Novel Statistical Methods for Causal Inference Based on Truncated and Censored Time-to-Event Data

Abstract

In this dissertation, we discuss two settings in which association parameters based on traditional models can be challenging to interpret causally, even when exposure level is randomized. The first setting pertains to human autopsy studies, in which a time-varying outcome is only measured at death. When the exposure affects survival, the distribution of outcome measurement times differs across exposure levels, and can produce misleading comparisons. We propose to study the causal effect of the exposure on the outcome process using a contrast inspired by the mediation literature and that we refer to as the natural-time direct effect. As a first step, we derive nonparametric debiased machine learning approaches for inference on survival integrals using left-truncated right-censored data. We then use these methods to assess the effect of the APOE-4 gene on autopsy measures of Braak staging using data from the Adult Changes in Thought study. In the second setting, a point-exposure of varying doses occurs at a random time, and we wish to characterize the (possibly exposure time-specific) effect of dose on survival. In this context, standard survival models are often not amenable to interpretably addressing the scientific question at hand. As an alternative, we propose to use an accelerated residual failure time model. We develop methods for inference on model parameters indexing a parametric accelerated residual failure time model using left-truncated right-censored data, and provide a causal interpretation under natural causal conditions. Using data from the Life Span Study, a long-term prospective cohort study of survivors of the atomic bombings of Hiroshima and Nagasaki, we use these methods to study how a point-exposure to radiation of differing doses affects survival.