The Logistic Regression Model for Gene–Environment Interactions Using Both Case‐Parent Trios and Unrelated Case–Controls

Summary One of the greatest challenges in genetic studies is the determination of gene–environment interactions due to underlying complications and inadequate statistical power. With the increased sample size gained by using case‐parent trios and unrelated cases and controls, the performance may be much improved. Focusing on a dichotomous trait, a two‐stage approach was previously proposed to deal with gene–environment interaction when utilizing mixed study samples. Theoretically, the two‐stage association analysis uses likelihood functions such that the computational algorithms may not converge in the maximum likelihood estimation with small study samples. In an effort to avoid such convergence issues, we propose a logistic regression framework model, based on the combined haplotype relative risk (CHRR) method, which intuitively pools the case‐parent trios and unrelated subjects in a two by two table. A positive feature of the logistic regression model is the effortless adjustment for either discrete or continuous covariates. According to computer simulations, under the circumstances in which the two‐stage test converges in larger sample sizes, we discovered that the performances of the two tests were quite similar; the two‐stage test is more powerful under the dominant and additive disease models, but the extended CHRR is more powerful under the recessive disease model.