Innovative Bayesian Methods for Leveraging Historical Data in Clinical Trials

The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as a discounting parameter. When the discounting parameter is modeled as random, the normalized power prior is recommended. Bayesian hierarchical modeling is a widely used method for synthesizing information from different sources, including historical data. In this work, we examine the analytical relationship between the normalized power prior (NPP) and Bayesian hierarchical models (BHM) for i.i.d. normal data. We establish a direct relationship between the prior for the discounting parameter of the NPP and the prior for the variance parameter of the BHM. Such a relationship is first established for the case of a single historical dataset, and then extended to the case with multiple historical datasets with dataset-specific discounting parameters. For multiple historical datasets, we develop and establish theory for the BHM-matching NPP (BNPP) which establishes dependence between the dataset-specific discounting parameters leading to inferences that are identical to the BHM. Establishing this relationship not only justifies the NPP from the perspective of hierarchical modeling, but also provides insight on prior elicitation for the NPP. We present strategies on inducing priors on the discounting parameter based on hierarchical models, and investigate the borrowing properties of the BNPP. 

There has been a growing interest in incorporating historical data to enhance the efficiency or reduce the sample size of randomized controlled trials (RCTs). A key challenge is that patient characteristics of historical data may differ from those of the current RCT. To address this issue, one well-known approach is to employ propensity score matching or inverse probability weighting to adjust for baseline heterogeneity, enabling the incorporation of historical data into the inference of the RCT. However, this approach is subject to bias when there are unmeasured confounders. We address this issue by incorporating a self-adapting mixture (SAM) prior with propensity score matching and inverse probability weighting to enable additional adaptation for information borrowing in the presence of unmeasured confounders. The resulting propensity score-integrated SAM (PS-SAM) priors are doubly robust in the sense that if there are no unmeasured confounders, they result in an unbiased causal estimate of the treatment effect; and if there are unmeasured confounders, they provide a notably less biased treatment effect with better-controlled type I error. Simulation studies demonstrate that the PS-SAM prior exhibits desirable operating characteristics, with reasonably controlled type I error rates or substantial power gain, small bias, and low MSE, regardless of the presence of unmeasured confounders. 

Most clinical trials involve the comparison of a new treatment to a control arm (e.g., the standard of care) and the estimation of a treatment effect. External data, including historical clinical trial data and real-world observational data, are commonly available for the control arm. With proper statistical adjustments, borrowing information from external data can potentially reduce the mean squared errors of treatment effect estimates and increase the power of detecting a meaningful treatment effect. In this article, we propose to use Bayesian additive regression trees (BART) for incorporating external data into the analysis of clinical trials, with a specific goal of estimating the conditional or population average treatment effect. BART naturally adjusts for patient-level covariates and captures potentially heterogeneous treatment effects across different data sources, achieving flexible borrowing. Simulation studies demonstrate that BART maintains desirable and robust performance across a variety of scenarios and compares favorably to alternatives. We illustrate the proposed method with an acupuncture trial and a colorectal cancer trial. 

Historical data or real-world data are often available in clinical trials, genetics, health care, psychology, environmental health, engineering, economics, and business. The power priors have emerged as a useful class of informative priors for a variety of situations in which historical data are available. In this paper, an overview of the development of the power priors is provided. Various variations of the power priors are derived under a binomial regression model and a normal linear regression model. The development of software on the power priors is also briefly reviewed. Throughout this paper, the data from the Kociba study and the National Toxicology Program (NTP) study as well as the data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study are used to demonstrate the derivations of the power priors and their variations. Detailed analyses of the Kociba, NTP, and ADNI data are carried out to further demonstrate the usefulness of the power priors and their variations in these real applications. Finally, the directions of future research on the power priors are discussed.