A bayesian view on causal inference for observational data

Abstract

Using the Bayesian paradigm to infer causal effects for observational data is a challenging task. Typically, the Bayesian paradigm follows combining the data and prior information to infer quantities of interest based on a single joint posterior distribution. However, when the goal is to infer causal effects in observational studies, a joint Bayesian specification may lead to a biased inference (e.g. propensity score methods). In this thesis, we aim at providing a Bayesian view on methods at which the model specification leads to inference based on a joint likelihood and discuss issues related to a coherent Bayesian approach. Firstly, we focus on using the propensity score to avoid bias due to confounding into a regression approach. Confounding arises when covariates affect exposure and outcome variables simultaneously. In such a situation, a joint Bayesian specification is well known to induce bias due to feedback of the outcome into the propensity score model. Presuming there is no unmeasured confounder, we start from the Bayesian first principles and provide a fully Bayesian specification wherein the feedback is not present. Additionally, we also provide an alternative to estimate populational-level estimands. We extend these ideas to the scenario of multilevel structured observations and discuss using a multilevel approach to deal with unmeasured confounders. The motivation to the latter is the discussion about the causal effect of the driven observed therapy in the cure of Tuberculosis. Finally, we also propose an alternative to estimate the effect of an intervention at a specific point in time in the presence of a mediator variable. Our proposal involves modelling mediator and outcome models separately by accounting for temporal evolution. We apply our proposed method to hospitalisation data due to respiratory diseases, with the coronavirus pandemic representing an intervention at a specific point in time.