where βk is the allelic log-odds ratio of the minor allele at the kth SNP, and zt is defined above. A likelihood ratio test of βk = 0 provides a “trend test” of association, adjusted for the effects of population structure. Within this framework, we can account for nongenetic (“environmental”) risk factors as additional covariates in the model and can incorporate alternative coding of the SNP genotypes to allow for different models of genetic risk, such as recessive, dominant, or heterozygote advantage.
