Haplotype-based regression analysis and inference of case-control studies with unphased genotypes and measurement errors in environmental exposures

Iryna Lobach, Raymond J. Carroll, Christine Spinka, Mitchell H. Gail, Nilanjan Chatterjee

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

It is widely believed that risks of many complex diseases are determined by genetic susceptibilities, environmental exposures, and their interaction. Chatterjee and Carroll (2005, Biometrika 92, 399-418) developed an efficient retrospective maximum-likelihood method for analysis of case-control studies that exploits an assumption of gene-environment independence and leaves the distribution of the environmental covariates to be completely nonparametric. Spinka, Carroll, and Chatterjee (2005, Genetic Epidemiology 29, 108-127) extended this approach to studies where certain types of genetic information, such as haplotype phases, may be missing on some subjects. We further extend this approach to situations when some of the environmental exposures are measured with error. Using a polychotomous logistic regression model, we allow disease status to have K + 1 levels. We propose use of a pseudolikelihood and a related EM algorithm for parameter estimation. We prove consistency and derive the resulting asymptotic covariance matrix of parameter estimates when the variance of the measurement error is known and when it is estimated using replications. Inferences with measurement error corrections are complicated by the fact that the Wald test often behaves poorly in the presence of large amounts of measurement error. The likelihood-ratio (LR) techniques are known to be a good alternative. However, the LR tests are not technically correct in this setting because the likelihood function is based on an incorrect model, i.e., a prospective model in a retrospective sampling scheme. We corrected standard asymptotic results to account for the fact that the LR test is based on a likelihood-type function. The performance of the proposed method is illustrated using simulation studies emphasizing the case when genetic information is in the form of haplotypes and missing data arises from haplotype-phase ambiguity. An application of our method is illustrated using a population-based case-control study of the association between calcium intake and the risk of colorectal adenoma.

Original languageEnglish (US)
Pages (from-to)673-684
Number of pages12
JournalBiometrics
Volume64
Issue number3
DOIs
StatePublished - Sep 2008
Externally publishedYes

Keywords

  • EM algorithm
  • Errors in variables
  • Gene-environment independence
  • Gene-environment interactions
  • Inferences in measurement error models
  • Likelihood-ratio tests in misspecified models
  • Profile likelihood
  • Semiparametric methods

ASJC Scopus subject areas

  • Statistics and Probability
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics

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