Analysing panel count data with informative observation times
1 Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland 20892, U.S.A. huangchi{at}niaid.nih.gov, 2 Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, Maryland 21205, U.S.A. ncwang{at}jhsph.edu, 3 Department of Biostatistics, University of Iowa, Iowa City, Iowa 52242, U.S.A. ying-j-zhang{at}uiowa.edu
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Abstract |
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In this paper, we study panel count data with informative observation times. We assume nonparametric and semiparametric proportional rate models for the underlying event process, where the form of the baseline rate function is left unspecified and a subject-specific frailty variable inflates or deflates the rate function multiplicatively. The proposed models allow the event processes and observation times to be correlated through their connections with the unobserved frailty; moreover, the distributions of both the frailty variable and observation times are considered as nuisance parameters. The baseline rate function and the regression parameters are estimated by maximising a conditional likelihood function of observed event counts and solving estimation equations. Large-sample properties of the proposed estimators are studied. Numerical studies demonstrate that the proposed estimation procedures perform well for moderate sample sizes. An application to a bladder tumour study is presented.
Key Words: Dependent censoring; Frailty; Poisson process; Rate function; Serial events.
Received February 2005. Revised April 2006.