Analysis of restricted mean survival time for length-biased data

In clinical studies with time-to-event outcomes, the restricted mean survival time (RMST) has attracted substantial attention as a summary measurement for its straightforward clinical interpretation. When the data are subject to length-biased sampling, which is frequently encountered in observational cohort studies, existing methods to estimate the RMST are not applicable. In this article, we consider nonparametric and semiparametric regression methods to estimate the RMST under the setting of length-biased sampling. To assess the covariate effects on the RMST, a semiparametric regression model that directly relates the covariates and the RMST is assumed. Based on the model, we develop unbiased estimating equations to obtain consistent estimators of covariate effects by properly adjusting for informative censoring and length bias. Stochastic process theories are used to establish the asymptotic properties of the proposed estimators. We investigate the finite sample performance through simulations and illustrate the methods by analyzing a prevalent cohort study of dementia in Canada.