Comparison of causal inference methods for observational data with a hierarchical structure

Randomised controlled trials (RCTs) are the gold standard for estimating causal treatment effects. When RCTs are not feasible or ethical, causal questions can be answered through observational data. However, analyses of observational data are prone to confounding bias and adequate statistical methods (under explicit assumptions) are needed for addressing it. Causal inference methods have been proposed to estimate treatment effects when covariates, treatment and outcome are defined at the same unit level (single-level setting). These can be broadly classified into those focusing on the outcome mechanism (e.g., g-computation), those modelling the treatment assignment (e.g., propensity scores) and those combining both (doubly robust methods). In practice, research questions could be about a system-level characteristic (e.g., general versus specialized hospital) or a patient-level characteristic (e.g., type of surgery), while patients are nested within hospital, geographic region, etc. Only few studies have extended causal techniques to hierarchical data, but they were not empirically evaluated for binary outcomes. In this thesis, we began with a review of three different causal methods, namely, g-computation, inverse probability-of-treatment weighting (IPTW) and augmented inverse probability-of-treatment weighting. We next extended them to hierarchical settings and evaluated their performance under different scenarios of unmeasured cluster-level confounding via Monte Carlo simulations, for the estimation of the population averaged treatment effect with treatment assigned at the individual level. We then derived unified formulas for IPTW variance estimators when targeting different populations like the treated or the overlap population, first starting within the single-level setting. These approximate closed formulas will form the basis of analytical extensions to the hierarchical setting, as an alternative to the bootstrap. To conclude, although common practice, ignoring clustering in causal analysis of observational studies can lead to incorrect inferences, so we extended tools to this setting and provided practical recommendations to applied researchers.