@article {12,
	title = {Multiple phenotype association tests using summary statistics in genome-wide association studies.},
	journal = {Biometrics},
	volume = {74},
	year = {2018},
	month = {2018 Mar},
	pages = {165-175},
	abstract = {<p>We study in this article jointly testing the associations of a genetic variant with correlated multiple phenotypes using the summary statistics of individual phenotype analysis from Genome-Wide Association Studies (GWASs). We estimated the between-phenotype correlation matrix using the summary statistics of individual phenotype GWAS analyses, and developed genetic association tests for multiple phenotypes by accounting for between-phenotype correlation without the need to access individual-level data. Since genetic variants often affect multiple phenotypes differently across the genome and the between-phenotype correlation can be arbitrary, we proposed robust and powerful multiple phenotype testing procedures by jointly testing a common mean and a variance component in linear mixed models for summary statistics. We computed the p-values of the proposed tests analytically. This computational advantage makes our methods practically appealing in large-scale GWASs. We performed simulation studies to show that the proposed tests maintained correct type I error rates, and to compare their powers in various settings with the existing methods. We applied the proposed tests to a GWAS Global Lipids Genetics Consortium summary statistics data set and identified additional genetic variants that were missed by the original single-trait analysis.</p>},
	keywords = {Analysis of Variance, Computer Simulation, Genome-Wide Association Study, Humans, Linear Models, Lipids, Models, Genetic, Phenotype},
	issn = {1541-0420},
	doi = {10.1111/biom.12735},
	author = {Liu, Zhonghua and Lin, Xihong}
}
@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}
}
