Topics and Applications of Weighting Methods in Case-Control and Observational Studies

Weighting methods have been widely used in statistics and related applications. For example, the inverse probability weighting is a standard approach to correct for survey non-response. The case-control design, frequently seen in epidemiologic or genetic studies, can be regarded as a special type of survey design; analogous inverse probability weighting approaches have been explored when the interest is the association between exposures and the disease (primary analysis) as well as when the interest is the association among exposures (secondary analysis). Meanwhile, in observational comparative effectiveness research, inverse probability weighting has been suggested as a valid approach to correct for confounding bias. This dissertation develops and extends weighting methods for case-control and observational studies.

The first part of this dissertation extends the inverse probability weighting approach for secondary analysis of case-control data. We revisit an inverse probability weighting estimator to offer new insights and extensions. Specifically, we construct its more general form by generalized least squares (GLS). Such a construction allows us to connect the GLS estimator with the generalized method of moments and motivates a new specification test designed to assess the adequacy of the inverse probability weights. The specification test statistic measures the weighted discrepancy between the case and control subsample estimators, and asymptotically follows a Chi-squared distribution under correct model specification. We illustrate the GLS estimator and specification test using a case-control sample of peripheral arterial disease, and use simulations to shed light on the operating characteristics of the specification test. The second part develops a robust difference-in-differences (DID) estimator for estimating causal effect with observational before-after data. Within the DID framework, two common estimation strategies are outcome regression and propensity score weighting. Motivated by a real application in traffic safety research, we propose a new double-robust DID estimator that hybridizes outcome regression and propensity score weighting. We show that the proposed estimator possesses the desirable large-sample robustness property, namely the consistency only requires either one of the outcome model or the propensity score model to be correctly specified. We illustrate the new estimator to study the causal effect of rumble strips in reducing vehicle crashes, and conduct a simulation study to examine its finite-sample performance. The third part discusses a unified framework, the balancing weights, for estimating causal effects in observational studies with multiple treatments. These weights incorporate the generalized propensity scores to balance the weighted covariate distribution of each treatment group, all weighted toward a common pre-specified target population. Within this framework, we further develop the generalized overlap weights, constructed as the product of the inverse probability weights and the harmonic mean of the generalized propensity scores. The generalized overlap weights corresponds to the target population with the most overlap in covariates between treatments, similar to the population in equipoise in clinical trials. We show that the generalized overlap weights minimize the total asymptotic variance of the nonparametric estimators for the pairwise contrasts within the class of balancing weights. We apply the new weighting method to study the racial disparities in medical expenditure and further examine its operating characteristics by simulations.