mdr.3WS: A function to perform MDR on a dataset using the three-way...
In MDR: Detect gene-gene interactions using multifactor dimensionality reduction

Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

Determines the best MDR model up to a specified size of interaction K by minimizing balanced accuracy (arithmetic mean of sensitivity and specificity), while using a three-way split internal validation method. The three-way split randomly separates the data into training, testing, and validation sets. The function mdr.3WS is essentially a wrapper for the function mdr.

1	mdr.3WS(data, K, x = NULL, proportion = NULL, ratio = NULL, equal = "HR", genotype = c(0, 1, 2))

`data`	the dataset; an n by (p+1) matrix where the first column is the binary response vector (coded 0 or 1) and the remaining columns are the p SNP genotypes (coded numerically)
`K`	the highest level of interaction to consider
`x`	the number of models from the training set to retain in the testing set
`proportion`	a three-dimensional vector specifying the ratio of split proportions training:testing:validation (default is 2:2:1 denoted as c(2,2,1))
`ratio`	the case/control ratio threshold to ascribe high-risk/low-risk status of a genotype combination
`equal`	how to treat genotype combinations with case/control ratio equal to the threshold; default is "HR" for high-risk, but can also consider "LR" for low-risk
`genotype`	a numeric vector of possible genotypes arising in `data`; default is c(0,1,2), but this vector can be longer or shorter depending on if more or fewer than three genotypes are possible

MDR is a non-parametric data-mining approach to variable selection designed to detect gene-gene or gene-environment interactions in case-control studies. This function uses balanced accuracy as the evaluation measure to rank potential models. An overall best model is chosen to minimize balanced accuracy, while also preventing model over-fitting with internal validation. This function uses a three-way split of the data (training set for model building, testing set for replication, and validation set for prediction) for internal validation.

An object of class 'mdr', which is a list containing:

`final model`	a numeric vector of the predictors included in the final model
`final model accuracy`	the balanced accuracy of the final model from the validation set
`top models`	a list containing the best model (with minimum BA) for each level of interaction, from 1 to `K`
`top model accuracies`	a matrix containing the training, testing, and validation accuracies for each level of interaction, from 1 to `K`
`high-risk/low-risk`	a vector of the high-risk/low-risk parameterizations of the genotype combinations for the final model
`genotypes`	the numeric vector of possible genotypes specified
`validation method`	"3WS", since a three-way split internal validation procedure was utilized

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MDR is a combinatorial search approach, so considering high-order interactions (i.e. large values for K) can be computationally expensive.

When determining the high-risk/low-risk status of a genotype combination, the order of combinations uses the convention that the genotypes of the first locus vary the most, based on the function expand.grid. For instance, with 3 genotypes (0,1,2), a two-way interaction results in the following 9 combinations: (0,0), (1,0), (2,0), (0,1), (1,1), (2,1), (0,2), (1,2), (2,2).

Stacey Winham

Ritchie et al (2001). Multifactor-dimensionality reduction reveals high-order interactions among estrogen-metabolism genes in sporadic breast cancer. Am J Hm Genet 69, 138-147.

Velez et al (2007). A balanced accuracy function for epistasis modeling in imbalanced datasets using multifactor dimensionality reduction. Genet Epidemiol 31, 306-315.

Winham SJ and Motsinger AA (2010). A comparison of internal validation techniques for multifactor dimensionality reduction. BMC Bioinformatics.

mdr.cv, mdr, boot.error, mdr.ca.adj, permute.mdr, plot.mdr, predict.mdr, summary.mdr

#load test data
data(mdr1)

fit<-mdr.3WS(data=mdr1[,1:11], K=3, x = NULL, proportion = NULL, ratio = NULL, equal = "HR", genotype = c(0, 1, 2)) #fit MDR with 3WS to a subset of the sample data, allowing for 1 to 3-way interactions

print(fit) #view the fitted mdr object

summary(fit) #create summary table of best MDR model

plot(fit, data=mdr1) #create contingency plot of best MDR model; may need to expand the plot window for large values of K