RESEARCH ARTICLE Iterative Usage of Fixed and Random Effect Models for Powerful and Efficient Genome- Wide Association Studies

False positives in a Genome-Wide Association Study (GWAS) can be effectively controlled by a fixed effect and random effect Mixed Linear Model (MLM) that incorporates population structure and kinship among individuals to adjust association tests on markers; however, the adjustment also compromises true positives. The modified MLMmethod, Multiple Loci Linear Mixed Model (MLMM), incorporates multiple markers simultaneously as covariates in a stepwise MLM to partially remove the confounding between testing markers and kin-ship. To completely eliminate the confounding, we divided MLMM into two parts: Fixed Effect Model (FEM) and a Random Effect Model (REM) and use them iteratively. FEM con-tains testing markers, one at a time, and multiple associated markers as covariates to con-trol false positives. To avoid model over-fitting problem in FEM, the associated markers are estimated in REM by using them to define kinship. The P values of testing markers and the associated markers are unified at each iteration. We named the new method as Fixed and random model Circulating Probability Unification (FarmCPU). Both real and simulated data analyses demonstrated that FarmCPU improves statistical power compared to curren