In addition, the calculation of IQS can be expanded to evaluate non-random error. When cases and controls are genotyped on different platforms (e.g., cases genotyped on the Affymetrix array and controls genotyped on the Illumina array), some SNPs are not genotyped in either array but are imputed from their respective arrays. This imposes non-random errors on the imputed genotypes. In particular, if we combine these imputed genotypes together, it will inflate false positive rates. IQS can take this into account by incorporating marginal frequencies into the calculation. For instance, if imputation from the Illumina array reports that for a particular SNP, the probabilities of AA, AB and BB are a1, a2, a3, and imputation from the Affymetrix array reports that the probabilities for the three genotypes are b1, b2, b3, then nij in the calculation of Po becomes
