Imputation in missing not at random SNPs data using EM algorithm

The relation between single nucleotide polymorphisms (SNPs) and some diseases has been concerned by many researchers. Also the missing SNPs are quite common in genetic association studies. Hence, this article investigates the relation between existing SNPs in DNMT1 of human chromosome 19 with colorectal cancer. This article aims is to presents an imputation method for missing SNPs not at random. In this case-control study, 100 patients suffering from colorectal cancer consulting with the Research Institute for Gastroenterology and Liver Disease of Shahid Beheshti University of Medical Sciences were considered as the case group and 100 other patients consulting with the same research institute were considered as the control group and the genetic test was applied in order to identify the genotype of the 6 SNPs of the DNMT1 of chromosom 19 for all the patients under investigation. The obtained data were analyzed using logistic regression, then a fraction of the data was eliminated both at random and not at random and the imputation was done through the EM algorithm and the logistic regression coefficients variation before and after the imputation was compared. The results of this study implied that in both methods, at random and not at random missing SNPs, the estimation of the logistic regression coefficients after the imputation through EM algorithm has a greater correspondence to the results obtained from the complete data in comparison with the method of eliminating the missing values.