Multifactor Dimensionality Reduction Laura Mustavich Introduction to Data Mining Final Project Presentation April 26, 2007

The Inspiration For a Method

The Nature of Complex Diseases Most common diseases are complex Caused by multiple genes Often interacting with one another This interaction is termed Epistasis

Epistasis When an allele at one locus masks the effect of an allele at another locus

The Failure of Traditional Methods Traditional gene hunting methods successful for rare Mendelian (single gene) diseases Unsuccessful for complex diseases:  Since many genes interact to cause the disease, the effect of any single gene is too small to detect  They do not take this interaction into account

MDR: The Algorithm

Multifactor Dimensionality Reduction A data mining approach to identify interactions among discrete variables that influence a binary outcome A nonparametric alternative to traditional statistical methods such as logistic regression Driven by the need to improve the power to detect gene-gene interactions

Multifactor Dimensionality Reduction

MDR Step 0 Divide data (genotypes, discrete environmental factors, and affectation status) into 10 distinct subsets

Multifactor Dimensionality Reduction

MDR Step 1 Select a set of n genetic or environmental factors (which are suspected of epistasis together) from the set of all variables in the training set

Multifactor Dimensionality Reduction

MDR Step 2 Create a contingency table for these multilocus genotypes, counting the number of affected and unaffected individuals with each multilocus genotype

Multifactor Dimensionality Reduction

MDR Step 3 Calculate the ratio of cases to controls for each multilocus genotype

Multifactor Dimensionality Reduction

MDR Step 4 Label each multilocus genotype as “high- risk” or “low-risk”, depending on whether the case-control ratio is above a certain threshold ****This is the dimensionality reduction step Reduces n-dimensional space to 1 dimension with 2 levels

Multifactor Dimensionality Reduction

MDR Step 5 Use labels to classify individuals as cases or controls, and calculate the misclassification rate

Multifactor Dimensionality Reduction

Repeat steps 1-5 for: All possible combinations of n factors All possible values of n Across all 10 training and testing sets

The Best Model Minimizes prediction error: the average misclassification rate across all the 10 cross-validation subsets Maximizes cross-validation consistency: the number of times a particular model was the best model across cross-validation subsets

Hypothesis test of best model: Evaluate magnitude of cross-validation consistency and prediction error estimates by permutation testing:  Randomize disease labels  Repeat MDR analysis several times to get distribution of cross-validation consistencies and prediction errors  Use distributions to determine p-values for your actual cross-validation consistencies and prediction errors

Permutation Testing: An illustration Sample Quantiles: 0% % % % % % % % % The probability that we would see results as, or more, extreme than , simply by chance, is between 5% and 10%

Strengths Facilitates simultaneous detection and characterization of multiple genetic loci associated with a discrete clinical endpoint by reducing the dimensionality of the multilocus data Non-parametric – no values are estimated Assumes no particular genetic model False-positive rate is minimized due to multiple testing

Weaknesses Computationally intensive (especially with >10 loci) The curse of dimensionality: decreased predictive ability with high dimensionality and small sample due to cells with no data

MDR Software

The Authors Multifactor dimensionality reduction software for detecting gene-gene and gene- environment interactions. Hahn, Ritchie, Moore,

Values Calculated by MDR MeasureFormula/Interpretation Balanced Accuracy(Sensitivity+Specificity)/2; fitness measure Accuracy is skewed in favor of the larger class, whereas balanced accuracy gives equal weight to each class Accuracy(TP+TN)/(TP+TN+FP+FN) Proportion of instances correctly classified SensitivityTP/(TP+FN); proportion of actual positives correctly classified SpecificityTN/(TN+FP); proportion of actual negatives correctly classified Odds Ratio(TP*TN)/(FP*FN); compares whether the probability of a certain event is the same for two groups X2X2 Chi-squared score for the attribute constructed by MDR from this attribute combination PrecisionTP/(TP+FP); the proportion of relevant cases returned Kappa2(TP*TN+FP*FN)/[(TP+FN)(FN+TN)+(TP+FP)*(FP+TN)] A function of total accuracy and random accuracy F-Measure2*TP/(2*TP+FP+FN); a function of sensitivity and precision

Sign Test n = number of cross-validation intervals C = number of cross-validation intervals with testing accuracy ≥ 0.5 The probability of observing c or more cross- validation intervals with testing accuracy ≥ 0.5 if each case were actually classified randomly

The Problem of Alcoholism A Case Study

Genes Associated With Alcoholism ADH enzymes ALDH2 enzyme Alcohol Acetaldehyd e Acetate ADH (alcohol dehydrogenase) and ALDH2 (acetaldehyde dehydrogenase 2) genes are associated with alcoholism involved in alcohol metabolism

ADH Genes ADH7ADH6ADH4ADH5ADH1BADH1AADH1C 5’ 3’ Class IV Class I Class VClass IIClass III 370 kb Chromosome 4

Taste Receptors and Aversion to Alcohol PTC TAS2R38 TastersNon-Tasters Alcohol Tastes BitterAlcohol Tastes Sweet Drink Less AlcoholDrink More Alcohol a person must be willing to drink in order to be an alcoholic TAS2R38 affects the amount of alcohol a person is willing to drink therefore, it is related to alcoholism, although no direct association has been found we hope to provide a direct link between TAS2R38 and alcoholism, by demonstrating that it acts epistatically with other genes associated with alcoholism

Actual Analysis

Data A sample of cases and controls (alcoholics and non-alcoholics) from three East Asian populations: the Ami, Atayal, and Taiwanese Genotyped for 98 markers within several genes: ALDH2, all ADH genes, and 2 taste receptor genes, TAS2R16 and TAS2R38 (PTC)

Computational Limitations 1. The software package has a problem reading missing data I was forced to use only complete records, dwindling my (already small) sample to 79 complete records

Computational Limitations 2. The computation time is way too long for higher order models, especially for high numbers of attributes I was advised to restrict my attributes to markers within ADHIC, and the 2 taste receptor genes, which left me with 36 attributes I considered models only up to order 4

Summary of Results: All Populations OrderModelTraining Bal. Acc.Testing Bal. Acc.Sign Test (p)CV Consistency 1X.04..ADH1C.dwstrm.Te (1.0000)5/10 2 X.07..TAS2R16.C_11431 X.04..ADH1C.dwstrm.Te (0.9453)6/10 3 X.07..TAS2R16.C_11431 X.04..ADH1C.dwstrm.Te X.04..ADH1C.rs (0.9990)4/10 4 X.07..TAS2R16.C_11431 X.07..PTC.C_ _1 X.07..PTC.C_ _1 X.04..ADH1C.dwstrm.Te (0.9893)6/10 Instances: 79Attributes: 36Ratio:

Summary of Results: Ami OrderModelTraining Bal. Acc.Testing Bal. Acc.Sign Test (p)CV Consistency 1X.07..TAS2R16.C_ (0.6230)5/10 2 X.07..TAS2R16.C_11431 X.04..ADH1C.C_ (0.9893)3/10 3 X.07..TAS2R16.C_11431 X.07..PTC.C_ _1 X.04..ADH1C.C_ (0.0010)10/10 4 X.07..TAS2R16.C_11431 X.07..TAS2R16.C_ X.07..PTC.C_ _1 X.04..ADH1C.C_ (0.0547)9/10 Instances: 30Attributes: 36Ratio:

Cross Validation Statistics Set MeasureTrainingTesting Balanced Accuracy Accuracy Sensitivity11 Specificity Odds Ratio∞∞ χ (p < ) (p = ) Precision Kappa F-Measure Sign Test: 10 (p = ) Cross-validation Consistency: 10/10

Whole Dataset Statistics: Training Balanced Accuracy: Training Accuracy: Training Sensitivity: Training Specificity: Training Odds Ratio: ∞ Training Χ²: (p < ) Training Precision: Training Kappa: Training F-Measure:

Graphical Model

Classification Rules X.07..TAS2R16.C_11431X.07..PTC.C_ _1X.04..ADH1C.C_ Class IF A\A AND C\G AND C\C THEN 0 A\AC\GC\T1 A\AC\GT\T0 A\AG\GC\C0 A\AG\GC\T0 A\AG\GT\T1 A\GC\CC\T1 A\GC\GC\C0 A\GC\GC\T0 A\GC\GT\T0 A\GG\GC\C1 A\GG\GC\T1 A\GG\GT\T0 G\GC\GC\T1 G\G C\C0 G\G C\T1 G\G T\T1

Locus Dendrogram

Future Work Simulations to calculate the power of MDR, especially in relation to sample size Comparison of MDR with logistic regression, and other proposed methods to detect epistasis, with respect to the current data set and simulated data Research how different methods to search the sample space can be incorporated into MDR implementation to improve computational feasibility