Table 5

d _il

1,2,...,G

Number of genes in a dataset with FDR lower than the threshold l

EL _g

(0,Inf)

Expected value of the log likelihood with respect to the FDR threshold

f _il

1,2,...,d _il

Number of false positives using the FDR threshold l

F _gi

(0,1)

Gene-specific false discovery rate in dataset i: proportion of false positives among the significant calls

FDR _g

(0,1)

Gene-specific false discovery rate for having consistently differentially expressed patterns among the datasets studied

g

1,2,...,G

Index for a gene from the union of gene sets across all datasets

h

1,2,...,H _i

Index for fold change comparison between a case and a control from a dataset, where m _i * n _i = H _i

i

1,2,...,D

Index for a gene expression microarray dataset (consists of m _i cases and n _i controls)

l

(0,1)

FDR threshold used to enumerate number of genes with FDR lower than this threshold in a dataset and to estimate the number of false positives under this threshold

L(r _gl |Data)

(0,1)

Gene- and FDR threshold- specific likelihood of observing the differential expressed pattern among the datasets

${M^{\overline{up}}}_i\left({M^{\overline{down}}}_i\right)$

1,2,...,G

number of genes that are not up(not down)-regulated in dataset i

Q _gl

(0,Inf)

Minus log likelihood

${{\widehat{r}}^{up}}_{il}({{\widehat{r}}^{down}}_{il}\mathsf{\text{ )}}$

(0,1)

False positive rate: the probability of a non-up-regulated (non-down-regulated) gene being falsely called as over-expressed (under-expressed)

${\delta }_{gil}^{up}$ (or ${\delta }_{gil}^{down}$)

0[1]

Binary variable indicating gene g is identified as up(or down)-regulated in dataset i for threshold l

γ _gih

1,2,...,G

rank of fold change for gene g in the h^th comparison of dataset i