Table 1.

Overview of named MDR-based methods

Name	Description	Data structure	Cov	Pheno	Small sample sizesa	Applications
Multifactor Dimensionality Reduction (MDR) [2]	Reduce dimensionality of multi-locus information by pooling multi-locus genotypes into high-risk and low-risk groups	U	No/yes, depends on implementation (see Table 2)	D	No	Numerous phenotypes, see refs. [2, 3–11]
Classification of cells into risk groups
Generalized MDR (GMDR) [12]	Flexible framework by using GLMs	U	Yes	D, Q	No	Numerous phenotypes, see refs. [4, 12–33]
Pedigree-based GMDR (PGMDR) [34]	Transformation of family data into matched case-control data	F	Yes	D, Q	No	Nicotine dependence [34]
Support-Vector-Machine-based PGMDR (SVM-PGMDR) [35]	Use of SVMs instead of GLMs	F	Yes	D, Q	Yes	Alcohol dependence [35]
Unified GMDR (UGMDR) [36]	Simultaneous handling of families and unrelateds	U and F	Yes	D, Q	No	Nicotine dependence [36]
Cox-based MDR (Cox-MDR) [37]	Transformation of survival time into dichotomous attribute using martingale residuals	U	Yes	S	No	Leukemia [37]
Multivariate GMDR (MV-GMDR) [38]	Multivariate modeling using generalized estimating equations	U	Yes	D, Q, MV	No	Blood pressure [38]
Robust MDR (RMDR) [39]	Handling of sparse/empty cells using ‘unknown risk’ class	U	No	D	Yes	Bladder cancer [39]
Log-linear-based MDR (LM-MDR) [40]	Improved factor combination by log-linear models and re-classification of risk	U	No	D	Yes	Alzheimer's disease [40]
Odds-ratio-based MDR (OR-MDR) [41]	OR instead of naïve Bayes classifier to classify its risk	U	No	D	Yes	Chronic Fatigue Syndrome [41]
Optimal MDR (Opt-MDR) [42]	Data driven instead of fixed threshold; $P$-values approximated by generalized EVD instead of permutation test	U	No	D	No
MDR for Stratified Populations (MDR-SP) [43]	Accounting for population stratification by using principal components; significance estimation by generalized EVD	U	No	D	No
Pair-wise MDR (PW-MDR) [44]	Handling of sparse/empty cells by reducing contingency tables to all possible two-dimensional interactions	U	No	D	Yes	Kidney transplant [44]
Evaluation of the classification result
Extended MDR (EMDR) [45]	Evaluation of final model by ${\chi }^2$ statistic; consideration of different permutation strategies	U	No	D	No
Different phenotypes or data structures
Survival Dimensionality Reduction (SDR) [46]	Classification based on differences between cell and whole population survival estimates; IBS to evaluate models	U	No	S	No	Rheumatoid arthritis [46]
Survival MDR (Surv-MDR) [47]	Log-rank test to classify cells; squared log-rank statistic to evaluate models	U	No	S	No	Bladder cancer [47]
Quantitative MDR (QMDR) [48]	Handling of quantitative phenotypes by comparing cell with overall mean; $t$-test to evaluate models	U	No	Q	No	Renal and Vascular End-Stage Disease [48]
Ordinal MDR (Ord-MDR) [49]	Handling of phenotypes with >2 classes by assigning each cell to most likely phenotypic class	U	No	O	No	Obesity [49]
MDR with Pedigree Disequilibrium Test (MDR-PDT) [50]	Handling of extended pedigrees using pedigree disequilibrium test	F	No	D	No	Alzheimer’s disease [50]
MDR with Phenomic Analysis (MDR-Phenomics) [51]	Handling of trios by comparing number of times genotype is transmitted versus not transmitted to affected child; analysis of variance model to assesses effect of PC	F	No	D	No	Autism [51]
Aggregated MDR (A-MDR) [52]	Defining significant models using threshold maximizing area under ROC curve; aggregated risk score based on all significant models	U	No	D	No	Juvenile idiopathic arthritis [52]
Model-based MDR (MB-MDR) [53]	Test of each cell versus all others using association test statistic; association test statistic comparing pooled high-risk and pooled low-risk cells to evaluate models	U	No	D, Q, S	No	Bladder cancer [53, 54], Crohn’s disease [55, 56], blood pressure [57]

Cov = Covariate adjustment possible, Pheno = Possible phenotypes with D = Dichotomous, Q = Quantitative, S = Survival, MV = Multivariate, O = Ordinal.

Data structures: F = Family based, U = Unrelated samples.

^aBasically, MDR-based methods are designed for small sample sizes, but some methods provide special approaches to deal with sparse or empty cells, typically arising when analyzing very small sample sizes.