Analyzing Survival Data Without Prospective Follow-Up

This article develops new approaches to estimate survival parameters based on two types of survival data without collecting survival times. The first one consists of incident and prevalent covariates and the other is a prevalent cohort sample with only covariates and truncation time. Our research aims to identify the effects of covariates on a failure time through more general single-index survival regression models. Under the assumption of covariate-independent truncation, the density ratio of incident and prevalent covariates and the hazard function of an observed truncation time are shown to be monotonic functions of the single-index in the proposed survival regression models. In light of these features, the rank correlation estimation technique can be naturally applied to estimate the index coefficients. Thus, existing theoretical frameworks can be used to establish the consistency and asymptotic normality of the proposed maximum rank correlation estimators. We further conduct a series of simulations to investigate the finite-sample performance of the estimators. In addition, our methodological ideas are illustrated by data from the National Comorbidity Survey Replicate.