We thus construct likelihood ratio tests of association of an accumulation of rare variants with disease by comparing the maximised likelihoods of two models via analysis of deviance: (i) the null model where λ = 0; and (ii) the alternative model for which λ is unconstrained. The contribution of the ith individual to the likelihood, f(yi | α,λ,β,ri,ni,xi), is weighted by ni to allow for differential call rates between samples. We denote the likelihood ratio test based on the proportion of rare variants at which an individual carries minor alleles by RVT1, and that based on the presence/absence of at least one minor allele at any rare variant by RVT2. Both RVT1 and RVT2 can be generalised to tests of association with a binary trait within a logistic regression-modelling framework.
