@article {20,
	title = {Testing for gene-environment interaction under exposure misspecification.},
	journal = {Biometrics},
	volume = {74},
	year = {2018},
	month = {2018 Jun},
	pages = {653-662},
	abstract = {<p>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.</p>},
	keywords = {Bias, Confounding Factors, Epidemiologic, Environmental Exposure, Gene-Environment Interaction, Humans, Linear Models, Models, Genetic, Scientific Experimental Error},
	issn = {1541-0420},
	doi = {10.1111/biom.12813},
	author = {Sun, Ryan and Carroll, Raymond J and Christiani, David C and Lin, Xihong}
}
@article {47,
	title = {Weighted pseudolikelihood for SNP set analysis with multiple secondary outcomes in case-control genetic association studies.},
	journal = {Biometrics},
	volume = {73},
	year = {2017},
	month = {2017 Dec},
	pages = {1210-1220},
	abstract = {<p>We propose a weighted pseudolikelihood method for analyzing the association of a SNP set, example, SNPs in a gene or a genetic pathway or network, with multiple secondary phenotypes in case-control genetic association studies. To boost analysis power, we assume that the SNP-specific effects are shared across all secondary phenotypes using a scaled mean model. We estimate regression parameters using Inverse Probability Weighted (IPW) estimating equations obtained from the weighted pseudolikelihood, which accounts for case-control sampling to prevent potential ascertainment bias. To test the effect of a SNP set, we propose a weighted variance component pseudo-score test. We also propose a penalized IPW pseudolikelihood method for selecting a subset of SNPs that are associated with the multiple secondary phenotypes. We show that the proposed variable selection procedure has the oracle properties and is robust to misspecification of the correlation structure among secondary phenotypes. We select the tuning parameter using a weighted Bayesian Information-like Criterion (wBIC). We evaluate the finite sample performance of the proposed methods via simulations, and illustrate the methods by the analysis of the multiple secondary smoking behavior outcomes in a lung cancer case-control genetic association study.</p>},
	keywords = {Case-Control Studies, Computer Simulation, Genetic Association Studies, Humans, Likelihood Functions, Lung Neoplasms, Phenotype, Polymorphism, Single Nucleotide, Smoking},
	issn = {1541-0420},
	doi = {10.1111/biom.12680},
	author = {Sofer, Tamar and Schifano, Elizabeth D and Christiani, David C and Lin, Xihong}
}
