In biostatistics applications interest often focuses on the estimation of the distribution of a time-variable T. If one only observes whether or not T exceeds an observed monitoring time C, then the data structure is called current status data, also known as interval censored data, case I. We consider this data structure extended to allow the presence of both time-independent covariates and time-dependent covariate processes that are observed until the monitoring time. We assume that the monitoring process satisfies coarsening at random.
Our goal is to estimate the regression parameter beta of the regression model T = Z*beta+epsilon where the conditional density of the error epsilon given Z is assumed to have location parameter equal to zero. Because of the curse of dimensionality no globally-efficient nonparametric estimator with good practical performance at moderate sample sizes exists. We present an estimator of the parameter beta that attains the semiparametric efficiency bound if we correctly specify (a) a model for the monitoring mechanism and (b) a lower dimensional model for the conditional distribution of T given the covariates. In addition, our estimator is robust to model misspecification. If only (a) is correctly specified, the estimator remains consistent and asymptotically normal. We conclude with a simulation experiment and a data analysis.
Statistical Methodology | Statistical Models | Statistical Theory | Survival Analysis
Andrews, Chris; van der Laan, Mark J.; and Robins, James M., "Locally Efficient Estimation of Regression Parameters Using Current Status Data" (September 2002). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 111.