Simulation Studies of the Nonparametric Maximum Likelihood Estimate in the Cox-Gene Model with a Fast Algorithm

by I-Shou Chang, Chao A. Hsiung, Chi-Chung Wen, Yuh-Jenn Wu, and Che-Chi Yang.

Abstract: The Cox model with the major gene effects for age of onset was introduced and studied by Li et al. (1998), and Li and Thompson (1997). This paper concerns the numerical performance of the nonparametric maximum likelihood estimate of the environmental effects and the genetic effects in this model. Based on the self-cosistency equations derived from the score functions, we propose a fast iterative algorithm for the computations of the nonparametric maximum likelihood estimate and its asymptotic variance. Simulation studies conducted using these algorithms indicate that the profile likelihood based normal approximations for the estimates are valid with reasonable sample sizes, and the bootstrap methods work well for smaller sample sizes and are computationally feasible.

Key Words: Age of Onset, Bootstrap, Frailty, Major Gene effect, Profile likelihood

Authors:
I-Shou Chang, ischang@nhri.org.tw
Chao A. Hsiung, hsiung@nhri.org.tw
Chi-Chung Wen, wenqz@nhri.org.tw
Yuh-Jenn Wu, yuhjenn@nhri.org.tw
Che-Chi Yang, yangzq@math.ncu.edu.tw

Editor: Chris Amos,camos@request.mdacc.tmc.edu

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