Multifactor-Dimensionality Reduction in the Presence of Missing Observations

An identification and characterization of susceptibility genes for common complex multifactorial diseases is a challengeable task, in which the effect of single genetic variation will be likely dependent on other genetic variations(gene-gene interaction) and environmental factors (gene-environment interaction). To address is issue, the multifactor dimensionality reduction (MDR) has been proposed and implemented by Ritchie et al. (2001), Moore et al. (2002), Hahn et al.(2003) and Ritchie et al. (2003). With MDR, multilocus genotypes effectively reduce the dimension of genotype predictors from n to one, which improves the identification of polymorphism combinations associated with disease risk. However, MDR cannot handle missing observations appropriately, in which missing observation is treated as an additional genotype category. This approach may suffer from a sparseness problem since when high-order interactions are considered, an additional missing category would make the contingency table cells more sparse. We propose a new MDR approach with minimum loss of sample sizes by considering missing data over all possible multifactor classes. We evaluate the proposed MDR by using the prediction errors and cross validation consistency.