AbstractCommonly in biomedical research, studies collect data in which an outcome measure contains informative excess zeros; for example, when observing the burden of neuritic plaques (NPs) in brain pathology studies, those who show none contribute to our understanding of neurodegenerative disease. The outcome may be characterized by a mixture distribution with one component being the “structural zero” and the other component being a Poisson distribution. We propose a novel variance components score test of genetic association between a set of genetic markers and a zero‐inflated count outcome from a mixture distribution. This test shares advantageous properties with single‐nucleotide polymorphism (SNP)‐set tests which have been previously devised for standard continuous or binary outcomes, such as the sequence kernel association test. In particular, our method has superior statistical power compared to competing methods, especially when there is correlation within the group of markers, and when the SNPs are associated with both the mixing proportion and the rate of the Poisson distribution. We apply the method to Alzheimer’s data from the Rush University Religious Orders Study and Memory and Aging Project, where as proof of principle we find highly significant associations with the APOE gene, in both the “structural zero” and “count” parameters, when applied to a zero‐inflated NPs count outcome.