Linear mixed models (LMMs) have emerged as the method of choice for confounded genome-wide association studies. However, the performance of LMMs in nonrandomly ascertained case-control studies deteriorates with increasing sample size. We propose a framework called LEAP (liability estimator as a phenotype; https://github.com/omerwe/LEAP) that tests for association with estimated latent values corresponding to severity of phenotype, and we demonstrate that this can lead to a substantial power increase.