The Use of Case-Parent Triads to Study Joint Effects of Genotype and Exposure

Abstract

Most noninfectious disease is caused by low-penetrance alleles interacting with other genes and environmental factors. Consider the simple setting where a diallelic autosomal candidate gene and a binary exposure together affect disease susceptibility. Suppose that one has genotyped affected probands and their parents and has determined each proband's exposure status. One proposed method for assessment of etiologic interaction of genotype and exposure, an extension of the transmission/disequilibrium test, tests for differences in transmission of the variant allele from heterozygous parents to exposed versus unexposed probands. We show that this test is not generally valid. An alternative approach compares the conditional genotype distribution of unexposed cases, given parental genotypes, versus that of exposed cases. This approach provides maximum-likelihood estimators for genetic relative-risk parameters and genotype-exposure-interaction parameters, as well as a likelihood-ratio test (LRT) of the no-interaction null hypothesis. We show how to apply this approach, using log-linear models. When a genotype-exposure association arises solely through incomplete mixing of subpopulations that differ in both exposure prevalence and allele frequency, the LRT remains valid. The LRT becomes invalid, however, if offspring genotypes do not follow Mendelian proportions in each parental mating type-for example, because of genotypic differences in survival-or if a genotype-exposure association reflects an influence of genotype on propensity for exposure-for example, through behavioral mechanisms. Because the needed assumptions likely hold in many situations, the likelihood-based approach should be broadly applicable for diseases in which probands commonly have living parents.

Tests of Gene‐Environment Interaction for Case‐Parent Triads with General Environmental Exposures

“…Umbach & Weinberg (2000) show that tests based on loglinear models maintain the correct type I error rate in the presence of population stratification. The null hypothesis of no geneenvironment interaction is tested using likelihood ratio tests or score tests with the degrees-of-freedom determined by the assumptions made regarding the penetrance function.…”

“…E-mail: Stephen.Lake@ channing.harvard.edu family-based designs for the study of gene-environment interaction have been proposed (Khoury & Flanders, 1996;Maestri et al 1997;Schaid, 1999;Waldman et al 1999;Witte et al 1999;Lunetta et al 2000). Recently, Umbach & Weinberg (2000) illustrated that tests of gene-environment interaction that involve a contrast, between exposed and unexposed trios, of the transmission rates of disease alleles from heterozygous parents to affected offspring are susceptible to type I error rate inflation from two sources. The first is that a difference of transmission rates between exposed and unexposed trios can be the consequence of population stratification even if there is no interaction.…”

“…The second cause of potentially spurious results is the nonindependence of disease allele transmissions between heterozygous parents under the null hypothesis of no interaction. As Umbach & Weinberg (2000) state, such bias may arise in any test of gene-environment interaction that is based on the counting of transmissions from heterozygous parents, including the logistic regression approaches of Maestri et al (1997) and Waldman et al (1999). While the method of Lunetta et al (2000) is robust to these potential pitfalls, the null hypotheses for the tests assume that there is no interaction as well as no main effects of the gene or environmental exposure.…”

“…Another approach to testing for gene-environment interaction is the extension of the loglinear model formulation for case-parent trios (Weinberg et al 1998;Umbach & Weinberg, 2000). Umbach & Weinberg (2000) show that tests based on loglinear models maintain the correct type I error rate in the presence of population stratification.…”

“…The null hypothesis of no geneenvironment interaction is tested using likelihood ratio tests or score tests with the degrees-of-freedom determined by the assumptions made regarding the penetrance function. As pointed out by Weinberg et al (1998) and Umbach & Weinberg (2000), the testing strategy based on the loglinear model is equivalent to the conditional likelihood methods of Schaid & Sommer (1993) and Schaid (1999). A limitation of the loglinear model is that it includes terms for each level of the environmental exposure thus making it infeasible to use with continuous exposures.…”