Functional variants change the protein product or the expression of genes. Due to the latest advances in sequencing technology, most known functional variants can now be assayed in a cost-effective manner. However, to fully use the information from functional variants, researchers need to model the joint effect of these variants. In this article, we propose methods that model the action/interaction of loss-of-function (LOF) mutations, i.e., those mutations that eliminate the protein product of a gene. When multiple LOFs occur in the same causal gene/region, their effect on a phenotype might depend on whether these mutations lie on the same DNA strand/haplotype. When compared to LOFs occurring on the same strand, if these mutations lie on different strands, both copies of the gene are impaired and the impact on the relevant phenotypes is likely to be more severe. To use the information from LOF strand colocalization, we propose three methods that utilize the information from the estimated number of affected strands. We compare the performance of the proposed and competing methods by using simulations of common and rare LOF variants. Two of the proposed methods exhibited desirable power profiles, the first for both common and rare LOFs and the second only for common LOFs. One of the existing methods, collapsed double heterozygosity, exhibits good power to detect compound models for rare variants, especially when no haplotype harbors two or more rare alleles. Consequently, we recommend these three methods to be used for the analysis of functional variants coming from sequencing studies.