A sibling-augmented case-only approach for assessing multiplicative gene-environment interactions

Abstract

Family-based designs protect analyses of genetic effects from bias that is due to population stratification. Investigators have assumed that this robustness extends to assessments of gene-environment interaction. Unfortunately, this assumption fails for the common scenario in which the genotyped variant is related to risk through linkage with a causative allele. Bias also plagues other methods of assessment of gene-environment interaction. When testing against multiplicative joint effects, the case-only design offers excellent power, but it is invalid if genotype and exposure are correlated in the population. The authors describe 4 mechanisms that produce genotype-exposure dependence: exposure-related genetic population stratification, effects of family history on behavior, genotype effects on exposure, and selective attrition. They propose a sibling-augmented case-only (SACO) design that protects against the former 2 mechanisms and is therefore valid for studying young-onset disease in which genotype does not influence exposure. A SACO design allows the ascertainment of genotype and exposure for cases and exposure for 1 or more unaffected siblings selected randomly. Conditional logistic regression permits assessment of exposure effects and gene-environment interactions. Via simulations, the authors compare the likelihood-based inference on interactions using the SACO design with that based on other designs. They also show that robust analyses of interactions using tetrads or disease-discordant sibling pairs are equivalent to analyses using the SACO design.

Figure 1.

Type I error rates for tests of genotype-exposure interaction for 6 study designs in a population with exposure-related stratification. A) This population has 2 equal-sized subpopulations with the same baseline risks and risk parameters relative to the causative variant: (R₁, R₂, I₁, I₂, R_e) = (2, 3, 1, 1, 1.5). Tests are 1-degree-of-freedom tests at nominal α = 0.05 for log-additive genotype-exposure interaction at an untyped causative variant using a marker that is related to risk only through linkage disequilibrium with that variant. The type I error rate is equivalent to the rate of coverage failure under the null for nominal 95% confidence intervals. The curves show the dependence of the type I error rate on the disparate exposure prevalences when the correlations between the causative single nucleotide polymorphism and marker are fixed at 0.5 and 0.1 in the respective subpopulations. E (pop 1) indicates the exposure prevalence in subpopulation 1; E (pop 2) indicates the exposure prevalence in subpopulation 2. Exposure-related stratification is absent when the subpopulation-specific exposure prevalences are equal (here at 0.2). B) As for Figure 1A, except that the curves now show the dependence of the type I error rate on differences in linkage disequilibrium when exposure prevalences are 0.08 and 0.32 in the 2 subpopulations. r (pop 1) indicates the correlation between the causative variant and the marker in subpopulation 1; r (pop 2) indicates the correlation between the causative variant and the marker in subpopulation 2. When the subpopulation-specific correlations (r) between the typed marker and the untyped causative variants are equal (here at 0.29), exposure-related stratification is eliminated, and all tests are unbiased. SACO, sibling-augmented case-only.

Figure 2.

Statistical power for testing genotype-exposure interaction for 6 study designs, assuming a homogenous population in which all tests are valid. A) Curves show the power for testing genotype-exposure interaction for the 6 designs, assuming a homogenous population in which all tests are valid, as a function of exposure prevalence when the causative variant frequency is 0.3. Tests are 1-degree-of-freedom tests at α = 0.05 for log-additive genotype-exposure interaction at a typed causative variant. On the left y-axis is the noncentrality parameter based on 1,000 cases; on the right y-axis is the corresponding power. Tick marks indicate selected power levels. B) As in Figure 2A, except that the curves are now shown in relation to the frequency of the causative variant when the exposure prevalence is 0.3. SACO, sibling-augmented case-only; SNP, single nucleotide polymorphism.