Estimating equation approach for regression analysis of failure time data in the presence of interval-censoring

This article discusses statistical inference for the proportional hazards model when there exists interval-censoring on both survival time of interest and covariates (J. Roy. Statist. Soc. B 34 (1972) 187; Encyclopedia of Biostatistics. Wiley, New York, 1998, pp. 2090-2095). In particular, we consider situations where observations on the survival time are doubly censored and observations on covariates are interval-censored. For inference about regression parameters, a general estimating equation approach is proposed. The proposed estimate of the parameter is a generalization of the maximum partial-likelihood estimate for right-censored failure time data with known or exactly observed covariates (The Statistical Analysis of Failure Time Data. Wiley, New York, 1980). The asymptotic properties of the proposed estimate are established and its finite sample properties are investigated through a simulation study.