Correcting systematic inflation in genetic association tests that consider interaction effects: application to a genome-wide association study of posttraumatic stress disorder

Abstract

Importance: Genetic association studies of psychiatric outcomes often consider interactions with environmental exposures and, in particular, apply tests that jointly consider gene and gene-environment interaction effects for analysis. Using a genome-wide association study (GWAS) of posttraumatic stress disorder (PTSD), we report that heteroscedasticity (defined as variability in outcome that differs by the value of the environmental exposure) can invalidate traditional joint tests of gene and gene-environment interaction.

Objectives: To identify the cause of bias in traditional joint tests of gene and gene-environment interaction in a PTSD GWAS and determine whether proposed robust joint tests are insensitive to this problem.

Design, setting, and participants: The PTSD GWAS data set consisted of 3359 individuals (978 men and 2381 women) from the Grady Trauma Project (GTP), a cohort study from Atlanta, Georgia. The GTP performed genome-wide genotyping of participants and collected environmental exposures using the Childhood Trauma Questionnaire and Trauma Experiences Inventory.

Main outcomes and measures: We performed joint interaction testing of the Beck Depression Inventory and modified PTSD Symptom Scale in the GTP GWAS. We assessed systematic bias in our interaction analyses using quantile-quantile plots and genome-wide inflation factors.

Results: Application of the traditional joint interaction test to the GTP GWAS yielded systematic inflation across different outcomes and environmental exposures (inflation-factor estimates ranging from 1.07 to 1.21), whereas application of the robust joint test to the same data set yielded no such inflation (inflation-factor estimates ranging from 1.01 to 1.02). Simulated data further revealed that the robust joint test is valid in different heteroscedasticity models, whereas the traditional joint test is invalid. The robust joint test also has power similar to the traditional joint test when heteroscedasticity is not an issue.

Conclusions and relevance: We believe the robust joint test should be used in candidate-gene studies and GWASs of psychiatric outcomes that consider environmental interactions. To make the procedure useful for applied investigators, we created a software tool that can be called from the popular PLINK package for analysis.

Figure 1

Quantile-Quantile Plot of Observed P Values vs Expected P Values (on a −log₁₀ Scale) for Joint and Marginal Genetic Analyses of the Beck Depression Inventory in the Posttraumatic Stress Disorder Genome-wide Association Study Joint analyses considered environmental exposures using the Childhood Trauma Questionnaire (CTQ) and Trauma Experiences Inventory (TEI). λ denotes the inflation factor (defined as the median of the test statistic divided by the median of the asymptotic distribution of the test statistic).

Figure 2

Quantile-Quantile Plot of Observed P Values vs Expected P Values (on a −log₁₀ Scale) for Joint and Marginal Genetic Analyses of Intrusive Symptoms of the Posttraumatic Stress Disorder (PTSD) Symptom Scale in the PTSD Genome-wide Association Study Joint analyses considered environmental exposures using the Childhood Trauma Questionnaire (CTQ) and Trauma Experiences Inventory (TEI). λ denotes the inflation factor (defined as the median of the test statistic divided by the median of the asymptotic distribution of the test statistic).

Figure 5

Quantile-Quantile Plot of Observed P Values vs Expected P Values (on a −log₁₀ Scale) for Joint Analyses of the Beck Depression Inventory (BDI) and the Intrusive Symptoms of the Posttraumatic Stress Disorder (PTSD) Symptom Scale (PSSint) in the PTSD Genome-wide Association Study Using Model-Based and Robust Variance Estimators Joint analyses considered environmental exposures using the Childhood Trauma Questionnaire (CTQ) and Trauma Experiences Inventory (TEI). λ denotes the inflation factor (defined as the median of the test statistic divided by the median of the asymptotic distribution of the test statistic). A, Joint test of the BDI (CTQ exposure); B, joint test of the BDI (TEI exposure); C, joint test of the PSSint (CTQ exposure); and D, joint test of the PSSint (TEI exposure).

Figure 4

Quantile-Quantile Plot of Observed P Values vs Expected P Values (on a −log₁₀ Scale) for Joint Analyses of Simulated Data Using Model-Based and Robust Variance Estimators A, Quantitative data generated assuming Var(Y|G,E = 0) = Var(Y|G,E = 1); B, quantitative data generated assuming Var(Y|G,E = 0)>Var(Y|G,E = 1); and C, quantitative data generated assuming Var(Y|G,E = 0)<Var(Y|G,E = 1). λ denotes the inflation factor (defined as the median of the test statistic divided by the median of the asymptotic distribution of the test statistic). For each simulation model, we evaluated 10 000 replicates of the data in which each data set was composed of 2000 individuals.