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Modeling Gene Interactions in Disease

Modeling Gene Interactions in Disease. CS 686 Bioinformatics. Some Definitions. Data mining : extracting hidden patterns and useful info from large data sets. Ex- clustering, machine learning. Should not be:

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Modeling Gene Interactions in Disease

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  1. Modeling Gene Interactions in Disease CS 686 Bioinformatics

  2. Some Definitions • Data mining: extracting hidden patterns and useful info from large data sets. Ex- clustering, machine learning. Should not be: "Torturing data until it confesses ... and if you torture it enough, it will confess to anything"  - Jeff Jonas, IBM • Machine learning: the ability of a program to learn from experience. Ex- neural networks, decision trees, rule-based methods, MDR.

  3. Methods • Regression methods: modeling the relationship between a dependent variable and one of more independent variables. • Data mining methods: Search the space of possible models efficiently. Better with non-linear and high-dimensional data, or data with many potential interactions. • Exhaustive Search: search all possible models for the best one.

  4. Linear regression • Relates outcome as a linear combination of the parameters (but not necessarily of the independent variables). • Ex: Let y = incidence of disease, n data points. Independent variables A,B 1) yi = b0 + b1Ai + εi, i = 1,…,n 2) yi = b0 + b2(Bi)2 + εi, i = 1,…,n where b0, b1,b2 = parameters, εi is error term. In both of these examples, the disease is modeled as linear in the parameters, although it is quadratic in variable B

  5. Linear regression Given a sample, we estimate the params (ex: can use least squares) to arrive at the linear regression model: [1]

  6. Multiple regression • Relates the the probability of an event to a linear combination of predictor variables. • Ex: Let y = incidence of disease, n data points. Independent variables x1, x2 yi = b0 + b1xi1 + b2xi2 + … + bpxip + εi, i = 1,…,n Best-fit line: For each unit increase in xip, is expected to increase by .

  7. Logistic regression[1] • Often used when the outcome is binary, relates the log-odds of the probability of an event to a linear combination of predictor variables. Ex: • ln(p/(1 – p)) = α + βxB + γxC + ixBxC, where xBand xC are measured binary indicator variables, and regression coefficients βand y represent main effects, i represents interaction.

  8. Other statistical methods [1] • Bayesian model selection: a statistical approach incorporating both prior distributions for parameters and observed data into the model. • Maximum likelihood: a statistical method used to make inferences about the combination of parameter values resulting in the highest probability of obtaining the observed data

  9. Modeling Terminology[1] • Saturated: a statistical model that is as full as possible (saturated) with parameters. • Marginal effects: the effects of one parameter averaged over the possible values taken by other parameters • Entropy: the uncertainty associated with a random variable

  10. Modeling Terminology[1] • Cross-validation: partitioning a data set into n subsets, then using each subset in turn as the test set while using the other n-1 to train. • Overfitting: a model that provides a good fit to a specific data set but generalizes poorly. • Marginal effects: the effects of one parameter averaged over the possible values taken by other parameters.

  11. Marginal Effects [2] Marginal penetrance: Ex: The probability P(D|A=Aa), irrespective of what value B has Table II. Penetrance values for combinations of genotypes from two single  nucleotide polymorphisms exhibiting interactions in the absence of independent main effects Genotype Genotype Marginal penetrance B AA (0.25)      Aa (0.50) aa (0.25) BB (0.25)         0          1          0 0.5 Bb (0.50)        1          0          1 0.5 bb (0.25)         0          1          0 0.5 Marginal          0.5          0.5          0.5 penetrance A Genotype frequencies are given in parentheses Marginal penetrance values for the A, B genotypes.

  12. Weka [3] • A collection of visualization tools and algorithms for data analysis and predictive modeling. • Preprocessing tools for reading data in a variety of formats and transforming it. • Classification algorithms include regression, neural network, support vector machine, decision tree. Display includes ROC curves • Clustering: k-means, expectation maximization • Visualization includes scatter-plot, bar graph

  13. References • Cordell, 2009, Detecting gene–gene interactions that underlie human diseases. Nature Review Genetics • McKinney et al, 2006, Machine Learning for Detecting Gene-Gene Interactions, A Review. Biomedical Genomics and Proteomics • Weka site: http://www.cs.waikato.ac.nz/ml/weka

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