The power prior with multiple historical controls for the linear regression model.

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Modeling

Background:

• Historical control data can reduce clinical trial size but requires similarity to current data.
• Bayesian methods like meta-analytic-predictive (MAP) prior and modified power prior (MPP) are used to incorporate historical data dynamically.
• Existing methods may not fully address scenarios with multiple, heterogeneous historical control groups.

Purpose of the Study:

• To generalize the modified power prior (MPP) approach for incorporating multiple historical control groups within a linear regression framework.
• To evaluate the performance of the proposed MPP approach against the meta-analytic-predictive (MAP) prior, particularly in the presence of covariate-dependent exchangeability.
• To investigate the frequentist properties and practical utility of the generalized MPP method through simulations and real-world data analysis.

Main Methods:

• Developed two generalized MPP approaches for multiple historical controls in linear regression: one with independent powers and another with a hierarchical structure.
• Conducted simulation studies to assess type I error rates and statistical power compared to the MAP prior.
• Applied the methods to a real-life dataset to demonstrate practical application and performance.

Main Results:

• The generalized MPP approach demonstrated approximately nominal type I error rates and increased power compared to the MAP prior when between-study variation existed in slopes or covariate distributions, provided covariates were included.
• The MPP approach showed a slightly inflated type I error rate when intercepts varied, unlike the MAP prior.
• The proposed MPP method proved to be a robust competitor to the MAP approach for linear regression models with multiple historical controls.

Conclusions:

• The generalized modified power prior (MPP) approach is a valuable method for integrating multiple, potentially heterogeneous, historical control groups in linear regression.
• Including covariates in the model is crucial for the MPP approach to maintain appropriate type I error rates and enhance power.
• This generalized MPP method offers a flexible and effective alternative for Bayesian clinical trial design, potentially reducing study sizes and improving efficiency.