After reviewing Multifactor Dimensionality Reduction(MDR) and its extensions, an approach to obtain P(larger than 1) risk scores is proposed to predict the continuous outcome for each subject. We study the mean square error(MSE) of dimensionality reduced models fitted with sets of 2 risk scores and investigate the MSE for several special cases of the covariance matrix. A methodology is proposed to select a best set of P risk scores when P is specified a priori. Simulation studies based on true models of different dimensions(larger than 3) demonstrate that the selected set of P(larger than 1) risk scores outperforms the single aggregated risk score generated in AQMDR and illustrate that our methodology can determine a best set of P risk scores effectively. With different assumptions on the dimension of the true model, we considered the preferable set of risk scores from the best set of two risk scores and the best set of three risk scores. Further, we present a methodology to access a set of P risk scores when P is not given a priori. The expressions of asymptotic estimated mean square error of prediction(MSPE) are derived for a 1-dimensional model and 2-dimensional model. In the last main chapter, we apply the methodology of selecting a best set of risk scores where P has been specified a priori to Alzheimer’s Disease data and achieve a set of 2 risk scores and a set of three risk scores for each subject to predict measurements on biomarkers that are crucially involved in Alzheimer’s Disease.

Prevalence of childhood asthma in Taiwan has increased 9 times from 1.3% to 10-14% in the past 4 decades. Many studies worldwide have demonstrated that many genes in different chromosomes are implicated in childhood asthma in different ethnic populations. A growing body of evidence suggests that allergic sensitization could occur in perinatal stage and correlate to the development of childhood asthma. Epidemiological studies, however, indicate that prevalence of childhood asthma is much higher in developed countries than that in developing countries; and prevalence of childhood asthma in metropolitan area is higher than that in country sites. This suggests that certain genes can interact with the environmental factors in developed countries to promote the development of childhood atopic disorders. Interests are now increasing on what is (are) the real pathogenic gene-gene interaction(s) for childhood atopic disorders under influence of age, gender and environmental factors? In a large perinatal cohort study with 1,211 pregnant women and their offspring from the obstetrics and pediatrics of Kaohsiung Chang Gung Memorial Hospital, we analyzed 159 allergy candidate genes with 384 single nucleotide polymorphisms and showed that 14 genes over 22 somatic and X chromosomes risk to or protective from cord blood immunoglobulin E (CBIgE) elevation are different from those genes associated with IgE elevation in children under 1.5, 3 and 6 years of age (12, 15 and 12 genes, respectively). CX3CL1, IL13, PDGFRA and FGF1 polymorphisms were associated with elevated IgE at earlier ages (newborn, 1.5 and 3 years); HLA-DPA1, HLA-DQA1, CCR5 and IL5RA polymorphisms were associated with IgE production at 6 years of age. Further analysis by multifactor dimensionality reduction (MDR) developed from data reduction strategy, we found that there are interactions among innate immunity, adaptive immunity, and response and remodeling genes on IgE production begin in prenatal stage. For example, The gene-gene interaction among IL13, rs1800925, CYFIP2, rs767007 and PDE2A, rs755933 was significantly associated with IgE production at 3 years of age. This suggests that different genotypes of genes interact one another on the IgE production contributing to the development of allergic diseases. Since the concentration of IgE is an important indicator of atopic disorders and allergic sensitization, we believe after clarifying the natural course of the genomic profiles on IgE elevation, certain early predictor(s) and preventive regimens for allergic sensitization or atopic disorders may be made possible.

A method to detect relationships between disease susceptibility and multilocus genetic interactions is the Multifactor-Dimensionality Reduction (MDR) technique pioneered by Ritchie et al. (2001). Since its introduction, many extensions have been pursued to deal with non-binary outcomes and/or account for multiple interactions simultaneously. Studying the effects of multilocus genetic interactions on continuous traits (blood pressure, weight, etc.) is one case that MDR does not handle. Culverhouse et al. (2004) and Gui et al. (2013) proposed two different methods to analyze such a case. In their research, Gui et al. (2013) introduced the Quantitative Multifactor-Dimensionality Reduction (QMDR) that uses the overall average of response variable to classify individuals into risk groups. The classification mechanism may not be efficient under some circumstances, especially when the overall mean is close to some multilocus means. To address such difficulties, we propose a new algorithm, the Ordered Combinatorial Quantitative Multifactor-Dimensionality Reduction (OQMDR), that uses a series of testings, based on ascending order of multilocus means, to identify best interactions of different orders with risk patterns that minimize the prediction error. Ten-fold cross-validation is used to choose from among the resulting models. Regular permutations testings are used to assess the significance of the selected model. The assessment procedure is also modified by utilizing the Generalized Extreme-Value distribution to enhance the efficiency of the evaluation process. We presented results from a simulation study to illustrate the performance of the algorithm. The proposed algorithm is also applied to a genetic data set associated with Alzheimer's Disease.

Introduction – Animal studies suggested that NFKB1, SOCS3 and IKBKB genes could be involved in the association between overnutrition and obesity. This study aims to investigate interactions involving these genes and nutrition affecting obesity-related phenotypes. Methods – We used multifactor dimensionality reduction (MDR) and penalized logistic regression (PLR) to better detect gene/environment interactions in data from the Toronto Nutrigenomics and Health Study (n=1639) using dichotomized body mass index (BMI) and waist circumference (WC) as obesity-related phenotypes. Exposure variables included genotypes on 54 single nucleotide polymorphisms, dietary factors and ethnicity. Results – MDR identified interactions between SOCS3 rs6501199 and rs4969172, and IKBKB rs3747811 affecting BMI in whites; SOCS3 rs6501199 and NFKB1 rs1609798 affecting WC in whites; and SOCS3 rs4436839 and IKBKB rs3747811 affecting WC in South Asians. PLR found a main effect of SOCS3 rs12944581 on BMI among South Asians. Conclusion – MDR and PLR gave different results, but support some results from previous studies.