Semi-parametric modelling and likelihood estimation with estimating equations
This paper proposes a semi-parametric modelling and estimating method for analysing censored survival data. The proposed method 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. The 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 & Zeger, 1986). This paper shows the existence and uniqueness of the proposed semi-parametric maximum likelihood estimates (SMLE) with estimating equations. 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.
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