SVSI: Fast and powerful set-valued system identification approach to identifying rare variants in sequencing studies for ordered categorical traits

In genetic association studies of an ordered categorical phenotype, it is usual to either regroup multiple categories of the phenotype into two categories and then apply the logistic regression (LG), or apply ordered logistic (oLG), or ordered probit (oPRB) regression, which accounts for the ordinal nature of the phenotype. However, they may lose statistical power or may not control type I error due to their model assumption and/or instable parameter estimation algorithm when the genetic variant is rare or sample size is limited. To solve this problem, we propose a set-valued (SV) system model to identify genetic variants associated with an ordinal categorical phenotype. We couple this model with a SV system identification algorithm to identify all the key system parameters. Simulations and two real data analyses show that SV and LG accurately controlled the Type I error rate even at a significance level of 10^-6 but not oLG and oPRB in some cases. LG had significantly less power than the other three methods due to disregarding of the ordinal nature of the phenotype, and SV had similar or greater power than oLG and oPRB. We argue that SV should be employed in genetic association studies for ordered categorical phenotype.