Linear Regression with Current Status Data

Abstract

In survival analysis, a linear model often provides an adequate approximation after a suitable transformation of the survival times and possibly of the covariates. This article proposes a semiparametric regression method for estimating the regression parameter in the linear model without specifying the distribution of the random error, where the response variable is subject to so-called case 1 interval censoring. The method uses a constructed random-sieve likelihood and constraints, combining the benefits of semiparametric likelihood with estimating equations. The estimation procedure is implemented, and the asymptotic distributions for the estimated regression parameter and for the profile likelihood ratio statistic are obtained. In addition, some model diagnostics aspects are described. Finally, the small-sample operating characteristics of the proposed method is examined via simulations, and its usefulness is illustrated on datasets from an animal tumorigenicity study and from a HIV study.

Key Words:

• Chi-squared approximation
• Current status data
• Normal approximation
• Profile
• Random sieve likelihood
• Regression
• Semiparametric model