This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. The identification and characterization of genes that increase the susceptibility to common complex multifactorial diseases is a challenging task in genetic association studies. The multifactor dimensionality reduction (MDR) method has been proposed and implemented by Ritchie et al. (2001) to identify the combinations of multilocus genotypes and discrete environmental factors that are associated with a particular disease. However, the original MDR method classifies the combination of multilocus genotypes into high-risk and low-risk groups in an ad hoc manner based on a simple comparison of the ratios of the number of case and controls. This method is prone to false positive and negative errors when the ratio of the number of cases and controls in a combination of genotypes is similar to that in the entire data, or when both the number of cases and controls is small. We developed an odds ratio based multifactor dimensionality reduction(OR MDR) method that uses the odds ratio as a new quantitative measure of disease risk, providing not only the odds ratio as a quantitative measure of risk, but also the ordering of the multilocus combinations from the highest risk to lowest risk groups. Furthermore, this method provides a confidence interval for the odds ratio for each multilocus combination, which is extremely informative in judging its importance as a risk factor. When a high-order interaction model is considered with multi-dimensional factors, there may be many sparse or empty cells in the contingency tables. Currently, there are four approaches available in MDR analysis to handle missing data. The first approach uses only complete observations that have no missing data, which can cause a severe loss of data. The second approach is to treat missing values as an additional genotype category, but interpretation of the results may then be not clear and the conclusions may be misleading. Furthermore, it performs poorly when the missing rates are unbalanced between the case and control groups. The third approach is a simple imputation method that imputes missing genotypes as the most frequent genotype, which may also produce biased results. The fourth approach, Available, uses all data available for the given loci to increase power. In any real data analysis, it is not clear which MDR approach one should use when there are missing data. We consider a new EM Impute approach to handle missing data more appropriately. Through simulation studies, we compared the performance of the proposed EM Impute approach with the current approaches. Our results showed that Available and EM Impute approaches perform better than the three other current approaches in terms of power and precision.
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