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Biometrika Advance Access originally published online on September 30, 2009
Biometrika 2009 96(4):861-872; doi:10.1093/biomet/asp046
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© 2009 Biometrika Trust

Article

Nonparametric estimation of the probability of illness in the illness-death model under cross-sectional sampling

M. Mandel

Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, 91905 Jerusalem, Israel msmic{at}huji.ac.il

R. Fluss

The Department of Health Services Research, Ministry of Health, 29 Rivka Street, 91010 Jerusalem, Israel rfluss{at}gmail.com

Received for publication 1 February 2008. Revision received 1 March 2009.
  Abstract

Cross-sectional sampling is an attractive design that saves resources but results in biased data. For proper inference, one should first discover the bias function and then weigh observations appropriately. We consider cross-sectioning of the illness-death model with the aim of estimating the probability of visiting the illness state before death. We develop simple consistent and asymptotically normal estimators under various assumptions on the model and data collection and, in particular, compare designs with and without a follow-up. These designs are common in surveillance of hospital acquired infections, but estimators currently in use do not properly correct the bias.

Key Words: Biased data • Disability model • Incidence • Nosocomial infection • Prevalence • Semi-competing risks


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