 8–10; age ≤63 vs >63 yr; PSA ≤65 vs >65 ng/ml; BMI ≤30 vs >30 kg/m²; pain raw score not at all vs other scores). Continuous variables were analyzed in both continuous and categorical forms. Following Glass and colleagues [7] , a recursive partitioning-tree method was used on the learning set to classify patients into distinct prognostic risk groups. Null martingale residuals were first derived from censored survival data and used as the input into a standard classification and regression tree (CART) algorithm, implemented in the R packagerpart. CART evaluates all possible dichotomous splits on candidate factors or regression covariates, and selects the best variable and split variable. The process was continued until a minimum of 20 observations in any terminal leaf was reached. Only baseline characteristics significantly associated with OS at the 0.15 level were considered as candidate split variables, and tenfold cross-validation was used to prune possible tree overgrowth. The prognostic significance and C-index of the final prognostic model were assessed in the validation set using a Cox regression model considering the terminal groups as categorical factors. To further compare the performance of our model strategy with that of more state-of-the-art methods keeping all continuous variables in continuous form, we carried out stepwise proportional hazards regression with backward elimination and evaluated its discriminatory ability. The level of significance for retaining variables in the model was set to 0.15.

Survival curves were estimated using the Kaplan-Meier method. The 5-yr survival rate and median times are presented. All statistical tests were two-tailed with a nominal statistical significance level of 0.05, and bilateral confidence intervals were all estimated with 95% coverage probability. All statistical analyses were performed in the R 3.0.0 environment.

3.1. Patient characteristics

Data were analyzed for 385 patients ( Table 2 ). Most patients had metastases at the time of prostate cancer diagnosis (72%). The most common metastatic site was bone (81%); only 13% of the patients had visceral metastases (10% lung and 3% liver). The remaining 6% had lymph node metastases only. The median pain intensity was 16.7 (range 0–100).

3.2. Overall survival

The median follow-up was 58.3 mo (50.5–68.6 mo), during which 176 patients died; median follow-up for the 209 survivors was 48.0 mo (45.4–49.4 mo). Median OS did not significantly differ between the treatment groups, at 58.9 mo (95% CI 50.8–69.1) for the ADT + T arm and 54.2 mo (95% CI 42.2 to not reached [NR]) for the ADT arm (hazard ratio [HR] 1.01, 95% CI 0.75–1.36).

3.3. Validation of Glass risk groups

Regardless of treatment group, OS was significantly longer in the good-prognosis subgroup (median 69.1 mo, 95% CI 60.9 mo to NR) than in the intermediate-prognosis (46.5 mo, 95% CI 37.7 mo to NR) and poor-prognosis (36.6 mo, 95% CI 28.5–58.9 mo) subgroups (p = 0.001), with no difference between the latter two ( Fig. 1 ). In a multivariate Cox model including Glass risk categories and treatment arm, Glass risk group was found to be significant. The HR was 1.6 (1.1–2.3;p = 0.007) for intermediate versus low risk, 2.1 (1.5–3.1;p < 0.0010 for high versus low risk, and 1.3 (0.9–1.9;p = 0.17) for high versus intermediate risk. However, the discriminatory value of the model was low, with a C-index of 0.59 (95% CI 0.54–0.63).

Fig. 1 Kaplan Meier overall survival curves by Glass risk groups.

3.4. Univariate analysis and predictive accuracy of patient characteristics

We explored the prognostic significance of each categorical and continuous variable ( Table 3 ). Visceral metastases, bone metastases, PS (0 vs 1–2), Hb, ALP, LDH, PSA (≤65 vs >65 ng/ml), metastases (at diagnosis vs onset after local treatment failure), and pain intensity (≤16.7 vs 16.7 or continuous) were significant univariate predictors of OS (p ≤ 0.05). Gleason score and log(PSA) were of borderline significance (p ≤ 0.15), whereas age and BMI were not significant. We quantified the predictive accuracy of each variable using the C-index measure derived from univariate Cox regression analysis. The variables with the greatest discriminatory power were ALP (C-index 0.65, 95% CI 0.61–0.68), pain intensity (C-index 0.61, 95% CI 0.57–0.68), Hb (C-index 0.59, 95% CI 0.55–0.62), LDH (C-index 0.57, 95% CI 0.54–0.61), and bone metastases (C-index 0.57, 95% CI 0.-0.59).

3.5. Identification of new prognostic risk groups using recursive partitioning

All covariates of significance or borderline significance at the 0.15 level were included in the recursive partitioning algorithm (RPART): visceral metastases, bone metastases, metastases at diagnosis, Hb (normal vs abnormal), ALP (normal vs abnormal), LDH (normal vs abnormal), PSA (continuous), Gleason score, and pain intensity (0–100 points). In the learning set, unpruned recursive tree partitioning identified ALP, Gleason score, and pain intensity as variables with the greatest degree of discrimination ( Fig. 2 ). Cross-validation results identified ALP as the first split variable and the strongest predictor of OS. In the learning set, median OS was 69.1 mo (95% CI 66.1 mo to NR) for patients with normal ALP and 33.6 mo (95% CI 28.0–39.0 mo) for patients with abnormal ALP, with 5-yr survival estimates of 62.1% (95% CI 53.3–72.4%) and 23.2% (95% CI 14.3–37.6%), respectively. Kaplan-Meier survival estimates for the prognosis groups, identified by recursive partitioning until a minimum of 20 patients was reached, are plotted in Figure 3 A for the learning set and Figure 3 B for the validation set.

Fig. 2 Unpruned recursive partitioning tree for overall survival (OS) endpoint. HR = hazard ratio.

Fig. 3 Kaplan Meier overall survival curves for the unpruned tree in (A) the learning set and (B) the validation set. Group 1: normal alkaline phosphatase (ALP), Gleason ≤8, and pain score ≤25; group 2: normal ALP, Gleason ≤8, and pain score >25; group 3: normal ALP, Gleason ≥9; group 4: abnormal ALP, Gleason score ≥8; group 5: abnormal ALP, Gleason ≤7.

3.6. Validation of abnormal versus normal ALP predictive value

In the validation set, median OS was 75.0 mo (95% CI 62.5–NR) in patients with normal ALP (good prognosis) and 33.5 mo (95% CI 22.9–54.2 mo) in patients with abnormal ALP (poor prognosis), with 5-yr survival estimates of 67.3% (95% CI 56.8–80.8%) and 20.9% (95% CI 9.4–46.3%), respectively. Figure 3 A shows OS curves for the prognosis groups, defined by ALP and Gleason score. The HR for ALP was 3.11 (95% CI 2.14–4.52) and 3.13 (95% CI 1.82–5.37) for the learning and validation sets, respectively. By comparison, HR for the intermediate and poor Glass prognostic risk groups was respectively 1.56 (95% CI: 1.0-2.42) and 2.20 (95% CI 1.42–3.38) in the learning set, and 1.77 (95% CI: 0.98-3.18) and 1.87 (95% CI: 0.94-3.74) in the validation set. The Cox model using the single independent factor ALP was found to be superior to the Glass model with regards to predictive accuracy: C-index = 0.64 (0.58-0.71) vs 0.59 (0.52-0.66). The upper bound of the 95% bootstrap confidence interval for the difference between C-indexes indicates statistically significant difference (95% CI: >0.001-0.13). Survival curves according to ALP in the whole population are displayed in Figure 4 (p < 0.001).

Fig. 4 Survival according to alkaline phosphatase (normal vs abnormal) in the whole population.

3.7. Discrimination ability of different models

A secondary analysis involved stepwise proportional hazards regression, keeping all continuous variables in a continuous form. Starting with all baseline characteristics significant at the 0.15 level, the final variables retained in the multivariable model after backward elimination were PS (0 vs 1–2), ALP (normal vs abnormal), LDH (normal vs abnormal), and pain intensity (scale 0–100). We determined the discrimination ability of four different models in the learning and validation sets ( Table 4 ): a stepwise selection model with backward elimination; models defining two to four risk categories using percentiles for the linear predictor of the Cox regression model; normal/abnormal ALP model; and the original Glass model. Only patients with no missing data were included, because those with missing data were excluded from Cox regression analyses. The performance of the different models did not improve the discrimination ability of the simple risk model with ALP as a single regression variable.

2.1. The GETUG-15 trial

The GETUG-15 study included 385 patients between October 2004 and December 2008 [9] . Randomization was centralized using a 1:1 ratio to androgen deprivation therapy (ADT) with docetaxel (D) or ADT alone. In the D + ADT arm, patients received D 75 mg/m²on day 1 of a 21-d cycle, for up to nine cycles. ADT consisted of orchiectomy or luteinizing hormone-releasing hormone agonists, alone or combined with nonsteroidal antiandrogens. Patients older than 18 yr were eligible if they had histologically confirmed adenocarcinoma of the prostate and radiologically proven metastatic disease, a Karnofsky score ≥70%, and life expectancy ≥3 months, with adequate hepatic, hematologic and renal function.

2.2. Prognostic factors

The following prognostic factors were recorded at baseline: age, Eastern Cooperative Oncology Group (ECOG) performance score (PS), Gleason score, hemoglobin (Hb; normal vs abnormal), PSA, alkaline phosphatase (ALP; normal vs abnormal), lactate dehydrogenase (LDH; normal vs abnormal), bone metastases (yes vs no), visceral disease (yes vs no), metastases at diagnosis versus after local treatment failure, and body mass index (BMI). LDH, ALP, and Hb were defined as abnormal for values above the upper limit or below the lower limit of the normal range for the laboratory in which the assay was performed. Pain was assessed using the European Organization for Research and Treatment of Cancer (EORTC) 30-item quality-of-life (QLQC-30) self-administered questionnaire. Item responses were recorded as not at all; a little; quite a bit; or very much. The categorical raw scores were then linearly transformed to a 100-point scale according to the EORTC guidelines [10] , with higher scores representing a higher level of pain.

2.3. Data

The Glass model was validated using the full GETUG-15 study population (n = 385). To develop a new prognostic model, the data were randomly split into two independent data sets, with two-thirds of the population assigned to the learning set (n = 257) and one-third to the validation set (n = 128). Allocation was balanced for the randomized treatment arm and the number of events (deaths) observed.

2.4. Statistical analysis

The primary endpoint of the GETUG-15 trial was overall survival (OS), defined as the time from randomization to death. Patients known to be alive or lost to follow-up on the date of last contact were censored. Baseline characteristics were summarized using descriptive statistics (median and range for continuous variables, number and percentage for categorical variables). A proportional hazards regression model was used to assess the prognostic significance of the Glass risk groups. The performance of the model was measured using the concordance index (C-index). All baseline characteristics were further tested for univariate association with OS. Before univariate analysis, all baseline characteristics (categorical or continuous) were grouped or categorized using predefined cutoffs (PS 0 vs 1–2; Gleason score 2–7 vs 8–10; age ≤63 vs >63 yr; PSA ≤65 vs >65 ng/ml; BMI ≤30 vs >30 kg/m²; pain raw score not at all vs other scores). Continuous variables were analyzed in both continuous and categorical forms. Following Glass and colleagues [7] , a recursive partitioning-tree method was used on the learning set to classify patients into distinct prognostic risk groups. Null martingale residuals were first derived from censored survival data and used as the input into a standard classification and regression tree (CART) algorithm, implemented in the R packagerpart. CART evaluates all possible dichotomous splits on candidate factors or regression covariates, and selects the best variable and split variable. The process was continued until a minimum of 20 observations in any terminal leaf was reached. Only baseline characteristics significantly associated with OS at the 0.15 level were considered as candidate split variables, and tenfold cross-validation was used to prune possible tree overgrowth. The prognostic significance and C-index of the final prognostic model were assessed in the validation set using a Cox regression model considering the terminal groups as categorical factors. To further compare the performance of our model strategy with that of more state-of-the-art methods keeping all continuous variables in continuous form, we carried out stepwise proportional hazards regression with backward elimination and evaluated its discriminatory ability. The level of significance for retaining variables in the model was set to 0.15.

Survival curves were estimated using the Kaplan-Meier method. The 5-yr survival rate and median times are presented. All statistical tests were two-tailed with a nominal statistical significance level of 0.05, and bilateral confidence intervals were all estimated with 95% coverage probability. All statistical analyses were performed in the R 3.0.0 environment.

3.1. Patient characteristics

Data were analyzed for 385 patients ( Table 2 ). Most patients had metastases at the time of prostate cancer diagnosis (72%). The most common metastatic site was bone (81%); only 13% of the patients had visceral metastases (10% lung and 3% liver). The remaining 6% had lymph node metastases only. The median pain intensity was 16.7 (range 0–100).

3.2. Overall survival

The median follow-up was 58.3 mo (50.5–68.6 mo), during which 176 patients died; median follow-up for the 209 survivors was 48.0 mo (45.4–49.4 mo). Median OS did not significantly differ between the treatment groups, at 58.9 mo (95% CI 50.8–69.1) for the ADT + T arm and 54.2 mo (95% CI 42.2 to not reached [NR]) for the ADT arm (hazard ratio [HR] 1.01, 95% CI 0.75–1.36).

3.3. Validation of Glass risk groups

Regardless of treatment group, OS was significantly longer in the good-prognosis subgroup (median 69.1 mo, 95% CI 60.9 mo to NR) than in the intermediate-prognosis (46.5 mo, 95% CI 37.7 mo to NR) and poor-prognosis (36.6 mo, 95% CI 28.5–58.9 mo) subgroups (p = 0.001), with no difference between the latter two ( Fig. 1 ). In a multivariate Cox model including Glass risk categories and treatment arm, Glass risk group was found to be significant. The HR was 1.6 (1.1–2.3;p = 0.007) for intermediate versus low risk, 2.1 (1.5–3.1;p < 0.0010 for high versus low risk, and 1.3 (0.9–1.9;p = 0.17) for high versus intermediate risk. However, the discriminatory value of the model was low, with a C-index of 0.59 (95% CI 0.54–0.63).

Fig. 1 Kaplan Meier overall survival curves by Glass risk groups.

3.4. Univariate analysis and predictive accuracy of patient characteristics

We explored the prognostic significance of each categorical and continuous variable ( Table 3 ). Visceral metastases, bone metastases, PS (0 vs 1–2), Hb, ALP, LDH, PSA (≤65 vs >65 ng/ml), metastases (at diagnosis vs onset after local treatment failure), and pain intensity (≤16.7 vs 16.7 or continuous) were significant univariate predictors of OS (p ≤ 0.05). Gleason score and log(PSA) were of borderline significance (p ≤ 0.15), whereas age and BMI were not significant. We quantified the predictive accuracy of each variable using the C-index measure derived from univariate Cox regression analysis. The variables with the greatest discriminatory power were ALP (C-index 0.65, 95% CI 0.61–0.68), pain intensity (C-index 0.61, 95% CI 0.57–0.68), Hb (C-index 0.59, 95% CI 0.55–0.62), LDH (C-index 0.57, 95% CI 0.54–0.61), and bone metastases (C-index 0.57, 95% CI 0.-0.59).

3.5. Identification of new prognostic risk groups using recursive partitioning

All covariates of significance or borderline significance at the 0.15 level were included in the recursive partitioning algorithm (RPART): visceral metastases, bone metastases, metastases at diagnosis, Hb (normal vs abnormal), ALP (normal vs abnormal), LDH (normal vs abnormal), PSA (continuous), Gleason score, and pain intensity (0–100 points). In the learning set, unpruned recursive tree partitioning identified ALP, Gleason score, and pain intensity as variables with the greatest degree of discrimination ( Fig. 2 ). Cross-validation results identified ALP as the first split variable and the strongest predictor of OS. In the learning set, median OS was 69.1 mo (95% CI 66.1 mo to NR) for patients with normal ALP and 33.6 mo (95% CI 28.0–39.0 mo) for patients with abnormal ALP, with 5-yr survival estimates of 62.1% (95% CI 53.3–72.4%) and 23.2% (95% CI 14.3–37.6%), respectively. Kaplan-Meier survival estimates for the prognosis groups, identified by recursive partitioning until a minimum of 20 patients was reached, are plotted in Figure 3 A for the learning set and Figure 3 B for the validation set.

Fig. 2 Unpruned recursive partitioning tree for overall survival (OS) endpoint. HR = hazard ratio.

Fig. 3 Kaplan Meier overall survival curves for the unpruned tree in (A) the learning set and (B) the validation set. Group 1: normal alkaline phosphatase (ALP), Gleason ≤8, and pain score ≤25; group 2: normal ALP, Gleason ≤8, and pain score >25; group 3: normal ALP, Gleason ≥9; group 4: abnormal ALP, Gleason score ≥8; group 5: abnormal ALP, Gleason ≤7.

3.6. Validation of abnormal versus normal ALP predictive value

In the validation set, median OS was 75.0 mo (95% CI 62.5–NR) in patients with normal ALP (good prognosis) and 33.5 mo (95% CI 22.9–54.2 mo) in patients with abnormal ALP (poor prognosis), with 5-yr survival estimates of 67.3% (95% CI 56.8–80.8%) and 20.9% (95% CI 9.4–46.3%), respectively. Figure 3 A shows OS curves for the prognosis groups, defined by ALP and Gleason score. The HR for ALP was 3.11 (95% CI 2.14–4.52) and 3.13 (95% CI 1.82–5.37) for the learning and validation sets, respectively. By comparison, HR for the intermediate and poor Glass prognostic risk groups was respectively 1.56 (95% CI: 1.0-2.42) and 2.20 (95% CI 1.42–3.38) in the learning set, and 1.77 (95% CI: 0.98-3.18) and 1.87 (95% CI: 0.94-3.74) in the validation set. The Cox model using the single independent factor ALP was found to be superior to the Glass model with regards to predictive accuracy: C-index = 0.64 (0.58-0.71) vs 0.59 (0.52-0.66). The upper bound of the 95% bootstrap confidence interval for the difference between C-indexes indicates statistically significant difference (95% CI: >0.001-0.13). Survival curves according to ALP in the whole population are displayed in Figure 4 (p < 0.001).

Fig. 4 Survival according to alkaline phosphatase (normal vs abnormal) in the whole population.

3.7. Discrimination ability of different models

A secondary analysis involved stepwise proportional hazards regression, keeping all continuous variables in a continuous form. Starting with all baseline characteristics significant at the 0.15 level, the final variables retained in the multivariable model after backward elimination were PS (0 vs 1–2), ALP (normal vs abnormal), LDH (normal vs abnormal), and pain intensity (scale 0–100). We determined the discrimination ability of four different models in the learning and validation sets ( Table 4 ): a stepwise selection model with backward elimination; models defining two to four risk categories using percentiles for the linear predictor of the Cox regression model; normal/abnormal ALP model; and the original Glass model. Only patients with no missing data were included, because those with missing data were excluded from Cox regression analyses. The performance of the different models did not improve the discrimination ability of the simple risk model with ALP as a single regression variable.

2.1. The GETUG-15 trial

The GETUG-15 study included 385 patients between October 2004 and December 2008 [9] . Randomization was centralized using a 1:1 ratio to androgen deprivation therapy (ADT) with docetaxel (D) or ADT alone. In the D + ADT arm, patients received D 75 mg/m²on day 1 of a 21-d cycle, for up to nine cycles. ADT consisted of orchiectomy or luteinizing hormone-releasing hormone agonists, alone or combined with nonsteroidal antiandrogens. Patients older than 18 yr were eligible if they had histologically confirmed adenocarcinoma of the prostate and radiologically proven metastatic disease, a Karnofsky score ≥70%, and life expectancy ≥3 months, with adequate hepatic, hematologic and renal function.

2.2. Prognostic factors

The following prognostic factors were recorded at baseline: age, Eastern Cooperative Oncology Group (ECOG) performance score (PS), Gleason score, hemoglobin (Hb; normal vs abnormal), PSA, alkaline phosphatase (ALP; normal vs abnormal), lactate dehydrogenase (LDH; normal vs abnormal), bone metastases (yes vs no), visceral disease (yes vs no), metastases at diagnosis versus after local treatment failure, and body mass index (BMI). LDH, ALP, and Hb were defined as abnormal for values above the upper limit or below the lower limit of the normal range for the laboratory in which the assay was performed. Pain was assessed using the European Organization for Research and Treatment of Cancer (EORTC) 30-item quality-of-life (QLQC-30) self-administered questionnaire. Item responses were recorded as not at all; a little; quite a bit; or very much. The categorical raw scores were then linearly transformed to a 100-point scale according to the EORTC guidelines [10] , with higher scores representing a higher level of pain.

2.3. Data

The Glass model was validated using the full GETUG-15 study population (n = 385). To develop a new prognostic model, the data were randomly split into two independent data sets, with two-thirds of the population assigned to the learning set (n = 257) and one-third to the validation set (n = 128). Allocation was balanced for the randomized treatment arm and the number of events (deaths) observed.

2.4. Statistical analysis

The primary endpoint of the GETUG-15 trial was overall survival (OS), defined as the time from randomization to death. Patients known to be alive or lost to follow-up on the date of last contact were censored. Baseline characteristics were summarized using descriptive statistics (median and range for continuous variables, number and percentage for categorical variables). A proportional hazards regression model was used to assess the prognostic significance of the Glass risk groups. The performance of the model was measured using the concordance index (C-index). All baseline characteristics were further tested for univariate association with OS. Before univariate analysis, all baseline characteristics (categorical or continuous) were grouped or categorized using predefined cutoffs (PS 0 vs 1–2; Gleason score 2–7 vs 8–10; age ≤63 vs >63 yr; PSA ≤65 vs >65 ng/ml; BMI ≤30 vs >30 kg/m²; pain raw score not at all vs other scores). Continuous variables were analyzed in both continuous and categorical forms. Following Glass and colleagues [7] , a recursive partitioning-tree method was used on the learning set to classify patients into distinct prognostic risk groups. Null martingale residuals were first derived from censored survival data and used as the input into a standard classification and regression tree (CART) algorithm, implemented in the R packagerpart. CART evaluates all possible dichotomous splits on candidate factors or regression covariates, and selects the best variable and split variable. The process was continued until a minimum of 20 observations in any terminal leaf was reached. Only baseline characteristics significantly associated with OS at the 0.15 level were considered as candidate split variables, and tenfold cross-validation was used to prune possible tree overgrowth. The prognostic significance and C-index of the final prognostic model were assessed in the validation set using a Cox regression model considering the terminal groups as categorical factors. To further compare the performance of our model strategy with that of more state-of-the-art methods keeping all continuous variables in continuous form, we carried out stepwise proportional hazards regression with backward elimination and evaluated its discriminatory ability. The level of significance for retaining variables in the model was set to 0.15.

Survival curves were estimated using the Kaplan-Meier method. The 5-yr survival rate and median times are presented. All statistical tests were two-tailed with a nominal statistical significance level of 0.05, and bilateral confidence intervals were all estimated with 95% coverage probability. All statistical analyses were performed in the R 3.0.0 environment.

3.1. Patient characteristics

Data were analyzed for 385 patients ( Table 2 ). Most patients had metastases at the time of prostate cancer diagnosis (72%). The most common metastatic site was bone (81%); only 13% of the patients had visceral metastases (10% lung and 3% liver). The remaining 6% had lymph node metastases only. The median pain intensity was 16.7 (range 0–100).

3.2. Overall survival

The median follow-up was 58.3 mo (50.5–68.6 mo), during which 176 patients died; median follow-up for the 209 survivors was 48.0 mo (45.4–49.4 mo). Median OS did not significantly differ between the treatment groups, at 58.9 mo (95% CI 50.8–69.1) for the ADT + T arm and 54.2 mo (95% CI 42.2 to not reached [NR]) for the ADT arm (hazard ratio [HR] 1.01, 95% CI 0.75–1.36).

3.3. Validation of Glass risk groups

Regardless of treatment group, OS was significantly longer in the good-prognosis subgroup (median 69.1 mo, 95% CI 60.9 mo to NR) than in the intermediate-prognosis (46.5 mo, 95% CI 37.7 mo to NR) and poor-prognosis (36.6 mo, 95% CI 28.5–58.9 mo) subgroups (p = 0.001), with no difference between the latter two ( Fig. 1 ). In a multivariate Cox model including Glass risk categories and treatment arm, Glass risk group was found to be significant. The HR was 1.6 (1.1–2.3;p = 0.007) for intermediate versus low risk, 2.1 (1.5–3.1;p < 0.0010 for high versus low risk, and 1.3 (0.9–1.9;p = 0.17) for high versus intermediate risk. However, the discriminatory value of the model was low, with a C-index of 0.59 (95% CI 0.54–0.63).

Fig. 1 Kaplan Meier overall survival curves by Glass risk groups.

3.4. Univariate analysis and predictive accuracy of patient characteristics

We explored the prognostic significance of each categorical and continuous variable ( Table 3 ). Visceral metastases, bone metastases, PS (0 vs 1–2), Hb, ALP, LDH, PSA (≤65 vs >65 ng/ml), metastases (at diagnosis vs onset after local treatment failure), and pain intensity (≤16.7 vs 16.7 or continuous) were significant univariate predictors of OS (p ≤ 0.05). Gleason score and log(PSA) were of borderline significance (p ≤ 0.15), whereas age and BMI were not significant. We quantified the predictive accuracy of each variable using the C-index measure derived from univariate Cox regression analysis. The variables with the greatest discriminatory power were ALP (C-index 0.65, 95% CI 0.61–0.68), pain intensity (C-index 0.61, 95% CI 0.57–0.68), Hb (C-index 0.59, 95% CI 0.55–0.62), LDH (C-index 0.57, 95% CI 0.54–0.61), and bone metastases (C-index 0.57, 95% CI 0.-0.59).

3.5. Identification of new prognostic risk groups using recursive partitioning

All covariates of significance or borderline significance at the 0.15 level were included in the recursive partitioning algorithm (RPART): visceral metastases, bone metastases, metastases at diagnosis, Hb (normal vs abnormal), ALP (normal vs abnormal), LDH (normal vs abnormal), PSA (continuous), Gleason score, and pain intensity (0–100 points). In the learning set, unpruned recursive tree partitioning identified ALP, Gleason score, and pain intensity as variables with the greatest degree of discrimination ( Fig. 2 ). Cross-validation results identified ALP as the first split variable and the strongest predictor of OS. In the learning set, median OS was 69.1 mo (95% CI 66.1 mo to NR) for patients with normal ALP and 33.6 mo (95% CI 28.0–39.0 mo) for patients with abnormal ALP, with 5-yr survival estimates of 62.1% (95% CI 53.3–72.4%) and 23.2% (95% CI 14.3–37.6%), respectively. Kaplan-Meier survival estimates for the prognosis groups, identified by recursive partitioning until a minimum of 20 patients was reached, are plotted in Figure 3 A for the learning set and Figure 3 B for the validation set.

Fig. 2 Unpruned recursive partitioning tree for overall survival (OS) endpoint. HR = hazard ratio.

Fig. 3 Kaplan Meier overall survival curves for the unpruned tree in (A) the learning set and (B) the validation set. Group 1: normal alkaline phosphatase (ALP), Gleason ≤8, and pain score ≤25; group 2: normal ALP, Gleason ≤8, and pain score >25; group 3: normal ALP, Gleason ≥9; group 4: abnormal ALP, Gleason score ≥8; group 5: abnormal ALP, Gleason ≤7.

3.6. Validation of abnormal versus normal ALP predictive value

In the validation set, median OS was 75.0 mo (95% CI 62.5–NR) in patients with normal ALP (good prognosis) and 33.5 mo (95% CI 22.9–54.2 mo) in patients with abnormal ALP (poor prognosis), with 5-yr survival estimates of 67.3% (95% CI 56.8–80.8%) and 20.9% (95% CI 9.4–46.3%), respectively. Figure 3 A shows OS curves for the prognosis groups, defined by ALP and Gleason score. The HR for ALP was 3.11 (95% CI 2.14–4.52) and 3.13 (95% CI 1.82–5.37) for the learning and validation sets, respectively. By comparison, HR for the intermediate and poor Glass prognostic risk groups was respectively 1.56 (95% CI: 1.0-2.42) and 2.20 (95% CI 1.42–3.38) in the learning set, and 1.77 (95% CI: 0.98-3.18) and 1.87 (95% CI: 0.94-3.74) in the validation set. The Cox model using the single independent factor ALP was found to be superior to the Glass model with regards to predictive accuracy: C-index = 0.64 (0.58-0.71) vs 0.59 (0.52-0.66). The upper bound of the 95% bootstrap confidence interval for the difference between C-indexes indicates statistically significant difference (95% CI: >0.001-0.13). Survival curves according to ALP in the whole population are displayed in Figure 4 (p < 0.001).

Fig. 4 Survival according to alkaline phosphatase (normal vs abnormal) in the whole population.

3.7. Discrimination ability of different models

A secondary analysis involved stepwise proportional hazards regression, keeping all continuous variables in a continuous form. Starting with all baseline characteristics significant at the 0.15 level, the final variables retained in the multivariable model after backward elimination were PS (0 vs 1–2), ALP (normal vs abnormal), LDH (normal vs abnormal), and pain intensity (scale 0–100). We determined the discrimination ability of four different models in the learning and validation sets ( Table 4 ): a stepwise selection model with backward elimination; models defining two to four risk categories using percentiles for the linear predictor of the Cox regression model; normal/abnormal ALP model; and the original Glass model. Only patients with no missing data were included, because those with missing data were excluded from Cox regression analyses. The performance of the different models did not improve the discrimination ability of the simple risk model with ALP as a single regression variable.