New approaches to propensity score-integrated mahalanobis matching methods

In observational studies where randomisation is not feasible, one commonly used method to reduce the effect of confounding variables for unbiased estimation of treatment effects is propensity score (PS) matching. For high-quality matching, it is important to be able to create the closest possible matches in terms of relevant covariates. In addition to the absolute PS difference, the Mahalanobis distance is also an alternative for best matching. However, instead of using only PS or only Mahalanobis distance, matching with the PS-integrated Mahalanobis distance is better for estimating the treatment effect. In this regard, performance differences between the matching methods used and uncertainties in caliper selection are fundamental issues. The primary objective of this thesis is to compare three methods proposed in the literature (absolute difference-based PS matching, Mahalanobis matching, Mahalanobis matching with PS integration) with three new approaches proposed in this thesis (MAHweightedPS, MAHlogPS, and MAHlogitPS) under different simulation scenarios. The secondary objective is to evaluate non-standard and different caliper approaches used in the literature to eliminate uncertainty in caliper selection in PS matching. The comparison of methods was conducted under simulation scenarios created considering sample size (n=250, 500, 1000, 2000), matching strategy (replacement, replacement without treatment order from largest to smallest, replacement without random treatment order), and varying caliper values. Simulation results revealed that the MAHlogPS and MAHlogitPS methods demonstrated superior performance compared to other methods in most scenarios. Consequently, it is recommended that these methods be preferred in matching methods due to their reduced error rates and ease of use.