Methodological Advances in Causal Inference for Functional Data and Survival Data
Open AccessIdentifying causal effects of certain policies has been increasingly studied in the filed of economics, epidemiology and sociology among others. Such effects are often estimated as the average treatment effect for a binary treatment design and more general treatment designs. Although randomized experiments are the gold standard for estimating causal effects, methods that mimic randomized experiments for observational data have been thoroughly studied during the past decades. However, some causal inference problems remain unsolved and new methods are still needed to identify causal effects in more complex settings. In this regard, we study two topics of causal inference in observational studies in this dissertation: (1) covariate balancing functional propensity score methods for functional treatments, and (2) RKHS-based covariate balancing for survival causal effect estimation.Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The effect of a functional variable on an outcome is an essential theme in functional data analysis, but a majorityof related studies are restricted to correlational effects rather than causal effects. The first chapter makes the first attempt to study the causal effect of a functional variable as a treatment in cross-sectional observational studies. Despite the lack of a probability density function for the functional treatment, the propensity score is properly defined in terms of a multivariate substitute. Two covariate balancing methods are proposed to estimate the propensity score, which minimize the correlation between the treatment and covariates. The appealing performance of the proposed method in both covariate balance and causal effect estimation is demonstrated by a simulation study. The proposed method is applied to study the causal effect of body shape on human visceral adipose tissue.Survival causal effect estimation based on right-censored data is of key interest in both survival analysis and causal inference. Propensity score weighting is one of the most popular methods in the literature. However, since it involves the inverse of propensity score estimates, its practical performance may be very unstable, especially when the covariate overlap is limited between treatment and control groups. To address this problem, a covariate balancing method is developed in the second chapter to estimate the counterfactual survival function. The proposed method is nonparametric and balances covariates in a reproducing kernel Hilbert space (RKHS). The uniform rate of convergence for the proposed estimator is shown to be the same as that for the classical Kaplan-Meier estimator. The appealing practical performance of the proposed method is demonstrated by a simulation study as well as two real data applications to study the causal effect of smoking on survival time of stroke patients and that of race on reinfection time for patients with sexually transmitted diseasesrespectively.
- All rights reserved
Notice to Authors
If you are the author of this work and you have any questions about the information on this page, please use the Contact form to get in touch with us.