Causal inference in sampling from finite populations

Abstract

Causal inference deals with estimating the effects of specific interventions on a response variable. The estimation strategy involves comparing units exposed to intervention factor’s levels, forming a treatment group, with those units not exposed, forming a control group. The control group serves as the base to estimate the counterfactual response of the treatment group. In observational studies, a major concern when building such groups is to ensure their comparability, controlling for characteristics others than the treatment itself, that may cause undesired interference on causal effects estimates, leading to systematic bias. Although the theory behind observational studies has advanced with methods to reduce such bias using conditional inference, in several of these studies data is obtained through complex probability sampling designs seldom taken into account in the estimation process. This thesis considers that, beyond representing a source of variability that must be incorporated in the analysis, sample design and estimation techniques can have a central role to estimate causal effects efficiently. Studies are carried out to investigate the use of balanced samples to ensure compa- rability between treatment and control groups with respect to the distributions of covariates, and the use of calibration estimates for the control group average response, improving es- timates of the average counterfactual treatment response. The methods are compared with those already available in the literature, via Monte Carlo simulation.