Two likelihood-based semiparametric estimation methods for panel count data with covariates

• 成果类型: Article
• 署名作者: Wellner, Jon A.; Zhang, Ying
• 署名单位: University of Washington; University of Washington Seattle; University of Iowa
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000181
• 发表日期: 2007
• 页码: 2106-2142
• 关键词: recurrent events; regression-analysis; tests; MODEL

摘要

We consider estimation in a particular semiparametric regression model for the mean of a counting process with panel count data. The basic model assumption is that the conditional mean function of the counting process is of the form E{N(t)vertical bar Z} = exp(beta(T)(0)Z)Lambda(0)(t) where Z is a vector of covariates and Lambda(0) is the baseline mean function. The panel count observation scheme involves observation of the counting process N for an individual at a random number K of random time points; both the number and the locations of these time points may differ across individuals. We study semiparametric maximum pseudo-likelihood and maximum likelihood estimators of the unknown parameters (beta(0), Lambda(0)) derived on the basis of a nonhomogeneous Poisson process assumption. The pseudo-likelihood estimator is fairly easy to compute, while the maximum likelihood estimator poses more challenges from the computational perspective. We study asymptotic properties of both estimators assuming that the proportional mean model holds, but dropping the Poisson process assumption used to derive the estimators. In particular we establish asymptotic normality for the estimators of the regression parameter beta(0) under appropriate hypotheses. The results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process.