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Associated Trial(s):- NCT01008995 - A Phase 3, Multicenter, Randomized, Double-blind, Placebo-controlled Study Evaluating the Efficacy and Safety of Ustekinumab in the Treatment of Chinese Subjects With Moderate to Severe Plaque-type Psoriasis
- NCT00747344 - A Phase 3, Multicenter, Randomized, Double-blind, Placebo-controlled Study Evaluating the Efficacy and Safety of Ustekinumab in the Treatment of Korean and Taiwanese Subjects With Moderate to Severe Plaque-type Psoriasis
- NCT00267969 - A Phase 3, Multicenter, Randomized, Double-blind, Placebo Controlled Trial Evaluating the Efficacy and Safety of Ustekinumab (CNTO 1275) in the Treatment of Subjects With Moderate to Severe Plaque-type Psoriasis
- NCT00307437 - A Phase 3, Multicenter, Randomized, Double-blind, Placebo-controlled Trial Evaluating the Efficacy and Safety of CNTO 1275 in the Treatment of Subjects With Moderate to Severe Plaque-type Psoriasis
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Status: OngoingResearch Proposal
Project Title: Bayesian dynamic borrowing of external controls using propensity score-integrated and model-assisted elastic evaluation of heterogeneity
Scientific Abstract:
Background: Borrowing external controls can reduce the sample size but may also introduce bias due to heterogeneity.
Objective: To illustrate the Bayesian dynamic borrowing based on our proposed elastic evaluation of heterogeneity using real data.
Study Design: This is a hybrid control arm study where a concurrent trial aims to borrow external controls from previously completed trials. In the design phase, propensity score matching, stratification, and weighting are employed to balance the covariates between external controls and the concurrent trial. In the analysis phase, the outcome model is fitted separately for each control arm, and heterogeneity is assessed by comparing the model coefficients and the means of covariates. Based on their differences, the discounting of external controls is determined via an elastic function. If any difference causes a change in the average control effect that exceeds the pre-specified clinically significant threshold, no borrowing occurs.
Participants: The concurrent trial is NCT01008995. The external controls are selected from NCT00747344, NCT00307437, and NCT00267969 using the inclusion/exclusion criteria of NCT01008995.
Outcome Measure: The main outcome is the proportion of patients achieving at least a 75% improvement in the Psoriasis Area and Severity Index at week 12.
Statistical analysis: Bayesian borrowing methods, including the Power Prior, Elastic Prior, and Robust Mixture Prior, are used. Based on our elastic evaluation of heterogeneity, the discounting parameter is considered fixed or random with a weakly-informative prior.
Brief Project Background and Statement of Project Significance:
Borrowing external controls from previously completed trials or real-world data (RWD) to create a hybrid control arm is a popular topic in clinical trials, as it can reduce the sample size while maintaining the desired statistical power. [1]. Several Bayesian dynamic borrowing methods have been proposed to adaptively discount external controls based on the heterogeneity of observed outcomes, known as prior-data conflict [2]. The Power Prior (PP) uses the power parameter to downweight external likelihood [3]. The Elastic Prior (ELP) inflates the variance of the prior distribution derived from external controls [4]. The Robust Mixture Prior (RMP) incorporates an additional non-informative prior with a weight to increase uncertainty [5]. Additionally, another class of methods is based on Bayesian hierarchical modeling, such as the (robust) Meta-analytic predictive prior [6] and the Commensurate Prior [7].
Borrowing external controls is inevitably challenged by heterogeneity between concurrent and external controls due to selection bias, unmeasured confounders, lack of concurrency, and measurement error, which can lead to biased estimation of the average treatment effect (ATE) and an inflated Type I error rate [8]. Recently, propensity score (PS) methodologies have been increasingly integrated with Bayesian dynamic borrowing methods to mitigate selection bias through a two-step strategy [9-13]. In the design phase, external controls are matched, stratified, or weighted based on their PS to create a pseudo-population with covariates more similar to the target population. Simulation studies have demonstrated that PS-integrated Bayesian borrowing performs better than solely using Bayesian methods when selection bias exists [10]. Additionally, some literature suggests using PS overlap as a fixed discounting parameter to proactively downweight external controls based on the similarity of covariates [10,11]. However, this method overlooks prior-data conflict, i.e., the similarity of observed outcomes. Furthermore, simulation studies have shown that unmeasured confounders can still significantly impact the performance of Bayesian borrowing of external controls [14]. Therefore, a more comprehensive evaluation of heterogeneity, considering the similarity of both covariates and outcomes, is essential for the dynamic discounting of external controls.
In this context, our proposed approach first employs PS methodologies to balance the covariates, then fits the outcome model separately for each control arm to account for the similarity of outcomes. Specifically, we compare the model coefficients and the means of covariates between different control arms to adaptively determine the discounting of external controls via an elastic function.
Specific Aims of the Project: This project will demonstrate the application of the Bayesian dynamic borrowing based on our proposed elastic evaluation of heterogeneity using real data. Our approach will be compared with existing methods, including 1) using only PS methodologies to balance covariates, 2) using only Bayesian dynamic borrowing methods (the Power Prior, Elastic Prior, and Robust Mixture Prior with a uniform initial prior) without PS methodologies, and 3) using PS-integrated Bayesian dynamic borrowing based on PS overlap instead of our proposed evaluation of heterogeneity. For the discounting parameter, we will consider it both fixed and random with a weakly informative prior. Additionally, we will investigate the influence of different proportions of external controls in the hybrid control arm on the posterior inference of ATE.
Study Design: Methodological research
What is the purpose of the analysis being proposed? Please select all that apply.: Develop or refine statistical methods Research on clinical trial methods
Software Used: RStudio
Data Source and Inclusion/Exclusion Criteria to be used to define the patient sample for your study: The concurrent trial is NCT01008995. The external controls come from NCT00747344, NCT00307437, and NCT00267969. The inclusion and exclusion criteria of the concurrent trial (NCT01008995) will be applied to the external trials to select comparable external controls. The trial data will be used in its entirety.
Primary and Secondary Outcome Measure(s) and how they will be categorized/defined for your study: The primary efficacy endpoint is the proportion of patients with a Psoriasis Area and Severity Index (PASI) 75 response at week 12. The PASI evaluates the extent and severity of skin disease on a scale of 0 (no psoriasis) to 72 (severe psoriasis), and the PASI 75 represents the 75% improvement of PASI from baseline.
Main Predictor/Independent Variable and how it will be categorized/defined for your study:
The following covariates are considered for the PS model and the outcome model:
1) Continuous covariates: Age (years), Baseline PASI (0--72), Duration of psoriasis (years);
2) Categorical covariates: Sex (male/female), Baseline body weight (no more than 65 kg vs more than 65 kg).
Other Variables of Interest that will be used in your analysis and how they will be categorized/defined for your study:
Other important baseline variables includes:
1) Continuous covariates: Baseline body mass index (BMI) defined as weight (kg) / height^2 (m^2); Proportion of body surface area (BSA) affected by psoriasis (%);
2) Categorical covariates: Physician's Global Assessment (PGA) (0 = cleared, 1 = minimal, 2 = mild, 3 = moderate, 4 = marked, and 5 = severe).
Statistical Analysis Plan:
The analysis involves estimating the PS, fitting the outcome model, and employing Bayesian borrowing methods. Both the PS, i.e., the probability of being from the current trial, and the primary binary outcome, PASI 75, are modeled as the function of covariates, including age, sex, baseline PASI, baseline body weight, and duration of psoriasis, via logistic regression. For PS matching, we use nearest-neighbor 1:1 matching without replacement, with a caliper of 0.1. For PS stratification, the number of strata is set to 3. For PS weighting, the standardized mortality ratio weighting is adopted, where the weight of concurrent control is one and the weight of external controls is PS/(1-PS).
To assess heterogeneity, we will simulate the scenario where PASI 75 is equal between concurrent and external controls (congruent case) and the scenario where PASI 75 is unequal, exceeding the pre-specified clinically significant threshold (incongruent case). We calculate the Chi-square statistic in these two scenarios, which inversely relates to the similarity of outcomes, and then determine the elastic function, a logistic function linking the Chi-square statistic to the congruence of PASI 75. For each external data source, we will evaluate the extent of incongruent PASI 75 that may arise from differences in the model coefficients and the means of covariates. We denote the congruence of PASI 75 derived from the elastic function as the H value, ranging from zero to one, to indicate the degree of heterogeneity.
The following Bayesian methods are used to dynamically borrow external controls: the Power Prior, Elastic Prior, and Robust Mixture Prior. Two types of discounting parameters are also considered: 1) fixed and equal to the H value, and 2) random with a weakly informative initial prior having a mean of H value. Additionally, we will analyze the data by 1) using only PS methodologies to balance the covariates, 2) using only Bayesian dynamic borrowing methods (the Power Prior, Elastic Prior, and Robust Mixture Prior with a uniform initial prior) without PS methodologies, and 3) using PS-integrated Bayesian dynamic borrowing based on PS overlap. The posterior mean of ATE and the length of its 95% credible interval are calculated, and their changes from the results without borrowing are compared. Moreover, we also consider sensitivity analyses of different sample size ratios between the concurrent and external controls.
Narrative Summary: Borrowing external controls can reduce the sample size of clinical trials, but heterogeneity due to population shifts, different study periods, and designs can introduce bias. Our proposed approach first balances the covariates using propensity score methodologies, then fits the outcome model separately for each control arm. Heterogeneity is assessed by comparing the model coefficients and the means of covariates. Based on their differences, the discounting of external controls is determined via an elastic function. If any difference leads to a change in the average control effect that exceeds the pre-specified clinically significant threshold, external controls will not be borrowed.
Project Timeline: The real-data analysis will begin as soon as data becomes available, and the manuscript finalization is anticipated to be completed by 30th December 2024. Results will be reported back to the YODA project once the manuscript is submitted for publication by 30th January 2025.
Dissemination Plan:
The project will result in a scientific paper with a target audience of the statistical community. Our target journals include Statistics in Biopharmaceutical Research, Biopharmaceutical Statistics, Biometrical Journal, Journal of Biopharmaceutical Statistics, and Contemporary Clinical Trials. The outcomes of this project will also be submitted to academic conferences, such as the Society for Clinical Trials. Acknowledgment of the YODA Project will be included in all project outputs.
Bibliography:
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[2] Viele K, Berry S, Neuenschwander B, Amzal B, Chen F, Enas N, et al. Use of historical control data for assessing treatment effects in clinical trials. Pharm Stat. 2014;13(1):41-54.
[3] Ibrahim JG, Chen MH. Power prior distributions for regression models. Stat Sci. 2000;15(1):46-60.
[4] Jiang LY, Nie L, Yuan Y. Elastic priors to dynamically borrow information from historical data in clinical trials. Biometrics. 2023;79(1):49-60.
[5] Yang P, Zhao Y, Nie L, Vallejo J, Yuan Y. SAM: Self‐adapting mixture prior to dynamically borrow information from historical data in clinical trials. Biometrics. 2023.
[6] Neuenschwander B, Capkun-Niggli G, Branson M, Spiegelhalter DJ. Summarizing historical information on controls in clinical trials. Clin Trials. 2010;7(1):5-18.
[7] Hobbs BP, Sargent DJ, Carlin BP. Commensurate Priors for Incorporating Historical Information in Clinical Trials Using General and Generalized Linear Models. Bayesian analysis. 2012;7(3):639-73.
[8] Shan M, Faries D, Dang A, Zhang X, Cui Z, Sheffield KM. A Simulation-Based Evaluation of Statistical Methods for Hybrid Real-World Control Arms in Clinical Trials. Statistics in biosciences. 2022;14(2):259-84.
[9] Lin J, Lin J. Incorporating propensity scores for evidence synthesis under bayesian framework: review and recommendations for clinical studies. J Biopharm Stat. 2021:1-22.
[10] Wang C, Li H, Chen WC, Lu N, Tiwari R, Xu Y, et al. Propensity score-integrated power prior approach for incorporating real-world evidence in single-arm clinical studies. J Biopharm Stat. 2019;29(5):731-48.
[11] Lin J, Gamalo-Siebers M, Tiwari R. Ensuring exchangeability in data-based priors for a Bayesian analysis of clinical trials. Pharm Stat. 2022;21(2):327-44.
[12] Harton J, Segal B, Mamtani R, Mitra N, Hubbard RA. Combining Real-World and Randomized Control Trial Data Using Data-Adaptive Weighting via the On-Trial Score. Statistics in biopharmaceutical research. 2022:1-13.
[13] Baron E, Zhu J, Tang RS, Chen MH. Bayesian Divide-and-Conquer Propensity Score Based Approaches for Leveraging Real World Data in Single Arm Clinical Trials. J Biopharm Stat. 2022:1-15.
[14] Wang X, Suttner L, Jemielita T, Li X. Propensity score-integrated Bayesian prior approaches for augmented control designs: a simulation study. J Biopharm Stat. 2021:1-21.