Propensity score stratified MAP prior and posterior inference for incorporating information across multiple potentially heterogeneous data sources.

Incorporation of external information is becoming increasingly common when designing clinical trials. Availability of multiple sources of information has inspired the development of methodologies that account for potential heterogeneity not only between the prospective trial and the pooled external data sources but also between the different external data sources themselves. Our approach proposes an intuitive way of handling such a scenario for the continuous outcomes setting by using propensity score-based stratification and then utilizing robust meta-analytic predictive priors for each stratum to incorporate the prior data to distinguish among different external data sources in each stratum. Through extensive simulations, our approach proves to be more efficient and less biased than the currently available methods. A real case study using clinical trials that study schizophrenia from multiple different sources is also included.

Addressing positivity violations in causal effect estimation using Gaussian process priors.

In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for every covariate combination, it should be possible to observe both treated and control subjects the covariate distributions should overlap between treatment arms. If the positivity assumption is violated, population-level causal inference necessarily involves some extrapolation. Ideally, a greater amount of uncertainty about the causal effect estimate should be reflected in such situations. With that goal in mind, we construct a Gaussian process model for estimating treatment effects in the presence of practical violations of positivity. Advantages of our method include minimal distributional assumptions, a cohesive model for estimating treatment effects, and more uncertainty associated with areas in the covariate space where there is less overlap. We assess the performance of our approach with respect to bias and efficiency using simulation studies. The method is then applied to a study of critically ill female patients to examine the effect of undergoing right heart catheterization.