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Semiparametric maximum likelihood estimation exploiting gene-environment independence in case-control studies

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  • Nilanjan Chatterjee
  • Raymond J. Carroll

Abstract

We consider the problem of maximum-likelihood estimation in case-control studies of gene-environment associations with disease when genetic and environmental exposures can be assumed to be independent in the underlying population. Traditional logistic regression analysis may not be efficient in this setting. We study the semiparametric maximum likelihood estimates of logistic regression parameters that exploit the gene-environment independence assumption and leave the distribution of the environmental exposures to be nonparametric. We use a profile-likelihood technique to derive a simple algorithm for obtaining the estimator and we study the asymptotic theory. The results are extended to situations where genetic and environmental factors are independent conditional on some other factors. Simulation studies investigate small-sample properties. The method is illustrated using data from a case-control study designed to investigate the interplay of BRCA1/2 mutations and oral contraceptive use in the aetiology of ovarian cancer. Copyright 2005, Oxford University Press.

Suggested Citation

  • Nilanjan Chatterjee & Raymond J. Carroll, 2005. "Semiparametric maximum likelihood estimation exploiting gene-environment independence in case-control studies," Biometrika, Biometrika Trust, vol. 92(2), pages 399-418, June.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:2:p:399-418
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    File URL: http://hdl.handle.net/10.1093/biomet/92.2.399
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    Cited by:

    1. Colin O. Wu & Gang Zheng & Minjung Kwak, 2013. "A Joint Regression Analysis for Genetic Association Studies with Outcome Stratified Samples," Biometrics, The International Biometric Society, vol. 69(2), pages 417-426, June.
    2. Summer S. Han & Philip S. Rosenberg & Nilanjan Chatterjee, 2012. "Testing for Gene--Environment and Gene--Gene Interactions Under Monotonicity Constraints," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1441-1452, December.
    3. Summer S. Han & Philip S. Rosenberg & Arpita Ghosh & Maria Teresa Landi & Neil E. Caporaso & Nilanjan Chatterjee, 2015. "An exposure‐weighted score test for genetic associations integrating environmental risk factors," Biometrics, The International Biometric Society, vol. 71(3), pages 596-605, September.
    4. Tina Tsz-Ting Chui & Wen-Chung Lee, 2014. "Estimating Risks and Relative Risks in Case-Base Studies under the Assumptions of Gene-Environment Independence and Hardy-Weinberg Equilibrium," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-5, August.
    5. Hua Yun Chen & Daniel E. Rader & Mingyao Li, 2015. "Likelihood Inferences on Semiparametric Odds Ratio Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1125-1135, September.
    6. Wu Cen & Zhong Ping-Shou & Cui Yuehua, 2018. "Additive varying-coefficient model for nonlinear gene-environment interactions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 17(2), pages 1-18, April.
    7. Jinbo Chen & Dongyu Lin & Hagit Hochner, 2012. "Semiparametric Maximum Likelihood Methods for Analyzing Genetic and Environmental Effects with Case-Control Mother–Child Pair Data," Biometrics, The International Biometric Society, vol. 68(3), pages 869-877, September.
    8. Bhramar Mukherjee & Li Zhang & Malay Ghosh & Samiran Sinha, 2007. "Semiparametric Bayesian Analysis of Case–Control Data under Conditional Gene-Environment Independence," Biometrics, The International Biometric Society, vol. 63(3), pages 834-844, September.
    9. Gustafson Paul, 2010. "Bayesian Inference for Partially Identified Models," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-20, March.
    10. Yulia V. Marchenko & Raymond K. Carroll & Danyu Y. Lin & Christopher I. Amos & Roberto G. Gutierrez, 2008. "Semiparametric analysis of case–control genetic data in the presence of environmental factors," Stata Journal, StataCorp LP, vol. 8(3), pages 305-333, September.
    11. Liang, Liang & Ma, Yanyuan & Carroll, Raymond J., 2019. "A semiparametric efficient estimator in case-control studies for gene–environment independent models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 38-50.
    12. Brisa N. Sánchez & Shan Kang & Bhramar Mukherjee, 2012. "A Latent Variable Approach to Study Gene–Environment Interactions in the Presence of Multiple Correlated Exposures," Biometrics, The International Biometric Society, vol. 68(2), pages 466-476, June.
    13. Bhramar Mukherjee & Nilanjan Chatterjee, 2008. "Exploiting Gene‐Environment Independence for Analysis of Case–Control Studies: An Empirical Bayes‐Type Shrinkage Estimator to Trade‐Off between Bias and Efficiency," Biometrics, The International Biometric Society, vol. 64(3), pages 685-694, September.
    14. James Y. Dai & Michael LeBlanc & Charles Kooperberg, 2009. "Semiparametric Estimation Exploiting Covariate Independence in Two-Phase Randomized Trials," Biometrics, The International Biometric Society, vol. 65(1), pages 178-187, March.
    15. Eric J. Tchetgen Tchetgen & James Robins, 2010. "The Semiparametric Case-Only Estimator," Biometrics, The International Biometric Society, vol. 66(4), pages 1138-1144, December.
    16. Bhramar Mukherjee & Jaeil Ahn & Stephen B. Gruber & Malay Ghosh & Nilanjan Chatterjee, 2010. "Case–Control Studies of Gene–Environment Interaction: Bayesian Design and Analysis," Biometrics, The International Biometric Society, vol. 66(3), pages 934-948, September.

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