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Testing for gene–environment interaction under exposure misspecification

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  • Ryan Sun
  • Raymond J. Carroll
  • David C. Christiani
  • Xihong Lin

Abstract

Complex interplay between genetic and environmental factors characterizes the etiology of many diseases. Modeling gene–environment (GxE) interactions is often challenged by the unknown functional form of the environment term in the true data†generating mechanism. We study the impact of misspecification of the environmental exposure effect on inference for the GxE interaction term in linear and logistic regression models. We first examine the asymptotic bias of the GxE interaction regression coefficient, allowing for confounders as well as arbitrary misspecification of the exposure and confounder effects. For linear regression, we show that under gene–environment independence and some confounder†dependent conditions, when the environment effect is misspecified, the regression coefficient of the GxE interaction can be unbiased. However, inference on the GxE interaction is still often incorrect. In logistic regression, we show that the regression coefficient is generally biased if the genetic factor is associated with the outcome directly or indirectly. Further, we show that the standard robust sandwich variance estimator for the GxE interaction does not perform well in practical GxE studies, and we provide an alternative testing procedure that has better finite sample properties.

Suggested Citation

  • Ryan Sun & Raymond J. Carroll & David C. Christiani & Xihong Lin, 2018. "Testing for gene–environment interaction under exposure misspecification," Biometrics, The International Biometric Society, vol. 74(2), pages 653-662, June.
  • Handle: RePEc:bla:biomet:v:74:y:2018:i:2:p:653-662
    DOI: 10.1111/biom.12813
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    References listed on IDEAS

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    1. Michael Rosenblum & Mark J. van der Laan, 2009. "Using Regression Models to Analyze Randomized Trials: Asymptotically Valid Hypothesis Tests Despite Incorrectly Specified Models," Biometrics, The International Biometric Society, vol. 65(3), pages 937-945, September.
    2. Arnab Maity & Raymond J. Carroll & Enno Mammen & Nilanjan Chatterjee, 2009. "Testing in semiparametric models with interaction, with applications to gene–environment interactions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 75-96, January.
    3. Vansteelandt, Stijn & VanderWeele, Tyler J. & Tchetgen, Eric J. & Robins, James M., 2008. "Multiply Robust Inference for Statistical Interactions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1693-1704.
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