Variable selection and causal treatment effect estimation based on interval-censored failure time data

[EMBARGOED UNTIL 6/1/2023] Variable selection has been discussed under many contexts and especially a great deal of literature has been established in the failure time context with constant coefficients. However, the time-varying effect sometimes could show more insight of how the influence changing through time. For example, the treatment effect may vanish because of mutation of virus. In addition, to identify important variables or covariates, a desired feature of a variable selection method is to distinguish time-varying coefficients from time-independent ones, which also presents an additional challenge. Nevertheless, only limited research exists on the variable selection for time-varying effect. Existing methods focused on right-censored data or generalized linear model. In Chapter 2 and Chapter 3, we discuss simultaneous parameter estimation and variable selection for interval censored data with time-varying effects, which can simultaneously select between time-dependent and time-independent covariate effects. To implement the proposed procedure, an EM algorithm is developed, and a simulation study is conducted and suggests that the proposed method works well in practical situations. What's more, the augmented Lagrangian method is used in implementation [Bertsekas, 1996] to deal with the compositional covariates in microbiome data. Finally, its usefulness is illustrated by the real data that motivated these studies. Another focus of this dissertation is the treatment effect estimation. In the presence of censoring, standard methods of summarizing the treatment effect estimates, Kaplan-Meier curves (survival function), the logrank test, etc., are not proper in observational studies as they all based on randomized experimental designs. For causal inference on survival outcomes, the commonly used causal estimands are: restricted average survival time, survival probability, survival quantile, and the marginal hazard ratio. But for the commonly used marginal hazard ratio in survival data analysis, it does not fit into Rubin's causal model framework because the observed baseline covariate balance is not guaranteed after the first failure happened in the sample. The susceptible subjects tend to experience failure events earlier, which will introduce selection bias problem to the analysis. For this reason, our target estimand is restricted average survival time, which is the difference between restricted mean survival time (RMST) defined on the potential survival time in treated and control groups. In Chapter 4, we propose a method for causal inference on interval-censored data in observational studies utilizing the pseudo observation approach. The pseudo observation for the interval-censored data is based on two methods. One is jack-knife method where the pseudo restricted mean survival time is calculated with the method proposed in Zhang et al. [2020]. Another approach uses the fast approximation of the jack-knife pseudo observations proposed by Bouaziz [2021]. With the calculated pseudo-observations, we propose to use IPW method to adjust the confounding effect arose in observation studies, where it tends to have different distributions of treatment assignment in treated and control group.