Anders Sjögren, Chalmers

Weighted Analysis of Microarray Experiments


Abstract

The nature of data from DNA microarray experiments brings interesting
statistical challenges. Typically, the expressions of thousands of
genes are measured simultaneously in a relatively small number of
biological samples and one test is performed for each gene, e.g. to
identify genes with different expression under different
conditions. An important challenge is then to use the structure of the
data to improve the performance of the individual tests.

Previously, the vast number of measured genes have been utilised to
identify a prior distribution for the variance of each gene, in effect
moderating the individual variance estimates. In [1] and [2] we
complement this by suggesting that data from different arrays may have
different variability, e.g. due to random deviations in quality from
some of the measurement steps.  Furthermore, data from arrays may be
correlated, e.g. due to similarities in the quality deviations. The
result is a generalised linear model with common covariance structure
for the different genes and a prior distribution for gene-wise
variance scales, giving rise to weighted moderated F-tests. Estimation
of the covariance structure is feasible under certain conditions and
the estimate is then precise thanks to the large number of genes.

Results on real data indicate that correlations often exist between
arrays and that inference results from procedures not taking this into
account may be biased. In particular, resample based simulations show
that the distribution of p-values under the null hypothesis often
deviate strongly from the expected uniform, which is largely corrected
in the proposed model. In case of a large number of strongly
differentially expressed genes, the proposed method will give
conservative p-values. Therefore, trusting microarray p-values seems
questionable at the current state of the art. Similar resample based
simulations with real noise and synthetic signal indicate that the
ranking according to the novel method is more powerful than the
studied alternatives.

References:

[1] Erik Kristiansson*, Anders Sjögren*, Mats Rudemo, and
Olle Nerman (2005) Weighted Analysis of Paired Microarray Experiments,
Statistical Applications in Genetics and Molecular Biology: 4(1),
Article 30.

[2] Erik Kristiansson , Anders Sjögren, Mats Rudemo, and
Olle Nerman (2006) Quality Influenced Analysis of General Paired
Microarray Experiments, Statistical Applications in Genetics and
Molecular Biology: 5(1), Article 10.