A Weighted Covariate Balancing Method of Estimating Causal Effects in Case-Control Studies

Propensity score methods have dominated the estimation of treatment effects based on observational data and particularly in the health and medical sciences. We propose a weighting method based on rank-based Mahalanobis distance, namely the covariate balancing rank-based Mahalanobis distance method, to estimate causal effects for observational data. Using Monte Carlo simulations, under different data structures and type of outcome variables, the proposed method is shown to have better performance, in terms of bias reduction and treatment effect estimation. Specifically, under the generalized linear model framework, we simulated datasets based on the Lalonde-PSID study, for linear link function; while datasets were simulated based on the Lindner study, for non-linear link functions. We further apply the proposed method to data extracted from the Nigeria Demographic Health Survey (2013), to investigate the effect of educational exposure on ideal family size among married couples in Nigeria. The proposed method is a viable alternative method that can improve covariates balance, bias reduction, and efficient estimation of treatment effects.