Semi-parametric Bayesian regression for subgroup analysis in clinical trials

Determining whether there are differential treatment effects in subgroups of trial participants remains an important topic in clinical trials as precision medicine becomes ever more relevant. Any assessment of differential treatment effect is predicated on being able to estimate the treatment response accurately while satisfying constraints of balancing the risk of overlooking an important subgroup with the potential to make a decision based on a false discovery. While regression models, such as marginal interaction model, have been widely used to improve accuracy of subgroup parameter estimates by leveraging the relationship between treatment and covariate, there is still a possibility that it can lead to excessively conservative or anti-conservative results. Conceivably, this can be due to the use of the normal distribution as a default prior, which forces outlying subjects to have their means over-shrunk towards the population mean, and the data from such subjects may be excessively influential in estimation of both the overall mean response and the mean response for each subgroup, or a model mis-specification. To address this issue, we investigate the use of nonparametric Bayes, particularly Dirichlet process priors, to create semi-parametric models. These models represent uncertainty in the prior distribution for the overall response while accommodating heterogeneity among individual subgroups. They also account for the effect and variation due to the unaccounted terms. As a result, the models do not force estimates to excessively shrink but still retain the attractiveness of improved precision given by the narrower credible intervals. This is illustrated in extensive simulations investigating bias, mean squared error, coverage probability and credible interval widths. We applied the method on a simulated data based closely on the results of a cystic fibrosis Phase 2 trial.