Sequential estimation for the proportional hazards model in the presence of nuisance parameters

Jinsoo Hwang, Purdue University

Abstract

We study the asymptotic behavior of the maximum partial likelihood estimator in the Cox proportional hazards model in the presence of nuisance parameters when entry of patients is staggered. When entry of patients is simultaneous and there is only one regression parameter in the Cox model, the efficient score process of the partial likelihood is a martingale and converges weakly to a time-changed Brownian motion. Our problem is to get a similar result in the presence of nuisance parameters when entry of patients is staggered. Let $\beta$ = ($\theta,\phi\sb1,\...,\phi\sb{p-1})\sp\prime$ be the parameter vector in the Cox model. Let $\theta$ be our parameter of interest and $\phi\sb1,\...,\phi\sb{p-1}$ be nuisance parameters. We show that the properly normalized maximum partial likelihood estimator process $\\theta(t)$ behaves like a standard Brownian motion when entry of patients is staggered, under suitable assumptions.

Degree

Ph.D.

Advisors

Sellke, Purdue University.

Subject Area

Statistics

COinS