Propensity Score Methods For Causal Subgroup Analysis

Subgroup analyses are frequently conducted in comparative effectiveness research and randomized clinical trials to assess evidence of heterogeneous treatment effect across patient subpopulations. Though widely used in medical research, causal inference methods for conducting statistical analyses on a range of pre-specified subpopulations remain underdeveloped, particularly in observational studies. This dissertation develops and extends propensity score methods for causal subgroup analysis.

In Chapter 2, we develop a suite of analytical methods and visualization tools for causal subgroup analysis. First, we introduce the estimand of subgroup weighted average treatment effect and provide the corresponding propensity score weighting estimator. We show that balancing covariates within a subgroup bounds the bias of the estimator of subgroup causal effects. Second, we propose to use the overlap weighting method to achieve exact balance within subgroups. We further propose a method that combines overlap weighting and LASSO, to balance the bias-variance tradeoff in subgroup analysis. Finally, we design a new diagnostic plot---the Connect-S plot---for visualizing the subgroup covariate balance. Extensive simulation studies are presented to compare the proposed method with several existing methods. We apply the proposed methods to the observational COMPARE-UF study to evaluate the causal effects of Myomectomy versus Hysterectomy on the relief of symptoms and quality of life (a continuous outcome) in a number of pre-specified subgroups of patients with uterine fibroids.

In Chapter 3, we investigate the propensity score weighting method for causal subgroup analysis with time-to-event outcomes. We introduce two causal estimands, the subgroup marginal hazard ratio and subgroup restricted average causal effect, and provide corresponding propensity score weighting estimators. We analytically established that the bias of subgroup restricted average causal effect is determined by subgroup covariate balance. Using extensive simulations, we compare the performance of various combination of propensity score models (logistic regression, random forests, LASSO, and generalized boosted models) and weighting schemes (inverse probability weighting, and overlap weighting) for estimating the survival causal estimands. We find that the logistic model with subgroup-covariate interactions selected by LASSO consistently outperforms other propensity score models. Also, overlap weighting generally outperforms inverse probability weighting in terms of balance, bias and variance, and the advantage is particularly pronounced in small subgroups and/or in the presence of poor overlap. Again, we apply the methods to the COMPARE-UF study with a time-to-event outcome, the time to disease recurrence after receiving a procedure.

In Chapter 4, we extend propensity score weighting methodology for covariate adjustment to improve the precision and power of subgroup analyses in RCTs. We fit a logistic regression propensity model with pre-specified covariate-subgroup interactions. We show that by construction, overlap weighting exactly balances the covariates with interaction terms in each subgroup. Extensive simulations are performed to compare the operating characteristics of unadjusted estimator, different propensity score weighting estimators and the analysis of covariance estimator. We apply these methods to the HF-ACTION trial to evaluate the effect of exercise training on 6-minute walk test in several pre-specified subgroups.