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Bayesian Models for Gene expression With DNA Microarray Data

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keitha
24 diapositives · 386 Views · Oct 23, 2014

This presentation discusses the development of a Bayesian model designed to compare gene expression levels in normal and tumor tissues using DNA microarray data. The goals include identifying genes that best distinguish between tissue types and creating model assessment techniques to evaluate competing models. Key components include the general model framework, gene selection algorithms, and prior distributions. Additionally, the use of likelihood functions and the L measure for model assessment is emphasized, alongside computational methods such as MCMC for effective evaluation.

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  1. Bayesian Models for Gene expression With DNA Microarray Data Joseph G. Ibrahim, Ming-Hui Chen, and Robert J. Gray Presented by Yong Zhang

  2. Goals: • To build a model to compare between normal and tumor tissues and to find the genes that best distinguish between tissue types. • to develop model assessment techniques so as to assess the fit of a class of competing models.

  3. Outline General Model Gene Selection Algo. Prior Distributions L measures(assessment) example

  4. Data structure x: the expression level for a given gene C0: threshold value for which a gene is considered as not expressed Let p = P(x=c0), then where y is the continuous part for x.

  5. j=1, 2 index the tissue type(normal vs. tumor) • i=1,2,…nj, ith individual • g=1,…G, gth gene • xjig : the gene expression mixture random variable for the jth tissue type for the ith individual and the gth gene.

  6. The General Model • Assume • δjig = 1(xjig=c0) • pjg=P(xjig=c0)=P(δjig = 1)

  7. =(,2,p) • Data D=(x111,…x2,n2,G, ) • Likelihood function for : L(|D)= In order to findwhich genes best discriminate between the normal and tumor tissues, let

  8. Then we set such that we can use g to judge them.

  9. Prior Distributions • jg2 ~ Inverse Gamma(aj0,bj0) • j0 ~ N(mj0,vj02), j=1,2

  10. bj0 ~ gamma(qj0,tj0) • ejg ~ N(uj0,kj0wj02)

  11. Gene Selection Algo. • For each gene, compute g and • Select a “threshold” value, say r0, to decide which genes are different. If • Once the gth genes are declared different, set 1g  2g, otherwise set 1g =2g  g , where g is treated as unknown.

  12. Gene Selection Algo. 4) Create several submodels using several values of r0. 5) Use L measure to decide which submodel is the best one(smallest L measure).

  13. The properties of this approach • Model the gene expression level as a mixture random variable. • Use a lognormal model for the continuous part of the mixture. • Use L measure statistic for evaluating models.

  14. L measure for model assessment • It relies on the notion of an imaginary replicate experiment. • Let z= (z111, …, z2,n2,G) denote future values of a replicate experiment.

  15. L measure is the expected squared Euclidean distance between x and z, A more general is The r.s. of the last formula can be got by MCMC.

  16. Computational Algo.(MCMC) 1.

  17. For 1–4 and 6, the generation is straightforward. • For 5, we can use an adaptive rejection algorithm(Gilks and Wild, 1992) because the corresponding conditional posterior densities are log-concave.

  18. Discussion • That model development and prior distributions in this paper can be easily extended to handle three or more tissue types. • More general classes of priors • The gene selection criterions