In observational studies with delayed entry, time-to-event outcomes are usually subject to left truncation where only subjects who haven't experienced the event at study entry are included, leading to selection bias. Conventional methods for handling left truncation tend to rely on the random left truncation or quasi-independence assumption. This assumption can be relaxed to conditional quasi-independence in regression settings when the dependence-inducing covariates are included as regressors. For estimating marginal estimands under covariate dependent left truncation, inverse probability weighting (IPW) approaches have recently been developed. This dissertation focuses on developing statistical approaches for handling dependent left truncation, where the dependence between the left truncation time and the event time is possibly induced by measured or unmeasured covariates.
Chapters 1 and 2 considers the scenario where the dependence between the left truncation time and the event time is induced by measured covariates, a setting referred to as covariate dependent left truncation. In Chapter 1, we derive the efficient influence curve (EIC) for the expectation of an arbitrarily transformed event time under covariate dependent left truncation, and we develop EIC-based estimators that enjoy model double robustness and rate double robustness. Chapter 2 extends the framework in Chapter 1 to the setting with covariate dependent left truncation and right censoring (LTRC). We propose a general framework for constructing Neyman orthogonal and doubly robust estimating functions and loss functions under LTRC, which can be applied to a wide range of estimation problems. We illustrate its use through two concrete examples: estimating the average treatment effect (ATE) and the conditional average treatment effect (CATE).
Chapter 3 considers the scenario with potentially unmeasured covariates that induce the dependence between the left truncation time and the event time. We propose a proximal weighting framework which admits measured covariates may only serve as imperfect proxies for explaining the underlying truncation-event time dependence.
