On the Convergence of Observed Partial Likelihood under Incomplete Data with Two Class Possibilities

Tomoyuki Sugimoto

Department of Mathematical Sciences, Hirosaki University, Hirosaki, Japan.

DOI: 10.4236/ojs.2014.42012                

Abstract

In this paper, we discuss the theoretical validity of the observed partial likelihood (OPL) constructed in a Coxtype model under incomplete data with two class possibilities, such as missing binary covariates, a cure-mixture model or doubly censored data. A main result is establishing the asymptotic convergence of the OPL. To reach this result, as it is difficult to apply some standard tools in the survival analysis, we develop tools for weak convergence based on partial-sum processes. The result of the asymptotic convergence shown here indicates that a suitable order of the number of Monte Carlo trials is less than the square of the sample size. In addition, using numerical examples, we investigate how the asymptotic properties discussed here behave in a finite sample.

Keywords

Cox’s Regression Model; Logistic Regression Model; Incomplete Binary Data; Partial Likelihood; Partial-Sum Processes; Profile Likelihood

Conflicts of Interest

The authors declare no conflicts of interest.

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