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  ["project_title"]=>
  string(121) "Heterogeneity in treatment effect of androgen receptor pathway inhibitors in metastatic hormone-sensitive prostate cancer"
  ["project_narrative_summary"]=>
  string(842) "This project aims to determine if the effectiveness of certain drugs for advanced prostate cancer varies from patient to patient. These drugs, called androgen receptor pathway inhibitors (ARPIs), have been shown to improve outcomes for men with metastatic hormone-sensitive prostate cancer (mHSPC). However, it is unclear if these drugs work equally well for everyone.
In this study, we will review data from past clinical trials where men with mHSPC were given either ARPIs or a placebo (a dummy drug). We will look at information like age, general health, cancer stage, and blood test results to see if these factors predict whether the treatment was more or less effective.
This research is important because knowing which patients benefit most from ARPIs can help doctors make better treatment plans for patients with mHSPC." ["project_learn_source"]=> string(12) "scien_public" ["principal_investigator"]=> array(7) { ["first_name"]=> string(6) "Wataru" ["last_name"]=> string(9) "Fukuokaya" ["degree"]=> string(2) "MD" ["primary_affiliation"]=> string(39) "The Jikei University School of Medicine" ["email"]=> string(20) "wfukuokaya@gmail.com" ["state_or_province"]=> string(5) "Tokyo" ["country"]=> string(5) "Japan" } ["project_key_personnel"]=> array(2) { [0]=> array(6) { ["p_pers_f_name"]=> string(8) "Takahiro" ["p_pers_l_name"]=> string(6) "Kimura" ["p_pers_degree"]=> string(7) "MD, PhD" ["p_pers_pr_affil"]=> string(39) "The Jikei University School of Medicine" ["p_pers_scop_id"]=> string(0) "" ["requires_data_access"]=> string(2) "no" } [1]=> array(6) { ["p_pers_f_name"]=> string(7) "Akihiro" ["p_pers_l_name"]=> string(8) "Hirakawa" ["p_pers_degree"]=> string(3) "PhD" ["p_pers_pr_affil"]=> string(26) "Institute of Science Tokyo" ["p_pers_scop_id"]=> string(0) "" ["requires_data_access"]=> string(2) "no" } } ["project_ext_grants"]=> array(2) { ["value"]=> string(2) "no" ["label"]=> string(68) "No external grants or funds are being used to support this research." } ["project_date_type"]=> string(18) "full_crs_supp_docs" ["property_scientific_abstract"]=> string(1242) "Background
Androgen receptor pathway inhibitors (ARPIs) improve outcomes for patients with metastatic hormone-sensitive prostate cancer. Whether the effects of ARPIs vary based on patient characteristics remains unclear.

Objective
To determine whether patient characteristics modify the effect of ARPIs versus placebo on overall survival in patients with mHSPC.

Study Design
Individual participant data meta-analysis.

Participants
Patients with mHSPC who were randomized to either ARPIs or placebo.

Primary and Secondary Outcome Measures
The primary outcome measure is overall survival (OS), defined as the time from randomization to death from any cause.

Statistical Analysis
The statistical analysis plan involves a systematic literature search to identify relevant RCTs on ARPIs for mHSPC. Eligible studies with available IPD will be included. The heterogeneity of treatment effect (HTE) will be analyzed using risk-modeling approaches. The risk-modeling approach will develop an internal risk prediction model for OS, assess model performance, and evaluate treatment effects of ARPI versus placebo across risk subgroups." ["project_brief_bg"]=> string(792) "Prostate cancer, the most commonly diagnosed malignancy in men globally in 2022, accounted for 7.3% of all cancer diagnoses worldwide (Bray et al., 2024). Landmark phase III randomized controlled trials (RCTs) have conclusively demonstrated the clinical benefit of androgen receptor pathway inhibitors (ARPIs) in the treatment of metastatic hormone-sensitive prostate cancer (mHSPC) (Armstrong et al., 2019; Chi et al., 2019; Fizazi et al., 2017; Smith et al., 2022). Prior studies suggested mHSPC has heterogeneity in prognosis, indicating possible heterogeneity in treatment effect (HTE) of ARPIs among those with mHSPC. Investigating the HTE of ARPIs in mHSPC would enable more precise benefit assessments and highlight the importance of considering HTE in the design and analysis of RCTs." ["project_specific_aims"]=> string(101) "This study aims to evaluate whether the treatment effect of ARPIs varies by baseline characteristics." ["project_study_design"]=> array(2) { ["value"]=> string(7) "meta_an" ["label"]=> string(52) "Meta-analysis (analysis of multiple trials together)" } ["project_purposes"]=> array(1) { [0]=> array(2) { ["value"]=> string(56) "new_research_question_to_examine_treatment_effectiveness" ["label"]=> string(114) "New research question to examine treatment effectiveness on secondary endpoints and/or within subgroup populations" } } ["project_research_methods"]=> string(916) "This study will include patients with mHSPC who are randomized to either ARPIs or placebo in clinical trials. RCTs will be eligible when patients with mHSPC are randomized to receive ARPIs or placebo with ADT. To provide clinically informative data for physicians, this study will include ARPIs approved by the Food and Drug Administration, such as abiraterone acetate, apalutamide, darolutamide, and enzalutamide. Open-label RCTs will be excluded to reduce potential bias in the analysis. Additionally, non-RCT studies and studies without available IPD will be excluded. The pharmaceutical companies sponsoring the pivotal RCTs for enzalutamide and apalutamide are members of Vivli. Therefore, all IPD will be merged and analyzed within the Vivli data analysis environment. We plan to request data from the following RCTs: ARAMIS (NCT02799602), ARCHES (NCT02677896), LATITUDE (NCT01715285), and TITAN (NCT02489318)." ["project_main_outcome_measure"]=> string(117) "The primary outcome measure is overall survival (OS), defined as the time from randomization to death from any cause." ["project_main_predictor_indep"]=> string(32) "Predicted risk of poor outcomes." ["project_other_variables_interest"]=> string(966) "The predictive Heterogeneity of Treatment Effect analysis will be performed using a subset of the following variables, selected based on their previously reported prognostic value, clinical relevance, and anticipated availability across participating trials.
The variables include: age at randomization, number of bone metastases, baseline hemoglobin, baseline neutrophil-to-lymphocyte ratio, baseline albumin, baseline prostate-specific antigen, baseline alkaline phosphatase, and baseline lactate dehydrogenase, all of which will be treated as continuous variables. Categorical variables include Eastern Cooperative Oncology Group (ECOG) performance status (categorized as 0 vs. ≥1), total biopsy Gleason score at diagnosis (≤8 vs. ≥9), opioid analgesic use (no vs. yes), de novo metastatic disease (no vs. yes), presence of visceral metastasis (absent vs. present), de novo metastatic disease (no vs. yes), and concomitant docetaxel use (no vs. yes)." ["project_stat_analysis_plan"]=> string(4934) "This study adheres to the PRISMA-IPD statement (Stewart et al., 2015) and TRIPOD-cluster checklist (Debray et al., 2023). The heterogeneity of treatment effect (HTE) will be evaluated using a risk-modeling analysis approach.

Overview
A risk-modeling framework will be used to explore the HTE of ARPIs in patients with mHSPC (Kent, Paulus, et al., 2020). This framework uses a multivariable risk prediction model to examine how treatment effects vary based on predicted risk levels. The model stratifies patients according to their calculated risk profiles to analyze these variations. A risk prediction model for OS will be developed internally using IPD from RCTs to estimate the risk of OS for each patient.

Missing Variable Imputation
Missing baseline covariate values will be multiply imputed using a multivariate imputation by chained equations (MICE) algorithm (van Buuren & Groothuis-Oudshoorn, 2011). To handle sporadic missing variables, a multilevel MICE approach will be used (Resche-Rigon & White, 2018). One hundred distinct imputed datasets will be generated, and the subsequent variable selection process will be performed on each imputed dataset, although the number of imputations may be adjusted if computational resources are insufficient.

Risk prediction model development
Cox proportional hazards regression will be the primary method for developing the risk prediction model. If the proportional hazards assumption is not met, alternative techniques, such as restricted mean survival time (RMST) regression using pseudo-observations, will be explored (Andersen & Perme, 2010).
Initially, a Cox model incorporating all potential predictors will be fitted. From this, predictors will be selected based on approaches used in previous clinical prediction modeling studies (Clift et al., 2020, 2023; Hippisley-Cox et al., 2017; Hippisley-Cox & Coupland, 2015). Binary or multilevel categorical predictors will be included if their exponentiated coefficients (hazard ratios [HRs]) are > 1.1 or < 0.9 with a corresponding P < 0.01. Continuous variables will be selected if their associated P < 0.01. This selection approach benefits from starting with a full, maximally complex model and then considering both clinical and statistical magnitude to select a parsimonious model using multiply imputed data. Interaction effects will be excluded to reduce the computational load. The selected predictors will then be used to construct the final Cox model. To adjust the model for overfitting, a heuristic shrinkage factor will be calculated and multiplied by the original beta coefficients. The resulting model will be used to compute a risk score for each patient, calculated as the linear combination of their covariate values and the final model coefficients (log HR).

Internal-external cross-validation
Internal-external cross-validation will be conducted to evaluate the generalizability and between-trial heterogeneity of the model's performance (Steyerberg & Harrell, 2016; Takada et al., 2021). Model discrimination will be evaluated with Harrell's C statistic, while calibration will be assessed by the calibration slope and the ratio of expected to observed outcomes. The process of internal-external cross-validation will involve systematically omitting each included trial in turn to serve as an external validation dataset. For each iteration, the risk prediction model for OS will be developed using the combined data from all other trials to obtain its beta coefficients and heuristic shrinkage factors. The performance of this model will then be assessed in the held-out study. This procedure will be repeated until each included study has served as the external validation dataset. Performance measures from the cross-validation will be summarized using a random-effects meta-analysis to provide a summary estimate of overall performance (Riley, 2021). Additionally, smoothed calibration plots will be generated to visualize the alignment between observed and predicted risks.

Heterogeneity in treatment effect assessment
For the risk-modelling predictive HTE analysis, we adhere to the Predictive Approaches to treatment effect heterogeneity (PATH) Statement (Kent, Paulus, et al., 2020). The treatment effect will be assessed using both relative (HRs) and absolute (difference in RMSTs) measures. To analyze treatment effects within subgroups, relative and absolute effects will be presented using HRs and differences in RMSTs. For both the relative and absolute effect analyses, a test for interaction between ARPI randomization and predicted risk will be performed. The analysis will be performed using a two-stage meta-analytic framework; however, a one-stage framework will be applied if the two-stage approach proves analytically difficult." ["project_software_used"]=> array(2) { [0]=> array(2) { ["value"]=> string(1) "r" ["label"]=> string(1) "R" } [1]=> array(2) { ["value"]=> string(7) "rstudio" ["label"]=> string(7) "RStudio" } } ["project_timeline"]=> string(193) "Day 0: Approval of the project
Day 30: Data transfer
Day 90: Data processing
Day 150: Data analysis
Day 210: Manuscript writing
Day 270: Manuscript submission" ["project_dissemination_plan"]=> string(204) "The results of this project are expected to result in the development of a manuscript suitable for publication in a uro-oncology journal. Results will be presented at appropriate uro-oncology conferences." ["project_bibliography"]=> string(11079) "

Andersen, P. K., & Perme, M. P. (2010). Pseudo-observations in survival analysis. Statistical Methods in Medical Research, 19(1), 71–99.

Armstrong, A. J., Szmulewitz, R. Z., Petrylak, D. P., Holzbeierlein, J., Villers, A., Azad, A., Alcaraz, A., Alekseev, B., Iguchi, T., Shore, N. D., Rosbrook, B., Sugg, J., Baron, B., Chen, L., & Stenzl, A. (2019). ARCHES: A randomized, phase III study of androgen deprivation therapy with enzalutamide or placebo in men with metastatic hormone-sensitive prostate cancer. Journal of Clinical Oncology: Official Journal of the American Society of Clinical Oncology, 37(32), 2974–2986.

Bray, F., Laversanne, M., Sung, H., Ferlay, J., Siegel, R. L., Soerjomataram, I., & Jemal, A. (2024). Global cancer statistics 2022: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA: A Cancer Journal for Clinicians, 74(3), 229–263.

Chi, K. N., Agarwal, N., Bjartell, A., Chung, B. H., Pereira de Santana Gomes, A. J., Given, R., Juárez Soto, Á., Merseburger, A. S., Özgüroğlu, M., Uemura, H., Ye, D., Deprince, K., Naini, V., Li, J., Cheng, S., Yu, M. K., Zhang, K., Larsen, J. S., McCarthy, S., … TITAN Investigators. (2019). Apalutamide for metastatic, castration-sensitive prostate cancer. The New England Journal of Medicine, 381(1), 13–24.

Clift, A. K., Coupland, C. A. C., Keogh, R. H., Diaz-Ordaz, K., Williamson, E., Harrison, E. M., Hayward, A., Hemingway, H., Horby, P., Mehta, N., Benger, J., Khunti, K., Spiegelhalter, D., Sheikh, A., Valabhji, J., Lyons, R. A., Robson, J., Semple, M. G., Kee, F., … Hippisley-Cox, J. (2020). Living risk prediction algorithm (QCOVID) for risk of hospital admission and mortality from coronavirus 19 in adults: national derivation and validation cohort study. BMJ (Clinical Research Ed.), 371, m3731.

Clift, A. K., Dodwell, D., Lord, S., Petrou, S., Brady, M., Collins, G. S., & Hippisley-Cox, J. (2023). Development and internal-external validation of statistical and machine learning models for breast cancer prognostication: cohort study. BMJ (Clinical Research Ed.), 381, e073800.

Debray, T. P. A., Collins, G. S., Riley, R. D., Snell, K. I. E., Van Calster, B., Reitsma, J. B., & Moons, K. G. M. (2023). Transparent reporting of multivariable prediction models developed or validated using clustered data: TRIPOD-Cluster checklist. BMJ (Clinical Research Ed.), 380, e071018.

Fizazi, K., Tran, N., Fein, L., Matsubara, N., Rodriguez-Antolin, A., Alekseev, B. Y., Özgüroğlu, M., Ye, D., Feyerabend, S., Protheroe, A., De Porre, P., Kheoh, T., Park, Y. C., Todd, M. B., Chi, K. N., & LATITUDE Investigators. (2017). Abiraterone plus prednisone in metastatic, castration-sensitive prostate cancer. The New England Journal of Medicine, 377(4), 352–360.

Hippisley-Cox, J., & Coupland, C. (2015). Development and validation of risk prediction algorithms to estimate future risk of common cancers in men and women: prospective cohort study. BMJ Open, 5(3), e007825.

Hippisley-Cox, J., Coupland, C., & Brindle, P. (2017). Development and validation of QRISK3 risk prediction algorithms to estimate future risk of cardiovascular disease: prospective cohort study. BMJ (Clinical Research Ed.), 357, j2099.

Kent, D. M., Paulus, J. K., van Klaveren, D., D’Agostino, R., Goodman, S., Hayward, R., Ioannidis, J. P. A., Patrick-Lake, B., Morton, S., Pencina, M., Raman, G., Ross, J. S., Selker, H. P., Varadhan, R., Vickers, A., Wong, J. B., & Steyerberg, E. W. (2020). The Predictive Approaches to treatment effect Heterogeneity (PATH) statement. Annals of Internal Medicine, 172(1), 35–45.

Kent, D. M., van Klaveren, D., Paulus, J. K., D’Agostino, R., Goodman, S., Hayward, R., Ioannidis, J. P. A., Patrick-Lake, B., Morton, S., Pencina, M., Raman, G., Ross, J. S., Selker, H. P., Varadhan, R., Vickers, A., Wong, J. B., & Steyerberg, E. W. (2020). The Predictive Approaches to treatment effect heterogeneity (PATH) Statement: Explanation and elaboration. Annals of Internal Medicine, 172(1), W1–W25.

Resche-Rigon, M., & White, I. R. (2018). Multiple imputation by chained equations for systematically and sporadically missing multilevel data. Statistical Methods in Medical Research, 27(6), 1634–1649.

Riley, R. D. (2021). Individual participant data meta-analysis: A handbook for healthcare research (R. D. Riley, J. F. Tierney, & L. A. Stewart (eds.)). John Wiley & Sons. https://doi.org/10.1002/9781119333784

Smith, M. R., Hussain, M., Saad, F., Fizazi, K., Sternberg, C. N., Crawford, E. D., Kopyltsov, E., Park, C. H., Alekseev, B., Montesa-Pino, Á., Ye, D., Parnis, F., Cruz, F., Tammela, T. L. J., Suzuki, H., Utriainen, T., Fu, C., Uemura, M., Méndez-Vidal, M. J., … ARASENS Trial Investigators. (2022). Darolutamide and survival in metastatic, hormone-sensitive prostate cancer. The New England Journal of Medicine, 386(12), 1132–1142.

Stewart, L. A., Clarke, M., Rovers, M., Riley, R. D., Simmonds, M., Stewart, G., & Tierney, J. F. (2015). Preferred reporting items for a systematic review and meta-analysis of individual participant data: The PRISMA-IPD statement. JAMA: The Journal of the American Medical Association, 313(16), 1657.

Steyerberg, E. W., & Harrell, F. E., Jr. (2016). Prediction models need appropriate internal, internal-external, and external validation. Journal of Clinical Epidemiology, 69, 245–247.

Takada, T., Nijman, S., Denaxas, S., Snell, K. I. E., Uijl, A., Nguyen, T.-L., Asselbergs, F. W., & Debray, T. P. A. (2021). Internal-external cross-validation helped to evaluate the generalizability of prediction models in large clustered datasets. Journal of Clinical Epidemiology, 137, 83–91.

van Buuren, S., & Groothuis-Oudshoorn, K. (2011). mice: Multivariate Imputation by Chained Equations inR. Journal of Statistical Software, 45(3). https://doi.org/10.18637/jss.v045.i03

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2025-0396

General Information

How did you learn about the YODA Project?: Scientific Publication

Conflict of Interest

Request Clinical Trials

Associated Trial(s):
  1. NCT01715285 - A Randomized, Double-blind, Comparative Study of Abiraterone Acetate Plus Low-Dose Prednisone Plus Androgen Deprivation Therapy (ADT) Versus ADT Alone in Newly Diagnosed Subjects With High-Risk, Metastatic Hormone-naive Prostate Cancer (mHNPC)
  2. NCT02489318 - A Phase 3 Randomized, Placebo-controlled, Double-blind Study of Apalutamide Plus Androgen Deprivation Therapy (ADT) Versus ADT in Subjects With Metastatic Hormone-sensitive Prostate Cancer (mHSPC)
What type of data are you looking for?: Individual Participant-Level Data, which includes Full CSR and all supporting documentation

Request Clinical Trials

Data Request Status

Status: Ongoing

Research Proposal

Project Title: Heterogeneity in treatment effect of androgen receptor pathway inhibitors in metastatic hormone-sensitive prostate cancer

Scientific Abstract: Background
Androgen receptor pathway inhibitors (ARPIs) improve outcomes for patients with metastatic hormone-sensitive prostate cancer. Whether the effects of ARPIs vary based on patient characteristics remains unclear.

Objective
To determine whether patient characteristics modify the effect of ARPIs versus placebo on overall survival in patients with mHSPC.

Study Design
Individual participant data meta-analysis.

Participants
Patients with mHSPC who were randomized to either ARPIs or placebo.

Primary and Secondary Outcome Measures
The primary outcome measure is overall survival (OS), defined as the time from randomization to death from any cause.

Statistical Analysis
The statistical analysis plan involves a systematic literature search to identify relevant RCTs on ARPIs for mHSPC. Eligible studies with available IPD will be included. The heterogeneity of treatment effect (HTE) will be analyzed using risk-modeling approaches. The risk-modeling approach will develop an internal risk prediction model for OS, assess model performance, and evaluate treatment effects of ARPI versus placebo across risk subgroups.

Brief Project Background and Statement of Project Significance: Prostate cancer, the most commonly diagnosed malignancy in men globally in 2022, accounted for 7.3% of all cancer diagnoses worldwide (Bray et al., 2024). Landmark phase III randomized controlled trials (RCTs) have conclusively demonstrated the clinical benefit of androgen receptor pathway inhibitors (ARPIs) in the treatment of metastatic hormone-sensitive prostate cancer (mHSPC) (Armstrong et al., 2019; Chi et al., 2019; Fizazi et al., 2017; Smith et al., 2022). Prior studies suggested mHSPC has heterogeneity in prognosis, indicating possible heterogeneity in treatment effect (HTE) of ARPIs among those with mHSPC. Investigating the HTE of ARPIs in mHSPC would enable more precise benefit assessments and highlight the importance of considering HTE in the design and analysis of RCTs.

Specific Aims of the Project: This study aims to evaluate whether the treatment effect of ARPIs varies by baseline characteristics.

Study Design: Meta-analysis (analysis of multiple trials together)

What is the purpose of the analysis being proposed? Please select all that apply.: New research question to examine treatment effectiveness on secondary endpoints and/or within subgroup populations

Software Used: R, RStudio

Data Source and Inclusion/Exclusion Criteria to be used to define the patient sample for your study: This study will include patients with mHSPC who are randomized to either ARPIs or placebo in clinical trials. RCTs will be eligible when patients with mHSPC are randomized to receive ARPIs or placebo with ADT. To provide clinically informative data for physicians, this study will include ARPIs approved by the Food and Drug Administration, such as abiraterone acetate, apalutamide, darolutamide, and enzalutamide. Open-label RCTs will be excluded to reduce potential bias in the analysis. Additionally, non-RCT studies and studies without available IPD will be excluded. The pharmaceutical companies sponsoring the pivotal RCTs for enzalutamide and apalutamide are members of Vivli. Therefore, all IPD will be merged and analyzed within the Vivli data analysis environment. We plan to request data from the following RCTs: ARAMIS (NCT02799602), ARCHES (NCT02677896), LATITUDE (NCT01715285), and TITAN (NCT02489318).

Primary and Secondary Outcome Measure(s) and how they will be categorized/defined for your study: The primary outcome measure is overall survival (OS), defined as the time from randomization to death from any cause.

Main Predictor/Independent Variable and how it will be categorized/defined for your study: Predicted risk of poor outcomes.

Other Variables of Interest that will be used in your analysis and how they will be categorized/defined for your study: The predictive Heterogeneity of Treatment Effect analysis will be performed using a subset of the following variables, selected based on their previously reported prognostic value, clinical relevance, and anticipated availability across participating trials.
The variables include: age at randomization, number of bone metastases, baseline hemoglobin, baseline neutrophil-to-lymphocyte ratio, baseline albumin, baseline prostate-specific antigen, baseline alkaline phosphatase, and baseline lactate dehydrogenase, all of which will be treated as continuous variables. Categorical variables include Eastern Cooperative Oncology Group (ECOG) performance status (categorized as 0 vs. >=1), total biopsy Gleason score at diagnosis (<=8 vs. >=9), opioid analgesic use (no vs. yes), de novo metastatic disease (no vs. yes), presence of visceral metastasis (absent vs. present), de novo metastatic disease (no vs. yes), and concomitant docetaxel use (no vs. yes).

Statistical Analysis Plan: This study adheres to the PRISMA-IPD statement (Stewart et al., 2015) and TRIPOD-cluster checklist (Debray et al., 2023). The heterogeneity of treatment effect (HTE) will be evaluated using a risk-modeling analysis approach.

Overview
A risk-modeling framework will be used to explore the HTE of ARPIs in patients with mHSPC (Kent, Paulus, et al., 2020). This framework uses a multivariable risk prediction model to examine how treatment effects vary based on predicted risk levels. The model stratifies patients according to their calculated risk profiles to analyze these variations. A risk prediction model for OS will be developed internally using IPD from RCTs to estimate the risk of OS for each patient.

Missing Variable Imputation
Missing baseline covariate values will be multiply imputed using a multivariate imputation by chained equations (MICE) algorithm (van Buuren & Groothuis-Oudshoorn, 2011). To handle sporadic missing variables, a multilevel MICE approach will be used (Resche-Rigon & White, 2018). One hundred distinct imputed datasets will be generated, and the subsequent variable selection process will be performed on each imputed dataset, although the number of imputations may be adjusted if computational resources are insufficient.

Risk prediction model development
Cox proportional hazards regression will be the primary method for developing the risk prediction model. If the proportional hazards assumption is not met, alternative techniques, such as restricted mean survival time (RMST) regression using pseudo-observations, will be explored (Andersen & Perme, 2010).
Initially, a Cox model incorporating all potential predictors will be fitted. From this, predictors will be selected based on approaches used in previous clinical prediction modeling studies (Clift et al., 2020, 2023; Hippisley-Cox et al., 2017; Hippisley-Cox & Coupland, 2015). Binary or multilevel categorical predictors will be included if their exponentiated coefficients (hazard ratios [HRs]) are > 1.1 or < 0.9 with a corresponding P < 0.01. Continuous variables will be selected if their associated P < 0.01. This selection approach benefits from starting with a full, maximally complex model and then considering both clinical and statistical magnitude to select a parsimonious model using multiply imputed data. Interaction effects will be excluded to reduce the computational load. The selected predictors will then be used to construct the final Cox model. To adjust the model for overfitting, a heuristic shrinkage factor will be calculated and multiplied by the original beta coefficients. The resulting model will be used to compute a risk score for each patient, calculated as the linear combination of their covariate values and the final model coefficients (log HR).

Internal-external cross-validation
Internal-external cross-validation will be conducted to evaluate the generalizability and between-trial heterogeneity of the model's performance (Steyerberg & Harrell, 2016; Takada et al., 2021). Model discrimination will be evaluated with Harrell's C statistic, while calibration will be assessed by the calibration slope and the ratio of expected to observed outcomes. The process of internal-external cross-validation will involve systematically omitting each included trial in turn to serve as an external validation dataset. For each iteration, the risk prediction model for OS will be developed using the combined data from all other trials to obtain its beta coefficients and heuristic shrinkage factors. The performance of this model will then be assessed in the held-out study. This procedure will be repeated until each included study has served as the external validation dataset. Performance measures from the cross-validation will be summarized using a random-effects meta-analysis to provide a summary estimate of overall performance (Riley, 2021). Additionally, smoothed calibration plots will be generated to visualize the alignment between observed and predicted risks.

Heterogeneity in treatment effect assessment
For the risk-modelling predictive HTE analysis, we adhere to the Predictive Approaches to treatment effect heterogeneity (PATH) Statement (Kent, Paulus, et al., 2020). The treatment effect will be assessed using both relative (HRs) and absolute (difference in RMSTs) measures. To analyze treatment effects within subgroups, relative and absolute effects will be presented using HRs and differences in RMSTs. For both the relative and absolute effect analyses, a test for interaction between ARPI randomization and predicted risk will be performed. The analysis will be performed using a two-stage meta-analytic framework; however, a one-stage framework will be applied if the two-stage approach proves analytically difficult.

Narrative Summary: This project aims to determine if the effectiveness of certain drugs for advanced prostate cancer varies from patient to patient. These drugs, called androgen receptor pathway inhibitors (ARPIs), have been shown to improve outcomes for men with metastatic hormone-sensitive prostate cancer (mHSPC). However, it is unclear if these drugs work equally well for everyone.
In this study, we will review data from past clinical trials where men with mHSPC were given either ARPIs or a placebo (a dummy drug). We will look at information like age, general health, cancer stage, and blood test results to see if these factors predict whether the treatment was more or less effective.
This research is important because knowing which patients benefit most from ARPIs can help doctors make better treatment plans for patients with mHSPC.

Project Timeline: Day 0: Approval of the project
Day 30: Data transfer
Day 90: Data processing
Day 150: Data analysis
Day 210: Manuscript writing
Day 270: Manuscript submission

Dissemination Plan: The results of this project are expected to result in the development of a manuscript suitable for publication in a uro-oncology journal. Results will be presented at appropriate uro-oncology conferences.

Bibliography:

Andersen, P. K., & Perme, M. P. (2010). Pseudo-observations in survival analysis. Statistical Methods in Medical Research, 19(1), 71--99.

Armstrong, A. J., Szmulewitz, R. Z., Petrylak, D. P., Holzbeierlein, J., Villers, A., Azad, A., Alcaraz, A., Alekseev, B., Iguchi, T., Shore, N. D., Rosbrook, B., Sugg, J., Baron, B., Chen, L., & Stenzl, A. (2019). ARCHES: A randomized, phase III study of androgen deprivation therapy with enzalutamide or placebo in men with metastatic hormone-sensitive prostate cancer. Journal of Clinical Oncology: Official Journal of the American Society of Clinical Oncology, 37(32), 2974--2986.

Bray, F., Laversanne, M., Sung, H., Ferlay, J., Siegel, R. L., Soerjomataram, I., & Jemal, A. (2024). Global cancer statistics 2022: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA: A Cancer Journal for Clinicians, 74(3), 229--263.

Chi, K. N., Agarwal, N., Bjartell, A., Chung, B. H., Pereira de Santana Gomes, A. J., Given, R., Juárez Soto, Á., Merseburger, A. S., Özgüroğlu, M., Uemura, H., Ye, D., Deprince, K., Naini, V., Li, J., Cheng, S., Yu, M. K., Zhang, K., Larsen, J. S., McCarthy, S., ... TITAN Investigators. (2019). Apalutamide for metastatic, castration-sensitive prostate cancer. The New England Journal of Medicine, 381(1), 13--24.

Clift, A. K., Coupland, C. A. C., Keogh, R. H., Diaz-Ordaz, K., Williamson, E., Harrison, E. M., Hayward, A., Hemingway, H., Horby, P., Mehta, N., Benger, J., Khunti, K., Spiegelhalter, D., Sheikh, A., Valabhji, J., Lyons, R. A., Robson, J., Semple, M. G., Kee, F., ... Hippisley-Cox, J. (2020). Living risk prediction algorithm (QCOVID) for risk of hospital admission and mortality from coronavirus 19 in adults: national derivation and validation cohort study. BMJ (Clinical Research Ed.), 371, m3731.

Clift, A. K., Dodwell, D., Lord, S., Petrou, S., Brady, M., Collins, G. S., & Hippisley-Cox, J. (2023). Development and internal-external validation of statistical and machine learning models for breast cancer prognostication: cohort study. BMJ (Clinical Research Ed.), 381, e073800.

Debray, T. P. A., Collins, G. S., Riley, R. D., Snell, K. I. E., Van Calster, B., Reitsma, J. B., & Moons, K. G. M. (2023). Transparent reporting of multivariable prediction models developed or validated using clustered data: TRIPOD-Cluster checklist. BMJ (Clinical Research Ed.), 380, e071018.

Fizazi, K., Tran, N., Fein, L., Matsubara, N., Rodriguez-Antolin, A., Alekseev, B. Y., Özgüroğlu, M., Ye, D., Feyerabend, S., Protheroe, A., De Porre, P., Kheoh, T., Park, Y. C., Todd, M. B., Chi, K. N., & LATITUDE Investigators. (2017). Abiraterone plus prednisone in metastatic, castration-sensitive prostate cancer. The New England Journal of Medicine, 377(4), 352--360.

Hippisley-Cox, J., & Coupland, C. (2015). Development and validation of risk prediction algorithms to estimate future risk of common cancers in men and women: prospective cohort study. BMJ Open, 5(3), e007825.

Hippisley-Cox, J., Coupland, C., & Brindle, P. (2017). Development and validation of QRISK3 risk prediction algorithms to estimate future risk of cardiovascular disease: prospective cohort study. BMJ (Clinical Research Ed.), 357, j2099.

Kent, D. M., Paulus, J. K., van Klaveren, D., D'Agostino, R., Goodman, S., Hayward, R., Ioannidis, J. P. A., Patrick-Lake, B., Morton, S., Pencina, M., Raman, G., Ross, J. S., Selker, H. P., Varadhan, R., Vickers, A., Wong, J. B., & Steyerberg, E. W. (2020). The Predictive Approaches to treatment effect Heterogeneity (PATH) statement. Annals of Internal Medicine, 172(1), 35--45.

Kent, D. M., van Klaveren, D., Paulus, J. K., D'Agostino, R., Goodman, S., Hayward, R., Ioannidis, J. P. A., Patrick-Lake, B., Morton, S., Pencina, M., Raman, G., Ross, J. S., Selker, H. P., Varadhan, R., Vickers, A., Wong, J. B., & Steyerberg, E. W. (2020). The Predictive Approaches to treatment effect heterogeneity (PATH) Statement: Explanation and elaboration. Annals of Internal Medicine, 172(1), W1--W25.

Resche-Rigon, M., & White, I. R. (2018). Multiple imputation by chained equations for systematically and sporadically missing multilevel data. Statistical Methods in Medical Research, 27(6), 1634--1649.

Riley, R. D. (2021). Individual participant data meta-analysis: A handbook for healthcare research (R. D. Riley, J. F. Tierney, & L. A. Stewart (eds.)). John Wiley & Sons. https://doi.org/10.1002/9781119333784

Smith, M. R., Hussain, M., Saad, F., Fizazi, K., Sternberg, C. N., Crawford, E. D., Kopyltsov, E., Park, C. H., Alekseev, B., Montesa-Pino, Á., Ye, D., Parnis, F., Cruz, F., Tammela, T. L. J., Suzuki, H., Utriainen, T., Fu, C., Uemura, M., Méndez-Vidal, M. J., ... ARASENS Trial Investigators. (2022). Darolutamide and survival in metastatic, hormone-sensitive prostate cancer. The New England Journal of Medicine, 386(12), 1132--1142.

Stewart, L. A., Clarke, M., Rovers, M., Riley, R. D., Simmonds, M., Stewart, G., & Tierney, J. F. (2015). Preferred reporting items for a systematic review and meta-analysis of individual participant data: The PRISMA-IPD statement. JAMA: The Journal of the American Medical Association, 313(16), 1657.

Steyerberg, E. W., & Harrell, F. E., Jr. (2016). Prediction models need appropriate internal, internal-external, and external validation. Journal of Clinical Epidemiology, 69, 245--247.

Takada, T., Nijman, S., Denaxas, S., Snell, K. I. E., Uijl, A., Nguyen, T.-L., Asselbergs, F. W., & Debray, T. P. A. (2021). Internal-external cross-validation helped to evaluate the generalizability of prediction models in large clustered datasets. Journal of Clinical Epidemiology, 137, 83--91.

van Buuren, S., & Groothuis-Oudshoorn, K. (2011). mice: Multivariate Imputation by Chained Equations inR. Journal of Statistical Software, 45(3). https://doi.org/10.18637/jss.v045.i03