Transformation model estimation of survival under dependent truncation and independent censoring

Truncation is a mechanism that permits observation of selected subjects from a source population; subjects are excluded if their event times are not contained within subject-specific intervals. Standard survival analysis methods for estimation of the distribution of the event time require quasi-independence of failure and truncation. When quasi-independence does not hold, alternative estimation procedures are required; currently, there is a copula model approach that makes strong modeling assumptions, and a transformation model approach that does not allow for right censoring. We extend the transformation model approach to accommodate right censoring. We propose a regression diagnostic for assessment of model fit. We evaluate the proposed transformation model in simulations and apply it to the National Alzheimer's Coordinating Centers autopsy cohort study, and an AIDS incubation study. Our methods are publicly available in an R package, tranSurv.