Semi-parametric Modeling and Likelihood Estimation with Estimating Equations

Abstract

For analyzing censored survival data, this presentation proposes a semi- parametric modeling and estimating method. The method proposed uses the empirical likelihood function to describe the information in data and formulates estimating equations to incorporate knowledge of the underlying distribution and regression structure. Our method is more flexible than the traditional methods such as the parametric maximum likelihood estimation (MLE), Cox's (1972) proportional hazards model, accelerated life test model, quasi- likelihood (Wedderburn (1974)) and generalized estimating equations (Liang and Zeger (1986)). This presentation shows the existence and uniqueness of the proposed semi-parametric maximum likelihood estimates (SMLE) with estimating equations. Considering the group-censored data, this presentation sketches derivations of the asymptotic distribution of the SMLE. The method is validated with known cases studied in the literature. Several finite sample simulation and large sample efficiency studies indicate that when the sample size is larger than 100, the SMLE is compatible with the parametric MLE; and in all case studies, the SMLE is about 15% better than the parametric MLE with a mis- specified underlying distribution.