BACKGROUND
investigating transcription profile by microarray technology has been one of the most promising genomic approaches in the last decade.
thousands of microarray experiments were performed for this purpose and their data made available through databases such as gene expression omnibus, arrayexpress and stanford microarray database  <cit> .
to utilize this massive amount of information, investigators have developed different meta-analysis techniques--parametric approaches such as t-statistic  <cit> ; fisher's inverse chi-square approach  <cit> ; bayesian  <cit> , and non-parametric approaches  <cit> .
however, these approaches still face many challenges in combining data from different sources  <cit> .
for example, parametric bayesian models used in meta-analysis  <cit>  are not appropriate due to the small sample size for many datasets, as suggested by kong et al.
<cit> .
on the other hand, non-parametric methods such as rankprod-based meta-analysis approach   <cit>  can be significantly influenced by the size of the dataset and hence biased toward genes that are only differentially expressed in a dataset with a large number of samples--an undesirable outcome for studies where the objective is to find genes with differentially expressed patterns common across the datasets.
the method of rhodes et al.
<cit> , which we refer to as meta-profile, combines a parametric and non-parametric approach and gives equal weight to each dataset when counting the number of times a gene is identified as differentially expressed in all datasets.
however, this is a significant simplification because the resulting power to identify differentially expressed genes and type i error rate  vary by dataset according to sample size and proportion of genes truly differentially expressed  <cit> .
the challenges faced by these methods are particularly evident when identifying genes differentially expressed across different cancer types by pooling datasets from various sources.
these datasets typically have small sample sizes  <cit>  and the analyses are influenced by cancer-type and/or cancer-subtype specific effects  <cit> .
in addition, some methods such as meta-rankprod do not handle varying numbers of differentially expressed genes from different datasets--an issue that needs to be addressed for a meta-analysis approach to be robust.
the objective of this study is to develop a robust meta-analysis approach to identify genes with consistent differential expression patterns across different datasets.
in our study, we combined fdr and the non-parametric rankprod approach to estimate the type i error rate in each dataset.
the estimated rates from all datasets were combined using a bernoulli likelihood to identify genes with common expression pattern.
the robustness of this approach in obtaining high statistical power was shown by simulation studies.
we then applied the method to analyze different microarray data that compared gene expressions between metastatic and primary cancers and identified a core gene set that is critical to cancer metastasis across different cancer types.
our analysis identified many genes annotated in pathways that are related to metastasis, as well as novel genes that have not been shown to associate with, but may play roles in, metastasis.
further sensitivity analysis indicates that the method is robust and can be applied to other datasets for similar analyses.
RESULTS
consistent differential expression pattern
the key components of cdep are the application of: 1) consistent fdr across datasets to identify significant genes  <cit> ; and 2) non-parametric rank product  approach to identify differentially expressed genes from microarray experiments  <cit> .
by first using a consistent fdr to estimate the type i error rates in each dataset, cdep avoids overemphasizing datasets with large sample sizes--a drawback of a previous rankprod-based meta-analysis approach   <cit> .
cdep then uses the error rates from all datasets to identify genes with consistent differential expression patterns.
figure  <dig> shows the workflow of cdep.
specifically, let dataset i, i =  <dig>   <dig>  ..., d, consist of gene expression levels for mi and ni samples in each of two conditions, respectively .
for dataset i, the geometric mean rank of gene g =  <dig>   <dig>  ..., g was computed across all mini = hi pairwise comparisons for up-regulation:
γ¯giup=∏h=1hiγgihup1∕hi
and down-regulation:
γ¯gidown=∏h=1hiγgihdown1∕hi
where γgih is the rank of fold change for gene g in the hth comparison of dataset i, h =  <dig>   <dig>  ..., hi.
genes with the smallest rankprod values  are more likely to be the differentially expressed genes.
we then computed the rankprod p-values and fdrs for up- and down-regulations for each gene in every dataset  <cit> .
briefly, we used permutation of the sample labels  to estimate false positives and the p-value by counting the number of times we observed the permutations' rankprod values smaller or equal to the experiment's rankprod value.
the fdr of a gene was then estimated by dividing the p-value by the rank of the rankprod value  <cit> .
each gene in every dataset was thus associated with an fdr, fgiup, for being up-regulated.
for genes not present in the platform of a dataset, the median fdr value computed for that dataset was assigned.
this computation in cdep was performed using the bioconductor  <cit>  package rankprod  <cit> , as hong and breitling  <cit>  indicated that rankprod is more reliable than other existing approaches .
the fdr threshold  is defined as the proportion of false positives among the genes declared to be positives for each dataset.
given an fdr threshold , we counted the number of genes identified to be
up-regulated:
dilup= ∑gi
and down-regulated:
dildown= ∑gi
therefore, the number of false positives in a dataset could be estimated as filup≈l*dupil.
to estimate the proportion of genes that are up-regulated, non-differentially expressed, and down-regulated, we used a beta mixture to model the genes' p-values for over -expression in each dataset .
we adopted the beta mixture model because the p-values calculated from our non-parametric approach do not have a uniform distribution for non-differentially expressed genes , in contrast to a previous mixture model based on this assumption  <cit> .
the beta mixture model and the estimation of the proportion of differentially expressed genes used the markov chain monte carlo  technique implemented in the bugs program  <cit> .
our implementation uses winbugs  <cit>  on the windows platform, but openbugs  <cit>  can be used on linux or mac platforms .
for each dataset, the false positive rate is defined as the probability of a non-up-regulated  gene being falsely called as over-expressed : r^upil≈filup∕mūp¯i, where mup¯i  are the number of genes that are not up-regulated in dataset i respectively, estimated by the beta mixture model.
based on this rate and using independent bernoulli distributions, we calculated the likelihood of a gene to be falsely identified as over or under-expressed among the datasets for each fdr threshold l, that is, the likelihood for false positives among the significant genes identified as
up-regulated:
l=∏i=1drilup
and down-regulated:
l=∏i=1drildown
where the binary variable δgilup  indicates whether gene g is identified to be up-regulated in dataset i for threshold l. to prevent underflow during computation, we worked with the minus log likelihood, q, e.g.
for up-regulation qupgl=-ln.
we took into consideration of multiple fdr thresholds l by specifying a probability density function  for l, p, l∈ and using the expected value of q to assess whether the gene is consistently over-expressed among the datasets.
in this assessment, low l values were emphasized because low fdr represents a higher proportion of true positives, and we used the linear decreasing function: p = -2l +  <dig>  the expected log likelihood across the fdr threshold is: elupg= ∫ 01qgluppdl, which was approximated by discretizing the range of fdr value  into one hundred bins with equal width and using the rectangular rule.
the same procedure was also performed for down-regulation.
the procedure was evaluated by estimating the false discovery rate  of observing the above expected log likelihood.
here, the fdrg is the proportion of false positives among the genes identified to be consistently differentially expressed.
the "null log likelihood" was computed by permuting the fgiup and fgidown values relative to the genes within each dataset and performing the same above procedures to calculate the expected value of the "null log likelihood" in each permutation b for every gene .
in b permutations, the fdrg of a gene could be determined as:
fdrg=∑b∑g′i∑g′i
the robustness of cdep in distinguishing different gene expression patterns is shown in figure  <dig> where the minus log likelihood value q was plotted against l. genes that are not differentially expressed in all datasets  have the lowest q values, while genes that are differentially expressed only in some datasets  have higher q values, and genes that are differentially expressed in all the datasets  have the highest q values.
for gn, the q values increase slightly with l. this is because when l increases, the likelihood value decreases as more gn are falsely called differentially expressed.
moreover, even at high l many gn are not declared differentially expressed.
on the other hand, the q values of both gc and gm decrease when l increases.
as l increases, r and the likelihood  increase, giving rise to a decreasing q. note that the q values for all  <dig> types of genes go to zero when l =  <dig>  this is because, in this situation, all genes in the array would be declared as differentially expressed and both r and l have values of one.
figure  <dig> shows the expected minus log likelihood  for the three types of genes, indicating cdep is robust in identifying genes that show common differential expression pattern across different datasets.
these genes have higher el values than the other two types of genes.
comparisons with other approaches
we compared cdep with meta-profile and meta-rankprod in a simulation study.
briefly, meta-profile is based on the number of times a gene is declared differentially expressed among the datasets, and meta-rankprod uses the rank product among all datasets.
both approaches use permutation to estimate the false discovery rate for the genes as being differentially expressed consistently among the datasets.
simulation scenarios were determined by three key parameters: the proportion of differentially expressed genes that are dataset-specific , the proportion of genes that are consistently differently expressed , and the mean difference between the expression values in the two conditions being compared  .
table  <dig> reports the statistical power and type i error rate of the three meta-analysis approaches, where statistical power is defined as the sensitivity of detecting genes that have consistent differential expression patterns across datasets.
the results show that raising fdr increases the statistical power and type i error rate for all three approaches.
increasing the mean difference  between the two conditions  of the differentially expressed genes also improves sensitivity.
in addition, the impact of the proportion of gm on cdep and meta-rankprod is obvious: the higher the proportion of gm , the lower the statistical power and type i error rate.
the reason is that obtaining fdr for these two approaches requires permutation and recalculation of elgb and rpgb.
after permutation, original gm genes would act as gc in cdep and gn in meta-rankprod.
as a result, when there is a higher proportion of gm from the datasets, including these genes to estimate fdr would potentially lead to over-estimation because the variance of these genes is different from the non-differentially expressed genes  <cit> .
therefore, under the same fdr, the statistical power and the type i error would be lower for higher q in cdep and meta-rankprod, especially when comparing q =  <dig>  with q =  <dig> .
in contrast, meta-profile takes a relatively conservative approach, and is insensitive to genes that do not have consistent differential expression patterns.
however, the tradeoff is the loss in statistical power.
as shown in table  <dig>  even though the type i error rate is amongst the lowest of the three approaches, the meta-profile method has the lowest statistical power.
overall, cdep emerges as a robust meta-analysis method that obtains comparably high statistical power while maintaining low type i error rate under different simulated conditions .
p is the proportion of genes differentially expressed only in a certain dataset, and q is the proportion of consistently differentially expressed genes; Δ is the simulated mean difference between the expression values in case and control condition for the differentially expressed genes.
fdr is the proportion of false positives among the genes identified to be consistently differentially expressed across all datasets.
the results in the table are the mean values of  <dig> different simulated datasets.
additional simulation results can be found in additional file  <dig>
using cdep to identify a core gene set that is differentially expressed in metastatic cancer
we used cdep to investigate the hypothesis that there exists a core gene set differentially expressed consistently in different types of metastatic cancer cells.
six different types of cancer were investigated for this purpose   <cit> .
totally there are  <dig> samples, of which  <dig> are from primary and  <dig> from metastatic cancer, respectively.
the diversity of these datasets  make them ideal for assessing the robustness of cdep and exploring our hypothesis.
we used rma  <cit>  to pre-process the raw data for each dataset, and the median expression value of the probesets matching to the same entrez gene id was used as the expression level for the gene.
raw data were downloaded from the ncbi geo database.
*oscc = oral squamous cell carcinoma; #rcc = renal cell carcinoma
at fdr ≤  <dig> , cdep identified  <dig> genes that are differentially expressed consistently between the primary and metastatic cancer conditions across different cancer types.
out of these  <dig> genes,  <dig> were up-regulated and  <dig> down-regulated .
table  <dig> shows the  <dig> most significantly up- and down-regulated genes identified.
using the same fdr criterion, we also performed meta-analysis by meta-profile and meta-rankprod.
both cdep and meta-rankprod recovered the same two significant genes  identified by meta-profile, and  <dig> genes were identified by both cdep and meta-rankprod .
a list of these genes identified by the three methods can be found in additional file  <dig>  these results further support using cdep for meta-analysis to select candidate genes: meta-profile has insufficient statistical power, and meta-rankprod tends to have high false positive rates.
on the other hand, cdep has the advantages of maintaining statistical power and keeping low false positive rates for identifying genes that are differentially expressed consistently.
the functional annotation of the  <dig> genes identified by cdep is consistent with previous findings that many of them are involved in cancer metastasis.
for instance, gpnmb overexpresses in a breast cancer cell line that could aggressively metastasize to bone  <cit> , and spp1's expression level  is elevated in a variety of metastatic cancers  <cit> , including colon cancer  <cit> , hepatocellular carcinoma  <cit> , and gastric cancer  <cit> .
among the down-regulated genes, the expression level of serpinb <dig> is negatively associated with the depth of invasion, metastasis, and tnm stage in gastric cancer  <cit> .
interestingly, serpinb <dig> also inhibits invasion and metastasis of epithelial ovarian cancer, which suggests its down-regulation could promote metastasis  <cit> .
mx <dig> was also predicted to have an inhibitory effect on tumor cell motility and invasion, an essential attribute for metastatic behavior.
while most of these previous findings are specific to different cancer types, analysis from cdep indicates that these genes could play important roles in metastatic mechanism common to all types of cancers.
the function of these  <dig> genes were further investigated by david  <cit>  through gene set enrichment analysis, using all genes present in the microarray platform as background.
the results indicate that the up-regulated genes in metastatic cancer cells are enriched in extracellular matrix  receptor interaction, focal adhesion, and angiogenesis, while down-regulated genes are enriched in genes functioning in immune and inflammatory response , and these include laminin, fibronectin, collagen, multimerin, caveolin, etc.. figure  <dig> shows the cdep identified genes mapped to the ecm receptor interaction and focal adhesion pathways.
it is widely recognized that these pathways contribute to the aggressiveness and the metastatic behavior of cancer cells  <cit> .
blood vessel development
the functional enrichment for the genes identified as consistently differentially expressed between primary and metastatic cancers.
not only had cdep identified genes known to be involved in cancer metastasis, but also it discovered novel genes that have not been implicated in metastatic mechanism.
for example, amigo <dig> , a gene identified as differentially expressed by only cdep out of the three meta-analysis approaches, is involved in anti-apoptosis  <cit>  and cell adhesion  <cit> , and cdep shows that this gene is up-regulated under metastases conditions.
gem is also differentially expressed consistently in metastatic cancer cells, even though no current literature indicates its role in metastasis.
however, the gene interacts with microtubule network  <cit>  and regulates actin dynamics  <cit> .
such activities are highly related to the migratory and invasive properties of cancer metastasis  <cit> .
another gene, cxcl <dig>  was shown to be consistently down-regulated by cdep analysis.
given that this gene has angiostatic property  <cit> , our results suggest that its down-regulation in metastatic cancer might interrupt the angiostasis process and promote angiogenesis--an important aspect of cancer metastasis.
discussion
meta-analysis provides a cost-efficient way to approach biological problems.
however, the heterogeneous nature of the data is always a significant challenge.
cdep aims to overcome this hurdle to identify genes that have a common differential expression pattern across different datasets.
we illustrated that cdep can:  obtain higher statistical power than existing meta-analysis approaches while maintaining low type i error rate in the simulation study, and  identify genes that are potentially involved in common metastatic behaviors and relevant biological pathways.
cdep borrows information from each dataset to identify genes differentially expressed consistently--a flexible approach that can be generalized to problems other than metastasis.
the high statistical power under diverse sets of parameters considered in the simulation study also suggests robustness of cdep to the diversity of data sources.
in cdep, the minus log likelihood q for different fdr values  was used because cdep does not intend to "filter out" genes in each dataset before performing meta-analysis.
this is in contrast to meta-profile where genes that only met the threshold  in each dataset were used for the meta-analysis.
in cdep, we emphasized low l values to calculate el and thus employed a linearly decreasing pdf for the log likelihood to: 1) balance the "filtering" behavior that would result from a convex decreasing pdf; and 2) emphasize small l. the pdf used in cdep outperformed meta-profile and meta-rankprod in obtaining high statistical power and lowering type i error rate.
cdep, meta-profile, and meta-rankprod use different permutation approaches to estimate fdrg.
meta-rankprod permutes gene expression values relative to the gene id for each array while meta-profile and cdep permute fdr relative to gene id for each dataset examined.
the null distribution produced by meta-rankprod permutation would lead to rpg representing genes that are non-differentially expressed in any dataset, while meta-profile and cdep would simply increase the proportion of genes that are differentially expressed in only a single dataset after permutation.
therefore, meta-rankprod tends to under-estimate fdrg, as it ignores genes that are only differentially expressed in a single dataset.
on the other hand, meta-profile and cdep would over-estimate fdrg because they have a higher proportion of gc genes in the null distribution compared to meta-rankprod.
even though inaccurate estimation of fdrg is inevitable due to the lack of prior knowledge about the proportion of genes only differentially expressed in one versus multiple datasets, both cdep and meta-profile employed a more conserved approach than meta-rankprod to obtain high precision.
CONCLUSIONS
cdep is a flexible meta-analysis approach that borrows information from each dataset in order to identify genes that are consistently differentially expressed.
cdep obtains higher statistical power than two existing approaches under a variety of scenarios considered in the simulation study, suggesting its robustness and insensitivity to data variation.
by application to metastatic cancer datasets as a case study, cdep allows identification of genes differentially expressed consistently in different types of metastatic cancer cells.
these identified genes could be further developed into universal biomarkers for cancer staging and diagnosis.

 investigating transcription profile by microarray technology has been one of the most promising genomic approaches in the last decade. thousands of microarray experiments were performed for this purpose and their data made available through databases such as gene expression omnibus, arrayexpress and stanford microarray database. to utilize this massive amount of information, investigators have developed different meta-analysis techniques--parametric approaches such as t-statistic; fisher's inverse chi-square approach; bayesian, and non-parametric approaches. however, these approaches still face many challenges in combining data from different sources. for example, parametric bayesian models used in meta-analysis are not appropriate due to the small sample size for many datasets, as suggested by kong et al.. on the other hand, non-parametric methods such as rankprod-based meta-analysis approach can be significantly influenced by the size of the dataset and hence biased toward genes that are only differentially expressed in a dataset with a large number of samples--an undesirable outcome for studies where the objective is to find genes with differentially expressed patterns common across the datasets. the method of rhodes et al., which we refer to as meta-profile, combines a parametric and non-parametric approach and gives equal weight to each dataset when counting the number of times a gene is identified as differentially expressed in all datasets. however, this is a significant simplification because the resulting power to identify differentially expressed genes and type i error rate vary by dataset according to sample size and proportion of genes truly differentially expressed. the challenges faced by these methods are particularly evident when identifying genes differentially expressed across different cancer types by pooling datasets from various sources. these datasets typically have small sample sizes and the analyses are influenced by cancer-type and/or cancer-subtype specific effects. in addition, some methods such as meta-rankprod do not handle varying numbers of differentially expressed genes from different datasets--an issue that needs to be addressed for a meta-analysis approach to be robust. the objective of this study is to develop a robust meta-analysis approach to identify genes with consistent differential expression patterns across different datasets. in our study, we combined fdr and the non-parametric rankprod approach to estimate the type i error rate in each dataset. the estimated rates from all datasets were combined using a bernoulli likelihood to identify genes with common expression pattern. the robustness of this approach in obtaining high statistical power was shown by simulation studies. we then applied the method to analyze different microarray data that compared gene expressions between metastatic and primary cancers and identified a core gene set that is critical to cancer metastasis across different cancer types. our analysis identified many genes annotated in pathways that are related to metastasis, as well as novel genes that have not been shown to associate with, but may play roles in, metastasis. further sensitivity analysis indicates that the method is robust and can be applied to other datasets for similar analyses.  consistent differential expression pattern the key components of cdep are the application of: 1) consistent fdr across datasets to identify significant genes; and 2) non-parametric rank product approach to identify differentially expressed genes from microarray experiments. by first using a consistent fdr to estimate the type i error rates in each dataset, cdep avoids overemphasizing datasets with large sample sizes--a drawback of a previous rankprod-based meta-analysis approach. cdep then uses the error rates from all datasets to identify genes with consistent differential expression patterns. figure shows the workflow of cdep. specifically, let dataset i, i =..., d, consist of gene expression levels for mi and ni samples in each of two conditions, respectively. for dataset i, the geometric mean rank of gene g =..., g was computed across all mini = hi pairwise comparisons for up-regulation: γ¯giup=∏h=1hiγgihup1∕hi and down-regulation: γ¯gidown=∏h=1hiγgihdown1∕hi where γgih is the rank of fold change for gene g in the hth comparison of dataset i, h =..., hi. genes with the smallest rankprod values are more likely to be the differentially expressed genes. we then computed the rankprod p-values and fdrs for up- and down-regulations for each gene in every dataset. briefly, we used permutation of the sample labels to estimate false positives and the p-value by counting the number of times we observed the permutations' rankprod values smaller or equal to the experiment's rankprod value. the fdr of a gene was then estimated by dividing the p-value by the rank of the rankprod value. each gene in every dataset was thus associated with an fdr, fgiup, for being up-regulated. for genes not present in the platform of a dataset, the median fdr value computed for that dataset was assigned. this computation in cdep was performed using the bioconductor package rankprod, as hong and breitling indicated that rankprod is more reliable than other existing approaches. the fdr threshold is defined as the proportion of false positives among the genes declared to be positives for each dataset. given an fdr threshold, we counted the number of genes identified to be up-regulated: dilup= ∑gi and down-regulated:  dildown= ∑gi therefore, the number of false positives in a dataset could be estimated as filup≈l*dupil. to estimate the proportion of genes that are up-regulated, non-differentially expressed, and down-regulated, we used a beta mixture to model the genes' p-values for over -expression in each dataset. we adopted the beta mixture model because the p-values calculated from our non-parametric approach do not have a uniform distribution for non-differentially expressed genes, in contrast to a previous mixture model based on this assumption. the beta mixture model and the estimation of the proportion of differentially expressed genes used the markov chain monte carlo technique implemented in the bugs program. our implementation uses winbugs on the windows platform, but openbugs can be used on linux or mac platforms. for each dataset, the false positive rate is defined as the probability of a non-up-regulated gene being falsely called as over-expressed: r^upil≈filup∕mūp¯i, where mup¯i are the number of genes that are not up-regulated in dataset i respectively, estimated by the beta mixture model. based on this rate and using independent bernoulli distributions, we calculated the likelihood of a gene to be falsely identified as over or under-expressed among the datasets for each fdr threshold l, that is, the likelihood for false positives among the significant genes identified as up-regulated: l=∏i=1drilup  and down-regulated: l=∏i=1drildown  where the binary variable δgilup indicates whether gene g is identified to be up-regulated in dataset i for threshold l. to prevent underflow during computation, we worked with the minus log likelihood, q, e.g. for up-regulation qupgl=-ln. we took into consideration of multiple fdr thresholds l by specifying a probability density function for l, p, l∈ and using the expected value of q to assess whether the gene is consistently over-expressed among the datasets. in this assessment, low l values were emphasized because low fdr represents a higher proportion of true positives, and we used the linear decreasing function: p = -2l + the expected log likelihood across the fdr threshold is: elupg= ∫ 01qgluppdl, which was approximated by discretizing the range of fdr value into one hundred bins with equal width and using the rectangular rule. the same procedure was also performed for down-regulation. the procedure was evaluated by estimating the false discovery rate of observing the above expected log likelihood. here, the fdrg is the proportion of false positives among the genes identified to be consistently differentially expressed. the "null log likelihood" was computed by permuting the fgiup and fgidown values relative to the genes within each dataset and performing the same above procedures to calculate the expected value of the "null log likelihood" in each permutation b for every gene. in b permutations, the fdrg of a gene could be determined as: fdrg=∑b∑g′i∑g′i the robustness of cdep in distinguishing different gene expression patterns is shown in figure where the minus log likelihood value q was plotted against l. genes that are not differentially expressed in all datasets have the lowest q values, while genes that are differentially expressed only in some datasets have higher q values, and genes that are differentially expressed in all the datasets have the highest q values. for gn, the q values increase slightly with l. this is because when l increases, the likelihood value decreases as more gn are falsely called differentially expressed. moreover, even at high l many gn are not declared differentially expressed. on the other hand, the q values of both gc and gm decrease when l increases. as l increases, r and the likelihood increase, giving rise to a decreasing q. note that the q values for all types of genes go to zero when l = this is because, in this situation, all genes in the array would be declared as differentially expressed and both r and l have values of one. figure shows the expected minus log likelihood for the three types of genes, indicating cdep is robust in identifying genes that show common differential expression pattern across different datasets. these genes have higher el values than the other two types of genes. comparisons with other approaches we compared cdep with meta-profile and meta-rankprod in a simulation study. briefly, meta-profile is based on the number of times a gene is declared differentially expressed among the datasets, and meta-rankprod uses the rank product among all datasets. both approaches use permutation to estimate the false discovery rate for the genes as being differentially expressed consistently among the datasets. simulation scenarios were determined by three key parameters: the proportion of differentially expressed genes that are dataset-specific, the proportion of genes that are consistently differently expressed, and the mean difference between the expression values in the two conditions being compared. table reports the statistical power and type i error rate of the three meta-analysis approaches, where statistical power is defined as the sensitivity of detecting genes that have consistent differential expression patterns across datasets. the results show that raising fdr increases the statistical power and type i error rate for all three approaches. increasing the mean difference between the two conditions of the differentially expressed genes also improves sensitivity. in addition, the impact of the proportion of gm on cdep and meta-rankprod is obvious: the higher the proportion of gm, the lower the statistical power and type i error rate. the reason is that obtaining fdr for these two approaches requires permutation and recalculation of elgb and rpgb. after permutation, original gm genes would act as gc in cdep and gn in meta-rankprod. as a result, when there is a higher proportion of gm from the datasets, including these genes to estimate fdr would potentially lead to over-estimation because the variance of these genes is different from the non-differentially expressed genes. therefore, under the same fdr, the statistical power and the type i error would be lower for higher q in cdep and meta-rankprod, especially when comparing q = with q =. in contrast, meta-profile takes a relatively conservative approach, and is insensitive to genes that do not have consistent differential expression patterns. however, the tradeoff is the loss in statistical power. as shown in table even though the type i error rate is amongst the lowest of the three approaches, the meta-profile method has the lowest statistical power. overall, cdep emerges as a robust meta-analysis method that obtains comparably high statistical power while maintaining low type i error rate under different simulated conditions. p is the proportion of genes differentially expressed only in a certain dataset, and q is the proportion of consistently differentially expressed genes; Δ is the simulated mean difference between the expression values in case and control condition for the differentially expressed genes. fdr is the proportion of false positives among the genes identified to be consistently differentially expressed across all datasets. the results in the table are the mean values of different simulated datasets. additional simulation results can be found in additional file using cdep to identify a core gene set that is differentially expressed in metastatic cancer we used cdep to investigate the hypothesis that there exists a core gene set differentially expressed consistently in different types of metastatic cancer cells. six different types of cancer were investigated for this purpose. totally there are samples, of which are from primary and from metastatic cancer, respectively. the diversity of these datasets make them ideal for assessing the robustness of cdep and exploring our hypothesis. we used rma to pre-process the raw data for each dataset, and the median expression value of the probesets matching to the same entrez gene id was used as the expression level for the gene. raw data were downloaded from the ncbi geo database. *oscc = oral squamous cell carcinoma; #rcc = renal cell carcinoma at fdr ≤, cdep identified genes that are differentially expressed consistently between the primary and metastatic cancer conditions across different cancer types. out of these genes, were up-regulated and down-regulated. table shows the most significantly up- and down-regulated genes identified. using the same fdr criterion, we also performed meta-analysis by meta-profile and meta-rankprod. both cdep and meta-rankprod recovered the same two significant genes identified by meta-profile, and genes were identified by both cdep and meta-rankprod. a list of these genes identified by the three methods can be found in additional file these results further support using cdep for meta-analysis to select candidate genes: meta-profile has insufficient statistical power, and meta-rankprod tends to have high false positive rates. on the other hand, cdep has the advantages of maintaining statistical power and keeping low false positive rates for identifying genes that are differentially expressed consistently. the functional annotation of the genes identified by cdep is consistent with previous findings that many of them are involved in cancer metastasis. for instance, gpnmb overexpresses in a breast cancer cell line that could aggressively metastasize to bone, and spp1's expression level is elevated in a variety of metastatic cancers, including colon cancer, hepatocellular carcinoma, and gastric cancer. among the down-regulated genes, the expression level of serpinb is negatively associated with the depth of invasion, metastasis, and tnm stage in gastric cancer. interestingly, serpinb also inhibits invasion and metastasis of epithelial ovarian cancer, which suggests its down-regulation could promote metastasis. mx was also predicted to have an inhibitory effect on tumor cell motility and invasion, an essential attribute for metastatic behavior. while most of these previous findings are specific to different cancer types, analysis from cdep indicates that these genes could play important roles in metastatic mechanism common to all types of cancers. the function of these genes were further investigated by david through gene set enrichment analysis, using all genes present in the microarray platform as background. the results indicate that the up-regulated genes in metastatic cancer cells are enriched in extracellular matrix receptor interaction, focal adhesion, and angiogenesis, while down-regulated genes are enriched in genes functioning in immune and inflammatory response, and these include laminin, fibronectin, collagen, multimerin, caveolin, etc.. figure shows the cdep identified genes mapped to the ecm receptor interaction and focal adhesion pathways. it is widely recognized that these pathways contribute to the aggressiveness and the metastatic behavior of cancer cells. blood vessel development the functional enrichment for the genes identified as consistently differentially expressed between primary and metastatic cancers. not only had cdep identified genes known to be involved in cancer metastasis, but also it discovered novel genes that have not been implicated in metastatic mechanism. for example, amigo, a gene identified as differentially expressed by only cdep out of the three meta-analysis approaches, is involved in anti-apoptosis and cell adhesion, and cdep shows that this gene is up-regulated under metastases conditions. gem is also differentially expressed consistently in metastatic cancer cells, even though no current literature indicates its role in metastasis. however, the gene interacts with microtubule network and regulates actin dynamics. such activities are highly related to the migratory and invasive properties of cancer metastasis. another gene, cxcl was shown to be consistently down-regulated by cdep analysis. given that this gene has angiostatic property, our results suggest that its down-regulation in metastatic cancer might interrupt the angiostasis process and promote angiogenesis--an important aspect of cancer metastasis. discussion meta-analysis provides a cost-efficient way to approach biological problems. however, the heterogeneous nature of the data is always a significant challenge. cdep aims to overcome this hurdle to identify genes that have a common differential expression pattern across different datasets. we illustrated that cdep can: obtain higher statistical power than existing meta-analysis approaches while maintaining low type i error rate in the simulation study, and identify genes that are potentially involved in common metastatic behaviors and relevant biological pathways. cdep borrows information from each dataset to identify genes differentially expressed consistently--a flexible approach that can be generalized to problems other than metastasis. the high statistical power under diverse sets of parameters considered in the simulation study also suggests robustness of cdep to the diversity of data sources. in cdep, the minus log likelihood q for different fdr values was used because cdep does not intend to "filter out" genes in each dataset before performing meta-analysis. this is in contrast to meta-profile where genes that only met the threshold in each dataset were used for the meta-analysis. in cdep, we emphasized low l values to calculate el and thus employed a linearly decreasing pdf for the log likelihood to: 1) balance the "filtering" behavior that would result from a convex decreasing pdf; and 2) emphasize small l. the pdf used in cdep outperformed meta-profile and meta-rankprod in obtaining high statistical power and lowering type i error rate. cdep, meta-profile, and meta-rankprod use different permutation approaches to estimate fdrg. meta-rankprod permutes gene expression values relative to the gene id for each array while meta-profile and cdep permute fdr relative to gene id for each dataset examined. the null distribution produced by meta-rankprod permutation would lead to rpg representing genes that are non-differentially expressed in any dataset, while meta-profile and cdep would simply increase the proportion of genes that are differentially expressed in only a single dataset after permutation. therefore, meta-rankprod tends to under-estimate fdrg, as it ignores genes that are only differentially expressed in a single dataset. on the other hand, meta-profile and cdep would over-estimate fdrg because they have a higher proportion of gc genes in the null distribution compared to meta-rankprod. even though inaccurate estimation of fdrg is inevitable due to the lack of prior knowledge about the proportion of genes only differentially expressed in one versus multiple datasets, both cdep and meta-profile employed a more conserved approach than meta-rankprod to obtain high precision.  cdep is a flexible meta-analysis approach that borrows information from each dataset in order to identify genes that are consistently differentially expressed. cdep obtains higher statistical power than two existing approaches under a variety of scenarios considered in the simulation study, suggesting its robustness and insensitivity to data variation. by application to metastatic cancer datasets as a case study, cdep allows identification of genes differentially expressed consistently in different types of metastatic cancer cells. these identified genes could be further developed into universal biomarkers for cancer staging and diagnosis. 
our simulation study showed that cdep achieved higher statistical power and maintained low type i error rate when compared with two recently proposed meta-analysis approaches. we have shown that cdep can gain higher statistical power than other existing approaches under a variety of settings considered in the simulation study, suggesting its robustness and insensitivity to data variation commonly associated with microarray experiments. the objective of this study is to develop a novel meta-analysis approach, consistent differential expression pattern, to identify genes with common differential expression patterns across different datasets. these type i error rates from all datasets were then used to identify genes with common differential expression patterns. cdep is a flexible approach that borrows information from each dataset in a meta-analysis in order to identify genes being differentially expressed consistently. to utilize the large volume of gene expression information generated from different microarray experiments, several meta-analysis techniques have been developed. we applied cdep to analyze microarray data from different laboratories that compared transcription profiles between metastatic and primary cancer of different types. despite these efforts, there remain significant challenges to effectively increasing the statistical power and decreasing the type i error rate while pooling the heterogeneous datasets from public resources. we combined false discovery rate estimation and the non-parametric rankprod approach to estimate the type i error rate in each microarray dataset of the meta-analysis. many genes identified as differentially expressed consistently across different cancer types are in pathways related to metastatic behavior, such as ecm-receptor interaction, focal adhesion, and blood vessel development. we also identified novel genes such as amigo gem, and cxcl that have not been shown to associate with, but may play roles in, metastasis.
 to utilize the large volume of gene expression information generated from different microarray experiments, several meta-analysis techniques have been developed. despite these efforts, there remain significant challenges to effectively increasing the statistical power and decreasing the type i error rate while pooling the heterogeneous datasets from public resources. the objective of this study is to develop a novel meta-analysis approach, consistent differential expression pattern, to identify genes with common differential expression patterns across different datasets.  we combined false discovery rate estimation and the non-parametric rankprod approach to estimate the type i error rate in each microarray dataset of the meta-analysis. these type i error rates from all datasets were then used to identify genes with common differential expression patterns. our simulation study showed that cdep achieved higher statistical power and maintained low type i error rate when compared with two recently proposed meta-analysis approaches. we applied cdep to analyze microarray data from different laboratories that compared transcription profiles between metastatic and primary cancer of different types. many genes identified as differentially expressed consistently across different cancer types are in pathways related to metastatic behavior, such as ecm-receptor interaction, focal adhesion, and blood vessel development. we also identified novel genes such as amigo gem, and cxcl that have not been shown to associate with, but may play roles in, metastasis.  cdep is a flexible approach that borrows information from each dataset in a meta-analysis in order to identify genes being differentially expressed consistently. we have shown that cdep can gain higher statistical power than other existing approaches under a variety of settings considered in the simulation study, suggesting its robustness and insensitivity to data variation commonly associated with microarray experiments. availability: cdep is implemented in r and freely available at: http://genomebioinfo.musc.edu/cdep/ contact: zhengw@musc.edu 