Log-linear models for assessing gene-age interaction and their application to case-control studies of the apolipoprotein E (apoE) gene in Alzheimer's disease.

Case-control studies provide a powerful approach for detecting disease-susceptibility genes or assessing gene-environment interactions. We investigated the situation in which the gene being studied plays a role in several diseases, and the allele frequency among subjects free of the disease of interest consequently decreases with age as subjects die from other diseases. The logistic model is one approach frequently used for analyzing case-control data, but it cannot accommodate this dependence of genotype and age. Using a log-linear model, we therefore proposed a hierarchical procedure that could be used as a valid method for assessing interactions in such situations. We then applied this procedure to observed data on Alzheimer's disease and the apolipoprotein E gene in Japan. We were able to derive an appropriate inference on whether the interaction was a gene-age interaction or merely a bias due to death from other diseases.