19 January 2023: Ilina Yozova

Speaker. Ilina Yozova (supervisors: Professor Ioanna Manolopoulou and Dr François-Xavier Briol).
Title. Bayesian Causal Forests Combining Randomised And Observational Data For Heterogeneous Treatment Effects Estimation
Abstract. Bayesian Causal Forests (BCFs) are designed to estimate heterogeneous treatment effects using observational data by teasing apart the model into 3 distinct pieces: prognostic effect - the influence of the covariates; treatment effect - the influence of the treatment; and propensity score, which captures the treatment assignment mechanism. However, when using data from different sources, the treatment assignment mechanism might differ greatly between each dataset. Additionally, the prognostic and/or treatment effects, as well as the sets of covariates, may also differ. A well-known example arises when combining randomised control trials (RCTs) and observational studies which can improve many aspects of causal inference, from increased statistical power to better external validity. Therefore, we extend the BCF model by introducing additional terms in the prognostic and treatment effects, which can absorb differences between two data sources, as well as capture some potential unobserved confounding of the observational data. Additionally, our model introduces a weighting parameter, allowing for adjustment of the influence of observational data points. During the model fitting process, the contribution of observational data to the posterior distribution is raised to a power following a semi-modular inference approach. The flexibility of the power is valuable because it allows us to prevent RCT data from being swamped by the larger possibly confounded observational dataset. We implement our methods on a number of simulated and real data examples.