STEPS: an efficient prospective likelihood approach to genetic association analyses of secondary traits in extreme phenotype sequencing.

It has been well acknowledged that methods for secondary trait (ST) association analyses under a case-control design (ST${\text{CC}}$) should carefully consider the sampling process to avoid biased risk estimates. A similar situation also exists in the extreme phenotype sequencing (EPS) designs, which is to select subjects with extreme values of continuous primary phenotype for sequencing. EPS designs are commonly used in modern epidemiological and clinical studies such as the well-known National Heart, Lung, and Blood Institute Exome Sequencing Project. Although naïve generalized regression or ST${\text{CC}}$ method could be applied, their validity is questionable due to difference in statistical designs. Herein, we propose a general prospective likelihood framework to perform association testing for binary and continuous STs under EPS designs (STEPS), which can also incorporate covariates and interaction terms. We provide a computationally efficient and robust algorithm to obtain the maximum likelihood estimates. We also present two empirical mathematical formulas for power/sample size calculations to facilitate planning of binary/continuous STs association analyses under EPS designs. Extensive simulations and application to a genome-wide association study of benign ethnic neutropenia under an EPS design demonstrate the superiority of STEPS over all its alternatives above.