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A Statistical Framework for
Integrating Different Microarray
Data Sets in Differential
Expression Analysis
Yinglei Lai, Ph.D.
Department of Statistics & Biostatistics Center
The George Washington University
The 5th Annual Rocky Mountain Bioinformatics Meeting
Supported by NIH/NIDDK DK-75004
Data Sets
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Huntington’s disease data sets
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Borovecki et al. (2005) PNAS
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14 healthy and 17 HD
Affymetrix U133A GeneChip (22,283 genes)
Amersham CodeLink Uniset Human I and II bioarrays (20,289 genes)
8597 common genes after thresholding and filtering
Can we integrate two data sets for the same study to achieve
an improved detection of differential expression?
A Framework
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Univariate test for detecting differential expression
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Mixture model based tests for concordance/discordance
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Student’s t-test
Obtain a pair of (one-sided) p-values for each gene
Transform (inverse normal c.d.f.) p-values into z-scores
A three-component normal-mixture model (Lai et al., 2007)
H0: complete concordance vs. H1: partial concordance/discordance
H0: complete discordance vs. H1: partial concordance/discordance
Mixture model based integration of a pair of z-scores
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If complete discordance, then data integration discouraged
If partial/complete concordance, then data integration considered
Complete/Partial Concordance/Discordance
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CC: 0.8[N(0,1), N(0,1)] + 0.1[N(-2,1), N(-2,1)] + 0.1[N(2,1), N(2,1)]
PCD: 0.8[N(0,1), N(0,1)] + 0.05[N(-2,1), N(-2,1)] + 0.05[N(2,1), N(2,1)] +
0.05[N(-2,1), N(2,1)] + 0.05[N(2,1), N(-2,1)]
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CD: [0.8N(0,1) + 0.1N(-2,1) + 0.1N(2,1), 0.8N(0,1) + 0.1N(-2,1) + 0.1N(2,1)]
An Integrative Score for Prioritizing Genes
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P( concordant differential expression |
observed pair of z-scores and fitted model )
= [ Pm( observed pair of z-scores both up-regulated )
+ Pm( observed pair of z-scores both down-regulated ) ]
/ Pm( observed pair of z-scores )
Results (HD data sets)
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Both complete concordance (CC) and complete discordance (CD) rejected
at p-value < 0.001