Relative‐risk regression models using cases and their parents

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Abstract
Relative-risk regression models are presented for studies of the association of genetic markers with disease status when the study design uses affected cases and their parents, with or without unaffected sibs. These models generalize the “haplotype relative-risk” method and allow for censored unaffected sibs; in this sense, these models resemble proportional hazards models that are commonly used in survival analysis. A critical distinction between these models and the usual Cox proportional hazards model is that the frequencies of the genotypes of the cases are compared to controls based on Mendelian expectations, and not simply to the genotypes of the sib controls who are at risk of disease. These models allow modeling of the contribution of specific alleles to the relative risk of disease, as well as interactions of allelic effects with environmental risk factors. To demonstrate the application of these models, we have fit them to the binary affection status of the Problem 2 data set. Four candidate-gene loci were found to have a significant association with affection status, after allowance for relative risks that decrease with age; two of these associations correctly identified two of the major gene loci, and the other two were false-positive associations.