Robust Methods for Causal Inference Using Penalized Splines

Abstract

Observational studies are important for evaluating treatment effects, especially when randomization of treatments is unethical or expensive. Without randomization, valid inferences about treatment effects can only be drawn by controlling for confounders. Propensity scores (PS) -- the probability of treatment assignment as a function of covariates -- are often used to control for confounders. PS-based methods are vulnerable to bias and inefficiency when outcome or propensity score models are misspecified or there is limited overlap in the propensity score distributions between treatment groups. In this dissertation, we develop new robust methods for estimating causal effects from observational studies and address two closely related topics on causal inference -- the problem of limited overlap and variable selection for propensity score model. In Chapter 2, we propose a robust multiple imputation based approach to causal inference called Penalized Spline of Propensity Methods for Treatment Comparison (PENCOMP). PENCOMP estimates causal effects by imputing missing potential outcomes with flexible spline models, and draws inference based on imputed and observed outcomes. Under the standard causal inference assumptions, PENCOMP is doubly robust, that is, yields consistent estimates of causal effects if either the propensity or the outcome model is correctly specified. Simulations suggest that it tends to outperform doubly-robust marginal structural modeling, especially when the weights are highly variable. We apply our method to the Multicenter AIDS Cohort study (MACS) to estimate the short term effect of antiretroviral treatment on CD4 counts in HIV+ patients. In Chapter 3, we address the issue of limited overlap in the propensity score distributions across treatment groups. We investigate appropriate restrictions of the causal estimand, and compare alternative estimation methods, including various simple and augmented inverse propensity weighting approaches, matching and PENCOMP. We demonstrate the flexibility of PENCOMP for estimating different estimands. We apply these methods to the MACS dataset to estimate the effects of antiretroviral treatment on CD4 counts in HIV+ patients. In Chapter 4, we consider variable selection techniques that seek to restrict predictors in the propensity model to true confounders, thus improving overlap in the propensity distributions and increasing efficiency. We also propose a new version of PENCOMP via bagging that incorporates the variability of model selection, which can be advantageous when the data are noisy. We examine by simulation studies the impact of various variable selection techniques, including an extension of the adaptive lasso, on inferences from PENCOMP and weighting approaches. We demonstrate our methods and variable selection techniques using the MACS dataset.