This subproject is one of many research subprojects utilizing theresources provided by a Center grant funded by NIH/NCRR. The subproject andinvestigator (PI) may have received primary funding from another NIH source,and thus could be represented in other CRISP entries. The institution listed isfor 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. The MDR method cannot classify an empty cell as high risk or low risk and leaves it as undetermined. We further propose the log-linear model-based multifactor dimensionality reduction (LM MDR) method to improve the MDR in classifying sparse or empty cells. The LM MDR method estimates frequencies for empty cells from a parsimonious log-linear model so that they can be assigned to high-and low-risk groups. In addition, LM MDR includes MDR as a special case when the saturated log-linear model is fitted. Simulation studies show that the LM MDR method has greater power and smaller error rates than the MDR method. The LM MDR method is also compared with the MDR method using as an example sporadic Alzheimer's disease.
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