Statistical methods for causal inference in observational studies.

Abstract

Estimating causal effects is essential in the evaluation of a treatment or intervention. It is particularly straightforward for well-designed experiments. However, when the treatment assignment is complicated by confounders, as in the case of observational studies, such inferences regarding the treatment effects, require more sophisticated adjustments. In this thesis, we investigated different matching techniques in terms of how well they balance the treatment groups on the covariates, as well as their efficiency in estimating treatment effects. We considered the various algorithm variants of these matching techniques, which include propensity score matching, Mahalanobis distance matching, and coarsened exact matching. Secondly, we proposed two new strategies for estimating treatment effects, namely, covariatebalancing rank-based Mahalanobis distance (CBRMD) and an improved version of CBRMD (iCBRMD).We evaluated their performance via simulations and some reallife datasets. Thirdly, we investigated a relatively new optimization-based alternative, known as entropy balancing, which has been used rarely in the applied biomedical literature. We shared our experiences learned from using entropy balancing in non-experimental studies, via Monte Carlo simulations and an empirical application. We further extended the evaluation of entropy balancing to some standard measures of causal treatment effects, namely; difference in means, odds ratios, rate ratios and hazard ratios. We pulled together our evaluations by conducting Monte Carlo simulations, evaluating both well-established methods and the more recently proposed methods. These adjustment techniques were evaluated under different scenarios that align with the practical reality. Finally, we utilized a dataset from a recently conducted HIV Incidence Provincial Surveillance System (HIPSS) study, to apply the considered techniques to a public health issue in South Africa.