pre-icm int. convention , 2008

29
Pre-ICM Int. Convention, 2008 By Naveen K. Bansal Marquette University Milwaukee, Wisconsin(USA) Email: [email protected] http://www.mscs.mu.edu/~naveen/ With Dr. Klaus Miescke University of Illinois-Chicago Illinois (USA) A Bayesian decision theoretic solution to the problem related to microarray data with consideration of intra-correlation among the affected genes

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A Bayesian decision theoretic solution to the problem related to microarray data with consideration of intra-correlation among the affected genes. By Naveen K. Bansal Marquette University Milwaukee, Wisconsin(USA) Email: [email protected] http://www.mscs.mu.edu/~naveen/ With - PowerPoint PPT Presentation

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Page 1: Pre-ICM Int. Convention , 2008

Pre-ICM Int. Convention, 2008

ByNaveen K. Bansal

Marquette UniversityMilwaukee, Wisconsin(USA)

Email: [email protected]://www.mscs.mu.edu/~naveen/

WithDr. Klaus Miescke

University of Illinois-ChicagoIllinois (USA)

A Bayesian decision theoretic solution to the problem related to microarray data with consideration of intra-correlation among the affected genes

Page 2: Pre-ICM Int. Convention , 2008

When the genes are altered under adverse condition, such as cancer, the affected genes show under or over expression in a microarray.

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The objective is to find the genes with under expressions and genes with over expressions.

Pre-ICM Int. Convention, 2008

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Directional Error (Type III error):

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Main points of these work is that if the objective is to find the true Direction of the alternative after rejecting the null, then a Type III error must be controlled instead of Type I error.

Type III error is defined as P( false directional error if the null is rejected). The traditional method does not control the directional error. For example,

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Pre-ICM Int. Convention, 2008

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Pre-ICM Int. Convention, 2008

Page 5: Pre-ICM Int. Convention , 2008

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Page 7: Pre-ICM Int. Convention , 2008

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Page 8: Pre-ICM Int. Convention , 2008

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Pre-ICM Int. Convention, 2008

Page 9: Pre-ICM Int. Convention , 2008

An Application:

An experiment was conducted to see the effect of a sequence knockdown from non-coding genes. Hypothesis was that this knockdown will cause the overexpression of the mRNAs of the coding genes. The implication of this is that this will shows how the non-coding genes interact with coding genes. In other words, non-coding genes also play a part in protein synthesis.

Here it can be assumed that that the effect of knockdown on the coding genes (if there is any) would be mostly overexpression of mRNAs than underexpression of mRNAs. The objective would be to detect as many of overexpressed genes as possible.

Pre-ICM Int. Convention, 2008

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Page 11: Pre-ICM Int. Convention , 2008

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Page 12: Pre-ICM Int. Convention , 2008

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Page 13: Pre-ICM Int. Convention , 2008

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Pre-ICM Int. Convention, 2008

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This theorem and our previous discussion on the Bayes decision rule implies that under the independent hypotheses testing setting, the Bayes rule obtained from a single test problem

Which minimizes the average expected false discoveries, can be used under multiple hypotheses problem. The false discovery rates of this procedure can be obtained by computing the posterior probabilities.

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Pre-ICM Int. Convention, 2008

Page 15: Pre-ICM Int. Convention , 2008

Pre-ICM Int. Convention, 2008

Posterior False Discovery Rate

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Page 16: Pre-ICM Int. Convention , 2008

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Page 17: Pre-ICM Int. Convention , 2008

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Page 18: Pre-ICM Int. Convention , 2008

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Page 19: Pre-ICM Int. Convention , 2008

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Page 20: Pre-ICM Int. Convention , 2008

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Pre-ICM Int. Convention, 2008

Page 21: Pre-ICM Int. Convention , 2008

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Pre-ICM Int. Convention, 2008

Page 22: Pre-ICM Int. Convention , 2008

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Pre-ICM Int. Convention, 2008

Page 23: Pre-ICM Int. Convention , 2008

Power Comparison:

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Pre-ICM Int. Convention, 2008

Page 24: Pre-ICM Int. Convention , 2008

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Pre-ICM Int. Convention, 2008

Page 25: Pre-ICM Int. Convention , 2008

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Pre-ICM Int. Convention, 2008

Page 26: Pre-ICM Int. Convention , 2008

Another Approach:

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Pre-ICM Int. Convention, 2008

Page 27: Pre-ICM Int. Convention , 2008

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Pre-ICM Int. Convention, 2008

Page 28: Pre-ICM Int. Convention , 2008

Pre-ICM Int. Convention, 2008

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Page 29: Pre-ICM Int. Convention , 2008

Pre-ICM Int. Convention, 2008