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Improved Semiparametric Analysis of Polygenic Gene–Environment Interactions in Case–Control Studies

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  • Tianying Wang

    (Tsinghua University)

  • Alex Asher

    (StataCorp LLC)

Abstract

Standard logistic regression analysis of case–control data has low power to detect gene–environment interactions, but until recently it was the only method that could be used on complex polygenic data for which parametric distributional models are not feasible. Under the assumption of gene–environment independence in the underlying population, Stalder et al. (Biometrika, 104:801–812, 2017) developed a retrospective method that treats both genetic and environmental variables nonparametrically. However, the mathematical symmetry of genetic and environmental variables is overlooked. We propose an improvement to the method of Stalder et al. that increases the efficiency of the estimates with no additional assumptions and modest computational cost. This improvement is achieved by treating the genetic and environmental variables symmetrically to generate two sets of parameter estimates that are combined to generate a more efficient estimate. We employ a semiparametric framework to develop the asymptotic theory of the estimator, show its asymptotic efficiency gain, and evaluate its performance via simulation studies. The method is illustrated using data from a case–control study of breast cancer.

Suggested Citation

  • Tianying Wang & Alex Asher, 2021. "Improved Semiparametric Analysis of Polygenic Gene–Environment Interactions in Case–Control Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 386-401, December.
    • Handle: RePEc:spr:stabio:v:13:y:2021:i:3:d:10.1007_s12561-020-09298-9
    DOI: 10.1007/s12561-020-09298-9
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    References listed on IDEAS

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    1. Iryna Lobach & Raymond J. Carroll & Christine Spinka & Mitchell H. Gail & Nilanjan Chatterjee, 2008. "Haplotype‐Based Regression Analysis and Inference of Case–Control Studies with Unphased Genotypes and Measurement Errors in Environmental Exposures," Biometrics, The International Biometric Society, vol. 64(3), pages 673-684, September.
    2. Frank Dudbridge, 2013. "Power and Predictive Accuracy of Polygenic Risk Scores," PLOS Genetics, Public Library of Science, vol. 9(3), pages 1-17, March.
    3. 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.
    4. Lin, D.Y. & Zeng, D., 2006. "Likelihood-Based Inference on Haplotype Effects in Genetic Association Studies," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 89-104, March.
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