Biostatistics Advance Access published online on February 24, 2006
Biostatistics, doi:10.1093/biostatistics/kxj021
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1 Department of Biostatistics, CB# 7420, University of North Carolina, Chapel Hill, NC 27599-7420, U.S.A.
* To whom correspondence should be addressed. Estimating the effects of haplotypes on the age of onset of a disease is an important step toward the discovery of genes that influence complex human diseases. A haplotype is a specific sequence of nucleotides on the same chromosome of an individual and can only be measured indirectly through the genotype. We consider cohort studies which collect genotype data on a subset of cohort members through case-cohort or nested case-control sampling. We formulate the effects of haplotypes and possibly time-varying environmental variables on the age of onset through a broad class of semiparametric regression models. We construct appropriate nonparametric likelihoods, which involve both finite- and infinite-dimensional parameters. The corresponding nonparametric maximum likelihood estimators are shown to be consistent, asymptotically normal and asymptotically efficient. Consistent variance-covariance estimators are provided, and efficient and reliable numerical algorithms are developed. Simulation studies demonstrate that the asymptotic approximations are accurate in practical settings and that case-cohort and nested case-control designs are highly cost-effective. An application to a major cardiovascular study is provided.
Received December 5, 2005
Accepted February 7, 2006
Article
Efficient semiparametric estimation of haplotype-disease associations in case-cohort and nested case-control studies
D. Zeng 1,
D. Y. Lin 1 *,
C. L. Avery 2,
K. E. North 2,
and
M. S. Bray 3
2 Department of Epidemiology, CB# 7435, University of North Carolina, Chapel Hill, NC 27599-7420, U.S.A.
3 Department of Pediatrics, Baylor College of Medicine, Houston, TX, U.S.A.
D. Y. Lin, E-mail: lin{at}bios.unc.edu
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