Early favorable prostate-specific antigen response prediction in metastatic hormone sensitive prostate cancer

Domain: physics
Published: 2025-12-17
Editorial outcome: minor_revision

Abstract
There is an unmet need for a tool that could predict early favorable prostate-specific antigen (PSA) response in metastatic hormone sensitive prostate cancer (mHSPC) patients receiving androgen receptor pathway inhibitor (ARPI). Here, we train and validate a multivariable logistic regression model to predict early favorable PSA response (≤0.2 ng/mL by 6 months) in these patients. Patients randomly allocated to the ARPI arms of the LATITUDE (abiraterone), TITAN (apalutamide), and ARASENS (darolutamide) trials, are split 60:40 into training (n = 1030) and internal validation (n = 688) cohorts. The locked model is validated in an independent external validation cohort - the enzalutamide arm of the ENZAMET trial (n = 540). The area under curve and Brier score for the locked model in the external validation cohort are 0.82 (95% confidence interval [CI] = 0.78–0.85) and 0.16, respectively. Stratification by predicted probability tertiles show PSA response rates of 92% (95% CI = 88–96), 74% (95% CI = 68–81), and 39% (95% CI = 32–47), respectively. Pending prospective validation, our model predicts early favorable PSA response supporting its potential role in guiding treatment decisions.

Introduction
Early PSA response is a well-established prognostic marker in metastatic hormone sensitive prostate cancer (mHSPC) patients treated with androgen deprivation therapy (ADT) alone or a combination of ADT plus androgen receptor pathway inhibitors (ARPI) with or without docetaxel1–7. Achieving a PSA response of ≤0.2 ng/mL within 6 months of treatment initiation predicts improved overall survival (OS) and mediates the treatment effect on subsequent mortality risk8. Conversely, failure to reach this response threshold portends inferior OS. Therefore, this clinical state may warrant an earlier treatment intensification, or a clinical trial enrollment. However, waiting until 6 months to assess PSA nadir may inadvertently delay timely intervention, allowing disease progression and evolution to a more treatment-resistant state, potentially diminishing the benefit of subsequent therapeutic intensification. Predicting PSA responses using pre-treatment variables, especially in ARPI-treated patients, could enable earlier, personalized treatment decisions before the optimal intervention window closes.

Conventional risk stratification methods in mHSPC, such as volume of metastatic disease based on conventional imaging9,10, have limited accuracy in predicting early PSA response. For example, one study demonstrated that over half of patients with favorable PSA responses had high-volume metastatic disease, while nearly 1/3 of those with suboptimal PSA response had low-volume disease8. These findings underscore the limitations of relying on a single variable for risk stratification and treatment optimization in mHSPC.

Therefore, there is an unmet need of an easily deployable clinical tool, which could predict favorable early PSA response. While such tool will not be a replacement for formal PSA monitoring, it will provide baseline prognostic insights that can enhance early risk stratification, guide treatment planning, and support enrollment in biomarker-driven studies.

In this work, we developed and validated the Nadir ARPI-Derived Integrative Response (NADIR) model using individual patient data from four phase III trials (ARASENS, ENZAMET, LATITUDE, and TITAN)11–14. This tool leverages pretreatment clinical and laboratory parameters to estimate the likelihood of achieving a PSA ≤0.2 ng/mL by 6 months of initiating ARPI-based therapy.

Results
Baseline characteristics
Overall, 1718 male patients were treated with ARPI agents in the ARASENS, LATITUDE, and TITAN trials, of whom the training cohort consisted of 1030 patients, while the internal validation cohort consisted of 688 patients. The external validation cohort consisted of 540 male patients from the ENZAMET trial (Fig. 1). Baseline characteristics have been summarized in Supplementary Table S1 (supplementary information). Overall, 54% (n = 551) in the training cohort, 56% (n = 383) in the internal validation cohort, and 69% (n = 371) in the external validation cohort experienced an early PSA response to ≤0.2 ng/mL by 6 months.

Modeltrainingandvalidation
After the NADIR model (https://bit.ly/42Ec1lP) was built utilizing the training cohort, it was locked and applied to the two validation cohorts. The model coefficients with 95% confidence intervals (CI) are summarized in Table 1. In the internal validation cohort, the AUC for the NADIR model was 0.76 (95% CI = 0.72–0.79) with a Brier score of 0.20. In the external validation cohort, the AUC was 0.82 (95% CI = 0.78–0.85) with a Brier score of 0.16. The receiver operating curves are shown in Fig. 2. The calibration plots showed alignment between the predicted probabilities and the actual outcomes in the training, internal and external validation cohorts (Supplementary Figs. S1, S2, S3, respectively, in the supplementary information). In the external validation cohort, the sensitivity, specificity, PPV, and NPV of the model were 0.83 (95% CI = 0.79–0.86), 0.62 (95% CI = 0.54–0.69), 0.83 (95% CI = 0.79–0.86), and 0.62 (95% CI = 0.54–0.69), respectively (Supplementary Table S2, supplementary information). On LOOCV, the model demonstrated consistent performance (AUC values ranging between 0.78 and 0.82; Brier scores ranging from 0.16 to 0.19) across trials (Supplementary Table S3, supplementary information). There was substantial heterogeneity in the distribution of predicted probability of achieving early PSA response based on metastatic volume by CHAARTED definition across the internal validation cohort (Supplementary Fig. S4, supplementary information) and external validation cohort (Supplementary Fig. S5, supplementary information), respectively. Removing baseline PSA from the multivariable model led to a substantial drop in predictive accuracy in external validation, confirming PSA as an important predictor but not a sufficient one (Table 2). Importantly, the full NADIR model outperformed PSA-only model across exploratory subgroups within the external validation cohort stratified by baseline PSA levels with greater benefits among patients with baseline PSA value higher than 5 ng/mL (Supplementary Table S4, supplementary information).

RiskstratificationbyNADIRmodel
When stratified by decreasing order of tertiles of predicted probability of early PSA response, the proportions achieving a favorable early PSA response to ≤0.2 ng/mL in the upper (n = 229), middle (n = 229), and lower tertile (n = 230) were 83% (95% CI = 78–88), 52% (95% CI = 46–59), and 32% (95% CI = 26–38) in the internal validation cohort (Supplementary Fig. S6, supplementary information). Similarly, the proportions achieving a favorable early PSA response to ≤0.2 ng/mL in the upper (n = 180), middle (n = 180), and lower tertile (n = 180) were 92% (95% CI = 88–96), 74% (95% CI = 68–81), and 39% (95% CI = 32–47) in the external validation cohort (Supplementary Fig. S7, supplementary information). Quartile-based stratification demonstrated similar differences in the proportion of patients with early favorable PSA responses in the internal and external validation cohort, respectively (Supplementary Figs. S8 and S9, supplementary information). On decision curve analysis in the external validation cohort, the NADIR model was most useful for identifying patients at a range of risk that is clinically meaningful (threshold probabilities between 25% and 60%) for early PSA drop in patients treated with ARPI with a higher net benefit in this range compared to both baseline assumptions (no patient has early PSA response, and all patients have early PSA response) (Supplementary Fig. S10, supplementary information).

We subsequently determined the OS estimates across the tertiles of predicted probability from the NADIR model using Kaplan–Meier methods. The 4-years OS probabilities in patients stratified by tertiles of predicted probability were 71% (95% CI = 65–79); 61% (95% CI = 55–69); and 47% (95% CI = 39–56), respectively in the internal validation cohort (n = 672) (Fig. 3) and 80% (95% CI = 75–86), 74% (95% CI = 68–81), and 56% (95% CI = 49–64), respectively in the external validation cohort (n = 540) (Fig. 4). On Cox proportional hazard regression modeling, compared to upper tertile, patients in the middle and lower tertile had inferior OS in the internal validation cohort (HR for middle tertile = 1.57 [95% CI = 1.11–2.21]; HR for lower tertile = 2.28 [95% CI = 1.65–3.16]) and in the external validation cohort (HR for middle tertile = 1.35 [95% CI = 0.92–1.69]; HR for lower tertile = 2.72 [95% CI = 1.91–3.88], respectively.

Exploratoryanalysisofinteractionwithdocetaxeleffect
In the combined validation cohort, we did not find any considerable evidence of difference in proportion of patients with early PSA response with and without use of docetaxel across the three risk score groups (Supplementary Table S5, supplementary information). We found a differential effect from docetaxel on OS across the predicted scores from the NADIR model (HR for the interaction term 0.41; 95% CI = 0.19–0.88; two-sided p-interaction = 0.0215) (Supplementary Fig. S11, supplementary information). Kaplan–Meier method-based OS estimates with and without docetaxel use in these groups are shown in Supplementary Figs. S12 and S13, respectively (supplementary information). For patients in the lower tertile of predicted probability of early favorable PSA response (n = 401), 4-year OS estimates with and without docetaxel were 55% (95% CI = 48–63) and 53% (95% CI = 46–61), respectively while for patients in the upper to middle tertiles (n = 811), the 4-year OS estimates with and without docetaxel were 66% (95% CI = 60–72) and 72% (95% CI = 68–77), respectively (Supplementary Fig. S12, supplementary information). For patients in the upper-tertile of predicted probability of early favorable PSA response (n = 408), 4-year OS estimates with and without docetaxel were 72% (95% CI = 65–80) and 78% (95% CI = 72–83), respectively while for patients in the lower to middle tertiles (n = 804), 4-year OS estimates with and without docetaxel were 58% (95% CI = 52–63) and 60% (95% CI = 56–65), respectively (Supplementary Fig. S13, supplementary information). Similar evidence of differential treatment effect from on OS across the predicted scores from the NADIR model (HR for the interaction term 0.28; 95% CI = 0.09–0.92; two-sided p-interaction = 0.03377) was found in the external validation cohort (n = 540) (Supplementary Fig. S14, supplementary information).

Additionalsensitivityanalyses
As an exploratory analysis, we applied the NADIR model on patients treated with ADT with/without docetaxel. In patients treated with ADT with/without docetaxel, the AUC of the NADIR model was 0.77 (95% CI = 0.75–0.79) with a Brier score of 0.24. On decision curve analysis, the NADIR model was useful for identifying patients at a range of risk that is clinically meaningful (threshold probabilities between 15% and 50%) for early PSA response to ≤0.2 ng/mL by 6 months (Supplementary Fig. S15, supplementary information). On sensitivity analysis, the random forest classifier model had an AUC and Brier scores similar to the logistic regression model in the internal validation cohort (AUC: 0.75 [95% CI = 0.72–0.80]; Brier score: 0.20) and in the external validation cohort (AUC: 0.83 [95% CI = 0.79–0.86]; Brier score: 0.17), respectively. Additional metrics for the random forest classifier model are summarized in Supplementary Table S6 (supplementary information). The decision curve analysis showed similar net benefit as the logistic regression model when compared to both baseline assumptions (Supplementary Fig. S16, supplementary information).

Methods
Studycohorts
Our research complies with all relevant ethical regulations by the institutional review board of University Hospitals Seidman Cancer Center (STUDY20251115) and data-sharing agreements with trial sponsors. All patients provided informed consent before they were enrolled in the respective trials. A literature search was performed using Medline and Clinicaltrials.gov to identify phase III randomized controlled trials of patients solely with mHSPC randomized to ADT with or without an ARPI, irrespective of docetaxel use. Each trial group or industry partner was contacted to obtain IPD. Four trials met criteria for which IPD access was granted for analysis: ARASENS (NCT02799602), ENZAMET (NCT02446405), LATITUDE (NCT01715285), and TITAN (NCT02489318). For ARASENS, LATITUDE, and TITAN, data were accessed via a peer-reviewed data access request on the Vivli platform (Project ID: 009912), while data from the ENZAMET (NCT02446405) trial were accessed through the Australian and New Zealand Urogenital and Prostate Cancer Trials Group. This post-hoc analysis was conducted in accordance with a pre-specified analysis plan approved by all relevant parties.

Patients eligible for this analysis were adult (≥18 years) patients with histologically or cytologically confirmed mHSPC, an Eastern Cooperative Oncology Group (ECOG) performance-status score of 0 or 1, and evidence of metastases on bone scans or cross-sectional imaging. All study participants were male, and sex was determined by clinical diagnosis. Patients were included if they were randomly assigned to and treated with ADT with or without docetaxel plus ARPI and had complete baseline and follow-up data for clinical outcomes, treatment assignments, and baseline (pre-ARPI) demographic and clinical characteristics, and laboratory variables such as age (in years), body mass index (BMI), metastatic disease volume (high versus low per CHAARTED criteria)9,10, visceral metastases (yes/no), baseline PSA (ng/mL), hemoglobin (g/L), docetaxel use (yes versus no), and metastatic stage at presentation (synchronous versus metachronous), respectively. All analyzes complied with the terms set by the data providers, and no identifiable patient information was used.

Statisticsandreproducibility
The primary endpoint was early favorable PSA response, defined as a decline in serum PSA level to ≤0.2 ng/mL by 6 months of random allocation among patients treated with an ARPI. Patients from ARASENS, LATITUDE, and TITAN trials were pooled and randomly split into training (60%) and internal validation (40%) cohorts using unstratified random allocation. We used a 60:40 split to prioritize a larger training cohort for model development, ensuring stable coefficient estimation while retaining a sufficiently large internal validation cohort for performance testing. The training cohort was used to build the model and once locked, the model’s performance was evaluated in the internal and external validation cohorts.

Model development utilized logistic regression, including baseline PSA fitted with restricted cubic splines with 4 degrees of freedom, log of baseline hemoglobin, baseline body mass index, and age at enrollment respectively, in addition to metastatic disease volume (low versus high by CHAARTED definition)9, visceral metastasis (yes versus no), and metastatic stage at presentation (synchronous versus metachronous). Variables election was based on clinical relevance, with final model specification determined by the Akaike Information Criterion. Model discrimination was assessed using the area under the receiver operating characteristic curve (AUC) with 95% confidence intervals from 5000 bootstrap iterations. Calibration was evaluated by comparing bootstrapped estimates of early PSA nadir probabilities with 95% confidence intervals across tertiles of predicted probabilities in both internal and external validation cohorts. We selected tertiles to ensure adequate sample sizes and event counts within each subgroup. This avoided over-stratification, which could lead to unstable estimates and wide confidence intervals. Additional performance metrics included Brier score (which measures the accuracy of predicted probabilities with lower Brier score indicating better calibration), sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and positive and negative likelihood ratio. No pre-specified probability threshold was selected to define clinical actionability; thresholds were explored post hoc to evaluate model performance across a range of values using decision curve analysis. Variable importance was estimated using loss of index of prediction accuracy (IPA). IPA is calculated by rescaling the Brier score.

External validation employed individual patient data from the ARPI arm of the ENZAMET trial to assess the model’s generalizability. A post-hoc power analysis confirmed adequate sample size to detect an AUC of 0.75 with a significance level of 0.05. To determine the validation of our model, we performed a leave-one-trial-out-validation (LOOCV). Each trial was sequentially excluded and used as an external validation cohort while the model was trained on the remaining three trials. Discrimination was assessed using the area under the AUC with 95% confidence intervals. Calibration was evaluated using Brier scores. This approach allows for evaluation of model generalizability and reduces potential overfitting to any single dataset. As an additional sensitivity analysis, a random forest classifier was developed and evaluated using the same framework.

Given the prognostic implications of early PSA response, overall survival (OS) was explored in a 6-month landmark population stratified by tertiles (upper, middle, and lower) of predicted probability from the NADIR model. Overall survival (OS) was reported at 4 years because follow-up beyond 4 years was limited in the training and validation cohorts. Cox proportional hazards models evaluated hazard of deaths across the tertiles, and the potential differential effect of docetaxel based on predicted probabilities from the NADIR model using an interaction term. Proportionality assumption was tested using Grambsch–Therneau test. No adjustment for multiple comparisons was made, and all reported p-values were 2-sided. All statistical analyzes were performed using R version 4.4.1 with its associated packages (tidymodels, tidyverse, pROC, riskRegression, survival, rms)37–40.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Reviewer Manuscript Overview:\nThis research is significant for its potential practical implications for improving the health and lives of patients with metastatic\nhormone-sensitive prostate cancer (mHSPC). The study is highly motivated and builds upon an extensive body of literature\nthat establishes a strong link between early, deep PSA response and better long-term clinical outcomes, including overall\nsurvival, in mHSPC patients.\nThe overall methods and approach are suitable for the prediction model and research purposes (barring additional\nquestions/comments I provided below). I commend in particular the efforts of the authors to obtain and utilize individual\npatient data (IPD) from each of the four pivotal mHSPC ARPI trials, as these efforts were instrumental in ensuring potential\nstudy/model robustness and reliability.\nReviewer Comments and Questions:\nComments by Manuscript Page and Line Number\n• Pg 13 15 – Why was baseline PSA fitted with restricted cubic splines with 4 DoF? Please clearly explain and justify the\nrationale given this particularly specific fit.\n• Pg 13 19 – How about Gleason Score? Considerations for controlling given its link to PSA response and longer term\nclinical outcomes?\n• Pg 13 19 – A key covariate/potential confounding factor that comes to mind for me is the temporal differences between the\ntrials. For example, changes in standard of care (in LPC and mPC), advanced/next generation imaging (NGS) to detect\nmPC, and other changes in recommended clinical care in this disease area between the time say LATITUDE and\nARASENS were conducted. Suggest to control for time or year of treatment (or initiation) across patient and trial cohorts or\nprovide rationale for it’s not controlled for.\n• Pg 13 20 – Why was AIC used to select model variables? Any considerations for Elastic Net, LASSO, or other ML\napproaches for variable selection to better handle potential overfitting or multicollinearity?\n• Pg 14 2 – Why were tertiles chosen, as opposed to say quartiles for example? Either is fine, but would be helpful to provide\na justification.\n• Pg 16 6 – What’s most interesting to me is that the greatest relative gains in the model were for patients in the middle 5-50\nng/mL group, suggest calling this out. Any ideas why this group has biggest relative gain in accuracy for the model?\n• Pg 16 20 – Why were 4-year OS probabilities modeled instead of the typical 5-year OS? Fine if due to data limitations or\nfollow-up counts, but please justify in the text if so.\n• Figure E6.1/E6.2 Interesting that the survival probability for upper-middle tertiles is higher for patients without docetaxel\n(72%) than with docetaxel (66%) (E6.1) and in upper tertile (72% and 78%) (E6.2), at least descriptively. Why is this the\ncase, residual confounding of patient characteristics? Maybe helpful to call out in manuscript, beyond the general limitation\n(given the relatively large difference).\nMajor Comments on Overall Methodology\n• My biggest question or concern is the lack of justification around why ENZAMET was specifically used for the external\nvalidation dataset. Some commonly established challenges and drawbacks of using only one trial/database for external\nvalidation (ENZAMET) include the potential for: overfitting risk and reduced generalizability, especially if additional\ndifferences between the internal training/external validation samples (e.g., patient characteristics, years of trial, etc.)\nI would suggest the use of leave-one-out cross-validation (LOOCV), which would aggregate model fit by using and rotating\neach of the 4 pivotal trial databases as the external validation arm, which can help reduce the potential for dataset-specific\noverfitting and bolster model generalizability with more equitable model evaluation across the 4 trial datasets.\n• IF it is not feasible for LOOCV or a more generalizable test/training validation to be done, or if there’s a rationale that\nsupports the given internal/external validation approach (with one external dataset) vs. LOOCV or other approaches, then\nplease be sure to provide adequate explanation and justification for your current approach of training/testing and why the\nauthors identified this as the best method and approach. Also, please give a strong rationale and justification for why\nENZAMET specifically was chosen as external validation cohort, of the four pivotal Phase 3 trials, and update the limitations\nsection as applicable.", "reviewer_2": "In this manuscript, Dr. Roy et al. described a novel tool developed to identify early favorable PSA response in mHSPC\npatients who would benefit from early treatment personalization. They used mHSPC patients treated on ADT+ARPI arm of\nLATITUDE, TITAN, ARANSES trials (training and internal validation cohort), and ENZAMET (as external validation cohort).\nThey concluded that their model satisfactorily predicts early favorable PSA response (≤0.2 ng/mL by 6 months) and needs\nprospective validation.\nThe reviewer has the following comments:\n1. Please describe the randomization process of pooled data into training (60%) and internal validation (40%) cohorts. Is\nthere a reason for 60%:40 % randomization vs 50%: 50% (which may seem logical).\n2. The ENZAMET trial had a planned evaluation of participants (including PSA) every 12 weeks, and allowed prior\ndocetaxel, which is different from other pooled trials, which are industry-sponsored and had more PSA data in the first 6\nmonths. Is there a reason why ENZAMET was selected as an external validation cohort? Please comment.\n3. Discussion (Page 19). What are the values of PSA of “patients with lower baseline PSA values” and “patients with higher\nbaseline PSA values. Please be more specific.\n4. The number of figures is extensive. For instance, Figures E1.1, E1.2, and E4 can be moved to the supplementary figures."}, "author_response": "Author Response 1st Revision:\nOn behalf of my co-authors, I would like to thank the reviewers for the time taken to\ncritically appraise this manuscript and for allowing us the opportunity to respond to their\ncomments. We have addressed, item by item, the reviewers’ comments, with responses\nappearing below. Given the concern on validation, we have performed the leave-one-\ntrial-out validation in line with the reviewer suggestion. The model continues to show\ngood discrimination and calibration. Further, we have shortened the abstract to comply\nwith the word count limits. Revisions have been made to the manuscript with changes\ntracked and highlighted, and we have submitted the revised marked manuscript. The\npage and line numbers in our responses refer to the marked manuscript.\nReviewer 1\nReviewer Comments:\nComment 1: Why was baseline PSA fitted with restricted cubic splines with 4 DoF?\nPlease clearly explain and justify the rationale given this particularly specific fit.\nAuthors’ response: We tested models without splines and with spline degrees of\nfreedom (DoF) ranging from 3 to 5. The model with 4 DoF achieved the lowest AIC and\nthus was chosen for this model. We have mentioned in our manuscript that “Variable\nselection was based on clinical relevance, with final model specification determined by\nthe Akaike Information Criterion” on page no: 5, line no: 115 to 117.\nComment 2: How about Gleason Score? Considerations for controlling given its link to\nPSA response and longer term clinical outcomes?\nAuthors’ response: We agree with the reviewer that Gleason score does hold some\nprognostic value in metastatic prostate cancer. However, pre-ARPI Gleason score was\nnot readily available across the included trials. Further, the reported Gleason scores did\nnot account for difference between clinical Gleason scores from biopsy versus that\nderived from prostatectomy, old versus new grading system, and the differences in\nreporting pattern across various countries given these trials were multi-national. For\nexample, Canada and UK report synoptic Gleason score while USA reports maximum\nGleason score. For these reasons, we elected not to include Gleason score in our\nmodel. We have acknowledged this limitation in the revised manuscript (page no: 15,\nline no: 335).\nComment 3: A key covariate/potential confounding factor that comes to mind for me is\nthe temporal differences between the trials. For example, changes in standard of care\n(in LPC and mPC), advanced/next generation imaging (NGS) to detect mPC, and other\nchanges in recommended clinical care in this disease area between the time say\nLATITUDE and ARASENS were conducted. Suggest to control for time or year of\ntreatment (or initiation) across patient and trial cohorts or provide rationale for it’s not\ncontrolled for.\nAuthors’ response: We appreciate the reviewer’s point regarding temporal differences\nbetween trials. While an excellent point, fundamentally this will always exist given the\ntime between trial design and reporting of results in mHSPC trials will be 7+ years (1-2\nyears to design and activate trial, 2-5 years to enroll, 3-5+ years of follow-up).\nFortunately, all four included trials have established the standard-of-care (SOC)\nsystemic therapies for mHSPC and collectively define the evidence base guiding current\npractice, thereby reducing variability in therapeutic context. Importantly, our leave one\nout cross validation (LOOCV) analysis inherently addresses temporal heterogeneity, as\neach trial (spanning different eras) served as an independent validation cohort,\ndemonstrating consistent performance across time frames. The LOOCV analysis is\ndescribed on page no: 6, line no: 135 to 140 and reported on page no: 8, line no: 182 to\n184. We have also highlighted in the discussion that while these trials underpin the\npresent SOC, emerging tools such as PET imaging and evolving treatment paradigms\nare not fully captured (page no: 15, line no: 328 to 334), and future work will evaluate\nmodel performance in these contexts.\nComment 4: Why was AIC used to select model variables? Any considerations for\nElastic Net, LASSO, or other ML approaches for variable selection to better handle\npotential overfitting or multicollinearity?\nAuthors’ response: We thank the reviewer for this suggestion. We used AIC for variable\nselection because it provides a well-established, information-theoretic framework that\nbalances model fit and complexity, favoring parsimony and reducing the risk of\noverfitting. This approach is widely applied in clinical prediction model development\nwhere interpretability and generalizability are essential. As part of our sensitivity\nanalyses, we evaluated machine learning methods, including Random Forests, which\nare robust to multicollinearity and capable of modeling complex nonlinear relationships.\nRandom Forest achieved performance similar to our AIC-based logistic regression\nmodel in the external validation cohort (AUC: 0.83 [0.79-0.86] vs 0.82 [0.78-0.85]; Brier\nscore: 0.17 vs 0.16), confirming that our simpler logistic regression model achieved\ncomparable accuracy (page no: 11, line no: 243 to 245 and supplementary results R2).\nGiven its superior interpretability and ease of clinical implementation, we prioritized the\nlogistic regression model while acknowledging that more complex approaches did not\noffer meaningful incremental benefit (page no: 12, line no: 259 to 261).\nComment 5: Why were tertiles chosen, as opposed to say quartiles for example? Either\nis fine, but would be helpful to provide a justification.\nAuthors’ response: We thank the reviewer for this observation. We selected tertiles to\nensure adequate sample sizes and event counts within each subgroup. This avoided\nover-stratification, which could lead to unstable estimates and wide confidence intervals.\nWe have mentioned this on page no: 6, line no: 122 to 124. To confirm robustness, we\nperformed a sensitivity analysis using quartile-based stratification (page no: 9, line no:\n198 to 201; supplementary figure 4.1 and 4.2), which showed similar trends, supporting\nour choice of tertiles for the primary analysis.\nComment 6: What’s most interesting to me is that the greatest relative gains in the\nmodel were for patients in the middle 5-50 ng/mL group, suggest calling this out. Any\nideas why this group has biggest relative gain in accuracy for the model?\nAuthors’ response: We thank the reviewer for this insightful observation, which led us to\nre-examine the IPA values across baseline PSA strata. During this process, we\nidentified that the previously reported IPA for the multivariable logistic regression model\n(NADIR model) in the >50 ng/mL PSA group was not updated from an earlier draft\nversion of the table during manuscript assembly. This was a reporting oversight that did\nnot affect the main aspects of analysis or the primary findings.\nThe correct IPA for the NADIR model in this group is 10.9, compared to 6.0 for the PSA-\nonly model. With this corrected, the NADIR model demonstrates consistently greater\npredictive accuracy than the PSA-only model across all three PSA subgroups (≤5\nng/mL, >5–50 ng/mL, >50 ng/mL), with relatively higher incremental gains in those with\nPSA >5 ng/mL. We have verified all other subgroup results and confirm their accuracy.\nThe manuscript has been updated accordingly, and we appreciate the reviewer’s\ncomment for helping us strengthen the clarity and accuracy of our report.\nComment 7: Why were 4-year OS probabilities modeled instead of the typical 5-year\nOS? Fine if due to data limitations or follow-up counts, but please justify in the text if so.\nAuthors’ response: We appreciate this comment. As the reviewer highlighted, the follow-\nup was limited beyond 4 years in the training and validation cohorts. This is why we\nreported the 4-year overall survival estimates. We have now mentioned this clearly in\nour statistical consideration section – “Overall survival (OS) was reported at 4 years\nbecause follow-up beyond 4 years was limited in the training and validation cohorts.\n(page no: 7, line no: 145 to 147)”. Further, while 5 year OS estimates are preferred in\nthe context of oncology, studies on metastatic prostate cancer have often reported 3-\nyear overall survival estimates.\nComment 8: Interesting that the survival probability for upper-middle tertiles is higher\nfor patients without docetaxel (72%) than with docetaxel (66%) (E6.1) and in upper\ntertile (72% and 78%) (E6.2), at least descriptively. Why is this the case, residual\nconfounding of patient characteristics? Maybe helpful to call out in manuscript, beyond\nthe general limitation (given the relatively large difference).\nAuthors’ response: We agree with the astute comment from the reviewer. We have\ndescribed the 4-year OS estimates in the text (page no: 10, line no: 224 to 232).\nFurther, we have discussed this finding in the discussion – “In our study, we did not\nobserve an OS benefit with addition of docetaxel in those with a relatively higher\npredicted probability of early PSA response to ≤0.2 ng/mL by 6 months. Given the post-\nhoc exploratory nature, potential for residual confounding, and the lack of a trial\nrandomizing to ADT+ARPI +/- docetaxel, this finding is merely hypothesis generating\nand is liable to both type I and type II errors. Furthermore, patients referred for\ndocetaxel on trial might had other poor risk features not captured in the model which\nneeds further exploration with additional biomarkers (page no: 14, line no: 311 to 317).”\nComment 9: Major Comments on Overall Methodology\nMy biggest question or concern is the lack of justification around why ENZAMET was\nspecifically used for the external validation dataset. Some commonly established\nchallenges and drawbacks of using only one trial/database for external validation\n(ENZAMET) include the potential for: overfitting risk and reduced generalizability,\nespecially if additional differences between the internal training/external validation\nsamples (e.g., patient characteristics, years of trial, etc.)\nI would suggest the use of leave-one-out cross-validation (LOOCV), which would\naggregate model fit by using and rotating each of the 4 pivotal trial databases as the\nexternal validation arm, which can help reduce the potential for dataset-specific\noverfitting and bolster model generalizability with more equitable model evaluation\nacross the 4 trial datasets.\nIf it is not feasible for LOOCV or a more generalizable test/training validation to be done,\nor if there’s a rationale that supports the given internal/external validation approach\n(with one external dataset) vs. LOOCV or other approaches, then please be sure to\nprovide adequate explanation and justification for your current approach of\ntraining/testing and why the authors identified this as the best method and approach.\nAlso, please give a strong rationale and justification for why ENZAMET specifically was\nchosen as external validation cohort, of the four pivotal Phase 3 trials, and update the\nlimitations section as applicable.\nAuthors’ response: We thank the reviewer for highlighting the importance of robust\nvalidation. We used patients LATITUDE, TITAN, and ARASENS to randomly split into\ntraining and internal validation dataset. External validation employed individual patient\ndata from the ARPI arm of the ENZAMET trial to assess the locked model's\ngeneralizability. In line with the reviewer’s suggestion and with expanded access to all\nfour phase 3 trials (LATITUDE, TITAN, ARASENS, ENZAMET), we have now\nperformed Leave-One-Trial-Out Validation (LOOCV). In this approach, each trial served\nas an external validation set while training was conducted on the remaining three trials.\nThe model demonstrated consistent performance across all trials (AUC 0.78–0.82; Brier\n0.16–0.19; Supplementary Table 2), supporting its generalizability and addressing\nconcerns of dataset-specific overfitting. In the manuscript we have corresponding\nchanges in the methods section (page no: 6, line no: 135 to 140) and results section\n(page no: 8, line no: 182 to 184).\nReviewer 2\nReviewer Comments:\nIn this manuscript, Dr. Roy et al. described a novel tool developed to identify early\nfavorable PSA response in mHSPC patients who would benefit from early treatment\npersonalization. They used mHSPC patients treated on ADT+ARPI arm of LATITUDE,\nTITAN, ARANSES trials (training and internal validation cohort), and ENZAMET (as\nexternal validation cohort). They concluded that their model satisfactorily predicts early\nfavorable PSA response (≤0.2 ng/mL by 6 months) and needs prospective validation.\nThe reviewer has the following comments:\nComment 1: Please describe the randomization process of pooled data into training\n(60%) and internal validation (40%) cohorts. Is there a reason for 60%:40 %\nrandomization vs 50%: 50% (which may seem logical).\nAuthors’ Response: We thank the reviewer for this question. We used a 60:40 split to\nprioritize a larger training cohort for model development, ensuring stable coefficient\nestimation while retaining a sufficiently large internal validation cohort for performance\ntesting. This approach is consistent with prior predictive modeling studies where slightly\nlarger training sets are preferred to optimize parameter estimation, particularly in\nsettings with multiple covariates. We have clarified this in the Methods section and\nexplicitly stated that allocation was performed using random assignment without\nstratification (page no: 5, line no: 104 to 107).\nComment 2: The ENZAMET trial had a planned evaluation of participants (including\nPSA) every 12 weeks, and allowed prior docetaxel, which is different from other pooled\ntrials, which are industry-sponsored and had more PSA data in the first 6 months. Is\nthere a reason why ENZAMET was selected as an external validation cohort? Please\ncomment.\nAuthors’ response: We thank the reviewer for this comment. We used patients\nLATITUDE, TITAN, and ARASENS to randomly split into training and internal validation\ndataset. Subsequently, external validation employed individual patient data from the\nARPI arm of the ENZAMET trial to assess the locked model's generalizability. In line\nwith the reviewer’s suggestion, we performed Leave-One-Trial-Out Validation (LOOCV).\nIn this approach, each trial served as an external validation set while training was\nconducted on the remaining three trials. The model demonstrated consistent\nperformance across all trials (AUC 0.78–0.82; Brier 0.16–0.19; Supplementary Table 2),\nsupporting its generalizability and addressing concerns of dataset-specific overfitting. In\nthe manuscript we have corresponding changes in the methods section (page no: 6, line\nno: 135 to 140) and results section (page no: 8, line no: 182 to 184).\nComment 3: Discussion (Page 19). What are the values of PSA of “patients with lower\nbaseline PSA values” and “patients with higher baseline PSA values. Please be more\nspecific.\nAuthors’ response: We thank the reviewer for highlighting this. We have now mentioned\nin the discussion – “In patients with lower baseline PSA levels (≤5 ng/mL), the\nmultivariable model performed similarly to, or slightly better than, PSA alone. This likely\nreflects the inherently higher probability of achieving an early nadir in this subgroup,\nreducing the clinical need for additional predictive modeling. Conversely, in patients with\nhigher baseline PSA (>5 ng/mL) - where nadir prediction remains an unmet clinical need\n- the multivariable model demonstrated superior predictive performance compared to\nbaseline PSA alone”. (page no: 12, line no: 268 and 271)\nComment 4: The number of figures is extensive. For instance, Figures E1.1, E1.2, and\nE4 can be moved to the supplementary figures.\nAuthors’ response: We appreciate this comment from the reviewer. The supplementary\nfigures E1.1, E1.2 and E4 were part of the supplementary materials. All the tables and\nfigures starting with “E” were part of the supplementary materials. Following the Nature\nauthor guidelines, we have now edited them, and they are now simply “Supplementary\nFigure 1.1”, “Supplementary Figure 1.2”, “Supplementary Figure 4” etc."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Revisions and comment responses to my questions are suitable and sufficient. Recommend to accept for publication on my\nend.", "reviewer_2": "I think that the authors have adequately addressed the comments made by the reviewers in the revised version of the\nmanuscript.\nTherefore, I have no further comments."}, "author_response": ""}]

Decision letter