More and more large cohort studies have conducted or are conducting genome-wide association studies (GWAS) to reveal the genetic components of many complex human diseases. These large cohort studies often collected a broad array of correlated phenotypes that reflect common physiological processes. By jointly analyzing these correlated traits, we can gain more power by aggregating multiple weak effects and shed light on the mechanisms underlying complex human diseases. The majority of existing multi-trait association test methods are based on jointly modeling the multivariate traits conditional on the genotype as covariate, and can readily accommodate the imputed SNPs by using their imputed dosage as a covariate. An alternative class of multitrait association tests is based on the inverted regression, which models the distribution of genotypes conditional on the covariate and multivariate traits, and has been shown to have competitive performance. To our knowledge, all existing inverted regression approaches have implicitly used the "best-guess" genotypes, which is not efficient and known to lead to dramatic power loss, and there have not been any proposed methods of incorporating imputation uncertainty into inverted regressions. In this work, we propose a general and efficient framework that can account for the imputation uncertainty to further improve the association test power of inverted regression models for imputed SNPs. We demonstrate through extensive numerical studies that the proposed method has competitive performance. We further illustrate its usefulness by application to association test of diabetes-related glycemic traits in the Atherosclerosis Risk in Communities (ARIC) Study.