Semiparametric failure time regression with replicates of mismeasured covariates

This article proposes a general strategy for the regression analysis of univariate and multivariate failure time data when a subset of covariates cannot be measured precisely but replicate measurements of their surrogates are available. Multivariate failure time data include recurrent events and clustered Survival data. The number of replicate measurements can vary from subject to subject and can even depend on the failure time. No parametric assumption is imposed on the error or on any other random variable. Several semiparametric regression models are considered, including the Cox proportional hazards model for univariate failure time data, multiplicative intensity/rate models for recurrent events data, and marginal Cox proportional hazards models for general multivariate failure time data. The existing estimating functions in the absence of measurement error are corrected to yield consistent and asymptotically normal estimators of the regression parameters. The estimation of the underlying failure time distribution is also studied. The operating characteristics of the proposed estimators are assessed through extensive simulation studies. An application to multiple tumor recurrences from a cancer prevention trial is provided.