One of the greatest challenges facing human geneticists is the identification and characterization of susceptibility genes for common complex multifactorial human diseases. This challenge is partly due to the limitations of parametric-statistical methods for detection of gene effects that are dependent solely or partially on interactions with other genes and with environmental exposures. We introduce multifactor-dimensionality reduction (MDR) as a method for reducing the dimensionality of multilocus information, to improve the identification of polymorphism combinations associated with disease risk. The MDR method is nonparametric (i.e., no hypothesis about the value of a statistical parameter is made), is model-free (i.e., it assumes no particular inheritance model), and is directly applicable to case-control and discordant-sib-pair studies. Using simulated case-control data, we demonstrate that MDR has reasonable power to identify interactions among two or more loci in relatively small samples. When it was applied to a sporadic breast cancer case-control data set, in the absence of any statistically significant independent main effects, MDR identified a statistically significant high-order interaction among four polymorphisms from three different estrogen-metabolism genes. To our knowledge, this is the first report of a four-locus interaction associated with a common complex multifactorial disease.

All supplementary information can be found at http://phg.mc.vanderbilt.edu/Software/MDR.

The identification and characterization of genes that influence the risk of common, complex multifactorial diseases, primarily through interactions with other genes and other environmental factors, remains a statistical and computational challenge in genetic epidemiology. This challenge is partly due to the limitations of parametric statistical methods for detecting genetic effects that are dependent solely or partially on interactions with other genes and environmental exposures. We previously introduced multifactor dimensionality reduction (MDR) as a method for reducing the dimensionality of multilocus genotype information to improve the identification of polymorphism combinations associated with disease risk. The MDR approach is nonparametric (i.e., no hypothesis about the value of a statistical parameter is made), is model-free (i.e., assumes no particular inheritance model), and is directly applicable to case-control and discordant sib-pair study designs. Both empirical and theoretical studies suggest that MDR has excellent power for identifying high-order gene-gene interactions. However, the power of MDR for identifying gene-gene interactions in the presence of common sources of noise is not currently known. The goal of this study was to evaluate the power of MDR for identifying gene-gene interactions in the presence of noise due to genotyping error, missing data, phenocopy, and genetic or locus heterogeneity. Using simulated data, we show that MDR has high power to identify gene-gene interactions in the presence of 5% genotyping error, 5% missing data, or a combination of both. However, MDR has reduced power for some models in the presence of 50% phenocopy, and very limited power in the presence of 50% genetic heterogeneity. Extending MDR to address genetic heterogeneity should be a priority for the continued methodological development of this new approach.

It is now well recognized that gene-gene and gene-environment interactions are important in complex diseases, and statistical methods to detect interactions are becoming widespread. Traditional parametric approaches are limited in their ability to detect high-order interactions and handle sparse data, and standard stepwise procedures may miss interactions that occur in the absence of detectable main effects. To address these limitations, the multifactor dimensionality reduction (MDR) method [Ritchie et al., 2001: Am J Hum Genet 69:138-147] was developed. The MDR is well-suited for examining high-order interactions and detecting interactions without main effects. The MDR was originally designed to analyze balanced case-control data. The analysis can use family data, but requires a single matched pair be selected from each family. This may be a discordant sib pair, or may be constructed from triad data when parents are available. To take advantage of additional affected and unaffected siblings requires a test statistic that measures the association of genotype with disease in general nuclear families. We have developed a novel test, the MDR-PDT, by merging the MDR method with the genotype-Pedigree Disequilibrium Test (geno-PDT)[Martin et al., 2003: Genet Epidemiol 25:203-213]. MDR-PDT allows identification of single-locus effects or joint effects of multiple loci in families of diverse structure. We present simulations to demonstrate the validity of the test and evaluate its power. To examine its applicability to real data, we applied the MDR-PDT to data from candidate genes for Alzheimer disease (AD) in a large family dataset. These results show the utility of the MDR-PDT for understanding the genetics of complex diseases.

The detection of genotypes that predict common, complex disease is a challenge for human geneticists. The phenomenon of epistasis, or gene-gene interactions, is particularly problematic for traditional statistical techniques. Additionally, the explosion of genetic information makes exhaustive searches of multilocus combinations computationally infeasible. To address these challenges, neural networks (NN), a pattern recognition method, have been used. One limitation of the NN approach is that its success is dependent on the architecture of the network. To solve this, machine-learning approaches have been suggested to evolve the best NN architecture for a particular data set. In this study we provide a detailed technical description of the use of grammatical evolution to optimize neural networks (GENN) for use in genetic association studies. We compare the performance of GENN to that of a previous machine-learning NN application--genetic programming neural networks in both simulated and real data. We show that GENN greatly outperforms genetic programming neural networks in data sets with a large number of single nucleotide polymorphisms. Additionally, we demonstrate that GENN has high power to detect disease-risk loci in a range of high-order epistatic models. Finally, we demonstrate the scalability of the GENN method with increasing numbers of variables--as many as 500,000 single nucleotide polymorphisms.