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      string(278) "NCT02257736 - A Phase 3 Randomized, Placebo-controlled Double-blind Study of JNJ-56021927 in Combination With Abiraterone Acetate and Prednisone Versus Abiraterone Acetate and Prednisone in Subjects With Chemotherapy-naive Metastatic Castration-resistant Prostate Cancer (mCRPC)"
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      ["post_modified"]=>
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      string(171) "NCT02236637 - A Prospective Registry of Patients With a Confirmed Diagnosis of Adenocarcinoma of the Prostate Presenting With Metastatic Castrate-Resistant Prostate Cancer"
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  ["project_title"]=>
  string(89) "A Bayesian Response-Adaptive Randomization Design with Dynamic Borrowing of External Data"
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  string(854) "Leveraging external data, such as historical trial data or real-world data (RWD), into ongoing randomized controlled trials can improve estimation efficiency and reduce sample size requirements. We propose a Bayesian response‑adaptive randomization (RAR) design that dynamically borrows information from two types of external data: individual‑level RWD and summary‑level historical estimates. Summary-level historical estimates are incorporated as Bayesian prior information, and individual-level RWD are incorporated in the likelihood construction with a weight parameter to control borrowing strength. Allocation probabilities are updated based on the posterior probabilities of treatment efficacy. The proposed framework enhances estimation efficiency, lowers sample size needs, and remains robust to potential heterogeneity across data sources."
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    ["first_name"]=>
    string(2) "Qi"
    ["last_name"]=>
    string(3) "Han"
    ["degree"]=>
    string(16) "Master's student"
    ["primary_affiliation"]=>
    string(26) "Renmin University of China"
    ["email"]=>
    string(18) "hookid1107@163.com"
    ["state_or_province"]=>
    string(7) "Beijing"
    ["country"]=>
    string(5) "China"
  }
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      ["p_pers_f_name"]=>
      string(3) "Hao"
      ["p_pers_l_name"]=>
      string(3) "Mei"
      ["p_pers_degree"]=>
      string(3) "PhD"
      ["p_pers_pr_affil"]=>
      string(26) "Renmin University of China"
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  ["project_ext_grants"]=>
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    ["label"]=>
    string(68) "No external grants or funds are being used to support this research."
  }
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  string(18) "full_crs_supp_docs"
  ["property_scientific_abstract"]=>
  string(1591) "1. Background

RAR adjusts treatment allocation probabilities and directs more participants toward therapies showing greater promise. Integrating RWD from patients on standard care into such designs may offset power reductions due to allocation imbalances and reduce resource requirements.

2. Objective

To develop a Bayesian RAR design that dynamically borrows both individual-level external RWD and summary-level historical data.

3. Study Design

A Bayesian RAR design incorporating both individual-level external RWD and summary-level historical data. Summary-level historical estimates are incorporated as Bayesian prior information, and individual-level RWD are included in the likelihood construction with a weight parameter to control borrowing strength. 

4. Participants

Men with metastatic castration-resistant prostate cancer.

5. Primary/Secondary Outcome Measure(s)

Radiographic Progression-free Survival and overall survival.

6. Statistical Analysis

Internal trial data (NCT02257736) will be combined with RWD (NCT02236637) and historical summary estimates. The primary endpoint will be converted to a binary outcome at a fixed landmark time. A weighted joint likelihood incorporates individual-level external data, with borrowing strength governed by spike-and-slab priors, while historical estimates inform priors for covariate effects. Posterior inference is updated sequentially to guide adaptive randomization. Performance will be evaluated using allocation proportions, bias, and mean squared error."
  ["project_brief_bg"]=>
  string(2162) "RAR represents a sequential approach to treatment assignment, wherein allocation probabilities are revised based on incoming data to favor more effective interventions. This characteristic makes RAR ethically appealing compared to fixed allocation schemes like complete randomization. 



However, similar to fixed designs, RAR demands considerable resources in terms of time, cost, and participant enrollment. Moreover, the imbalance in patient assignment between arms—a known concern in adaptive designs—can compromise statistical power. External data offer a promising solution. When judiciously incorporated into the control arm, external data supports maintaining statistical power with smaller trial sizes, reducing overall costs. 



This study provides a unified Bayesian framework that simultaneously leverages two distinct types of external information: individual‑level external data (e.g., patient‑level records from historical trials or real‑world sources, containing complete covariates, treatments, and outcomes) and summary‑level external data (e.g., published estimates and variances of model parameters from previous studies, where individual records are unavailable). To our knowledge, existing methods either focus solely on individual level external data, such as LEAP (Alt et al., 2024), or solely on summary level external data, with numerous examples including the robust meta‐analytic‐predictive prior (Schmidli et al., 2014), the commensurate prior (Hobbs et al., 2011), and the elastic prior (Jiang et al., 2023).



Our framework integrates individual‑level external data directly into the likelihood through study‑level borrowing proportions and individual‑level similarity weights, while summary‑level external data inform priors for the covariate coefficients via meta‑analytic estimates. This dual‑pathway approach maximizes the use of available evidence, enhances treatment effect estimation, and maintains robustness against heterogeneity between internal and external sources, all within a coherent Bayesian design that supports response‑adaptive randomization."
  ["project_specific_aims"]=>
  string(499) "The project will introduce a response‑adaptive randomization (RAR) method that simultaneously leverages both individual‑level external data (e.g., patient‑level records from historical trials or real‑world sources) and summary‑level external data (e.g., published parameter estimates and variances). The approach dynamically borrows information from these two types of external sources within the RAR framework, enabling adaptive updating of allocation probabilities as the trial proceeds."
  ["project_study_design"]=>
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    ["label"]=>
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  ["project_purposes"]=>
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    [0]=>
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      ["value"]=>
      string(37) "develop_or_refine_statistical_methods"
      ["label"]=>
      string(37) "Develop or refine statistical methods"
    }
    [1]=>
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      ["value"]=>
      string(34) "research_on_clinical_trial_methods"
      ["label"]=>
      string(34) "Research on clinical trial methods"
    }
  }
  ["project_research_methods"]=>
  string(297) "We request two data sources: NCT02257736 (the trial data) and NCT02236637 (the real-world data). The full trial dataset will be used, whereas the real-world data will be restricted to participants treated with Abiraterone acetate plus prednisone or prednisolone. No exclusion criteria are applied."
  ["project_main_outcome_measure"]=>
  string(696) "The primary outcome measure will be Radiographic Progression-Free Survival (rPFS), with the definition consistent with that used in the clinical trial NCT02257736. The primary outcome will be a binary indicator of event-free status at a fixed landmark time (e.g., 40 months). For patients with incomplete follow‑up, the outcome will be imputed using a conditional probability approach based on the Kaplan‑Meier estimator.

The secondary outcome measure, overall survival, will be handled in an analogous manner, defined as a binary indicator at a fixed landmark time, with incomplete follow up imputed using the same conditional probability approach based on the Kaplan Meier estimator."
  ["project_main_predictor_indep"]=>
  string(367) "The main predictor is the treatment that patients received.

Experimental Group: apalutamide (240 mg once daily) and abiraterone acetate (1000 mg once daily) plus prednisone (5 mg twice daily)

Placebo Comparator: placebo and abiraterone acetate plus prednisone in clinical trial (NCT02257736), or abiraterone acetate plus prednisone in RWD (NCT02236637)."
  ["project_other_variables_interest"]=>
  string(365) "Continuous covariates: Age, PSA level, Alkaline phosphatase, LDH (and ULN for LDH), Hemoglobin.

Categorical covariates: Ethnicity, Race, Geographic region (North America, Europe, and Rest of world), Metastasis stage at diagnosis (M0, M1, all others), presence of metastases (number and/or location), Opiate use (yes vs. no), Previous prostate cancer therapy."
  ["project_stat_analysis_plan"]=>
  string(3173) "We will conduct the analysis using clinical trial data (NCT02257736) as the internal dataset and real-world data (NCT02236637) as the external dataset. In addition, summary-level historical estimates will be obtained from published studies in which the control arm employed the same treatment as in the current trial. 

The primary endpoint is radiographic progression-free survival (rPFS). To facilitate integration within a generalized linear model framework and enable adaptive updating, rPFS will be transformed into a binary indicator representing event-free status at a prespecified landmark time (e.g., 40 months). For patients with incomplete follow‑up, the outcome will be imputed using a conditional probability approach based on the Kaplan‑Meier estimator (Li et al., 2025).

We propose a unified Bayesian framework that integrates internal and external data through a weighted joint likelihood. Individual-level external data are incorporated using similarity-based weights, while the overall degree of borrowing is governed by study-level parameters assigned spike-and-slab priors, allowing adaptive and data-driven control of information sharing. In parallel, summary-level historical estimates are incorporated via meta-analytic priors on covariate effects to improve estimation efficiency. 

The response-adaptive randomization (RAR) design will be implemented in two stages. First, a burn-in period with equal randomization will be used to stabilize early estimation and reduce variability due to limited sample size. Following this, the adaptive phase will begin, during which treatment allocation probabilities are updated sequentially as data accrue. 

At each interim analysis during the adaptive phase, the following steps will be performed: 

First, to address potential distributional differences between the internal trial population and the external real-world cohort, inverse probability weighting based on propensity scores will be applied. These weights are estimated using baseline covariates to improve comparability and reduce confounding.

Second, a joint likelihood is constructed that combines internal data with weighted contributions from external sources. Individual-level external data enter the likelihood with subject-specific similarity weights and study-level borrowing parameters, while summary-level data inform prior distributions through meta-analytic estimates. This structure enables flexible borrowing while accounting for heterogeneity across data sources.

Third, posterior inference for model parameters is updated sequentially, and response-adaptive randomization is implemented based on the posterior probability of treatment superiority. Treatment allocation probabilities for incoming patients will be adaptively updated following the Bayesian adaptive design approach of Thall and Wathen (2007). The adaptive randomization process will continue until all patients in the trial have been enrolled and assigned.

Finally, design performance will be assessed using metrics such as allocation proportion, bias and mean squared error of the treatment effect estimator."
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      ["label"]=>
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  ["project_timeline"]=>
  string(420) "The project has already begun. Currently, simulation studies are underway to evaluate the performance of our proposed method under various scenarios.

We aim to complete the simulation studies and finalize the statistical analysis plan by December 2026. Real data analysis and the corresponding manuscript drafting will be completed by March 2027, and the manuscript will be submitted for publication by June 2027."
  ["project_dissemination_plan"]=>
  string(133) "Project results will be disseminated via a journal of Statistics or Biostatistics or Medical Statistics, like Statistics in Medicine."
  ["project_bibliography"]=>
  string(3024) "
Thall, P. F., & Wathen, J. K. (2007). Practical Bayesian adaptive randomisation in clinical trials. European Journal of Cancer.
 
Alt, E. M., Chang, X., tJiang, X., Liu, Q., Mo, M., Xia, H. A., & Ibrahim, J. G. (2024). LEAP: The latent exchangeability prior for borrowing information from historical data. Biometrics, 80(3), ujae083.
 
Hobbs, B. P., Carlin, B. P., Mandrekar, S. J., & Sargent, D. J. (2011). Hierarchical commensurate and power prior models for adaptive incorporation of historical information in clinical trials. Biometrics, 67(3), 1047–1056.
 
Jiang, L., Nie, L., & Yuan, Y. (2023). Elastic priors to dynamically borrow information from historical data in clinical trials. Biometrics, 79(1), 49–60.
 
Schmidli, H., Gsteiger, S., Roychoudhury, S., O’Hagan, A., Spiegelhalter, D., & Neuenschwander, B. (2014). Robust meta‑analytic‑predictive priors in clinical trials with historical control information. Biometrics, 70(4), 1023–1032.
 
Wei W, Zhang Y, Roychoudhury S, et al. Propensity score weighted multi‐source exchangeability models for incorporating external control data in randomized clinical trials[J]. Statistics in Medicine, 2024, 43(20): 3815-3829.
 
Lin X, Cai B, Wang L, et al. A Bayesian proportional hazards model for general interval-censored data[J]. Lifetime data analysis, 2015, 21: 470-490.
 
Kim E S, Herbst R S, Wistuba I I, et al. The BATTLE trial: personalizing therapy for lung cancer[J]. Cancer discovery, 2011, 1(1): 44-53
 
Mukherjee A, Coad D S, Jana S. Covariate-adjusted response-adaptive designs for censored survival responses[J]. Journal of Statistical Planning and Inference, 2023, 225: 219-242.
 
Su P F, Cheung S H. Response‐adaptive treatment allocation for survival trials with clustered right‐censored data[J]. Statistics in Medicine, 2018, 37(16): 2427-2439.
 
Barker A D, Sigman C C, Kelloff G J, et al. I‐SPY 2: an adaptive breast cancer trial design in the setting of neoadjuvant chemotherapy[J]. Clinical Pharmacology & Therapeutics, 2009, 86(1): 97-100.
 
Robertson D S, Lee K M, López-Kolkovska B C, et al. Response-adaptive randomization in clinical trials: from myths to practical considerations[J]. Statistical science, 2023, 38(2): 185-208.
 
Kim M O, Harun N, Liu C, et al. Bayesian selective response‐adaptive design using the historical control[J]. Statistics in medicine, 2018, 37(26): 3709-3722.
 
Pan W. A multiple imputation approach to Cox regression with interval-censored data[J]. Biometrics, 2000, 56(1): 199-203.
 
Li J, Zhang Q, Ma S, et al. Hierarchical multi-label classification with gene-environment interactions in disease modeling[J]. Statistics in Medicine, 2025, 44: e10330.
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