Proximal Survival Analysis for Dependent Left Truncation

In prevalent cohort studies with delayed entry, time-to-event outcomes are often subject to left truncation where only subjects that have not experienced the event at study entry are included, leading to selection bias. Existing methods for handling left truncation mostly rely on the (quasi-)independence assumption or the weaker conditional (quasi-)independence assumption which assumes that conditional on observed covariates, the left truncation time and the event time are independent on the observed region. In practice, however, our analysis of the Honolulu Asia Aging Study (HAAS) suggests that the conditional quasi-independence assumption may fail because measured covariates often serve only as imperfect proxies for the underlying mechanisms, such as latent health status, that induce dependence between truncation and event times. To address this gap, we propose a proximal weighting identification framework that admits the dependence-inducing factors may not be fully observed. We then construct an estimator based on the framework and study its asymptotic properties. We examine the finite sample performance of the proposed estimator by comprehensive simulations, and apply it to analyzing the cognitive impairment-free survival probabilities using data from the Honolulu Asia Aging Study.