Proximal Survival Analysis for Dependent Left Truncation

Music City Center 

In prevalent cohort studies with delayed entry, the time-to-event outcome is subject to left truncation when only subjects that have not experienced the event at study entry are included. This leads to selection bias, as subjects with early event times tend not to be captured. Conventional methods for handling left truncation usually rely on the random left truncation or the slightly weaker quasi-independence assumption that requires the left truncation time and the event time are independent on the observed region. This assumption can be further relaxed to conditional (quasi-)independent left truncation which assumes that the dependence-inducing covariates are measured. However, in practice, the conditional independent left truncation assumption may fail, and measured covariates may only serve as imperfect proxies for explaining the underlying mechanism that induces the dependence between the left truncation time and the event time. In this work, we propose a proximal weighting identification framework which admits that the measured covariates may only be imperfect proxies for capturing the dependence between the left truncation time and the event time. We then construct estimators based on the framework and study their asymptotic properties. We examine the finite sample performance of the proposed estimators by comprehensive simulations. We apply the proposed method to analyze cognitive impairment-free survival using data from the Honolulu Asia Aging Study.

selection bias

left truncation