BACKGROUND
microarray technology is a high-throughput method for measuring the expression levels of thousand of genes simultaneously.
recent completion of the microarray quality control  project ensures intra-platform consistency across test sites as well as a high level of inter-platform concordance  <cit> .
as a result, microarrays are increasingly being used in the medical and biological fields as a powerful tool for disease diagnosis, identifying biomarkers, and studying gene function.
however, observed intensities combine non-specific bindings including cross-hybridization or stray signals, which is a major disadvantage of microarray data.
the affymetrix genechip microarray, in which oligonucleotides of  <dig> bp are used to probe genes, is designed to include measures that allow the evaluation of non-specific hybridization.
each gene will be represented by 11~ <dig> pairs of olligonucleotides referred to as a probe set .
each of the probe pairs in a probe set consists of a perfect match  and a mismatch  probe.
the pm probes are designed to bind perfectly to the gene of interest and the mm probes are created by changing the middle  base to disrupt the bulk of specific hybridization  <cit> .
however, opinions vary regarding the usefulness of mm measures.
background correction algorithms for the affymetrix genechip microarray may be classified into two groups: those that use mm measures  and those that do not   <cit>  and its modified version, pm-only gc-rma  <cit> ).
rma and mas <dig> are representative algorithms used for background correction.
with the rma method, only pm is used to obtain a corrected intensity.
mas <dig> was originally provided as a default measure by affymetrix, in which pms are corrected by subtracting mms, but many researchers pointed out that direct subtraction of mm from pm is unlikely to be useful  <cit> .
the preprocessing step affects the stochastic properties of the final statistical summaries  <cit> .
biologists who want to analyze microarray data might be bewildered with the availability of so many preprocessing procedures with varying results  <cit> .
biologically, it is likely that not all observed intensities are associated with expressed genes -- that is, many of those are associated with unexpressed genes, of which measured values simply express noise due to non-specific binding, cross-hybridization, or stray signal  <cit> .
it has been reported that only 30-40% of the genes  <cit>  -- around  <dig> - <dig>  genes in total  <cit> -- are expressed in human cell lines in vitro.
identifying probe sets associated with un-expressed genes would allow the subsequent statistical analysis to be carried out with greater efficiency.
for example, in an analysis aimed at finding differentially expressed genes, filtering out these probe sets prior to analysis contributed to a decreased number of false discoveries  <cit> .
in previous work, we proposed a mathematical model based on the assumption that a gene has two separate functional states - 'on' means a gene is really expressed and 'off' means a gene is un-expressed - for identifying differentially expressed genes between two cell types  <cit> .
furthermore, we proposed to identify 'off' genes using an order relationship between pm and mm measures using affymetrix genechip probe level data  <cit> .
we applied the 'on/off' model to real medical or biological data and obtained meaningful results  <cit> .
in this study, we propose to quantify a gene as being expressed using a weibull-normal mixture distribution with two components corresponding to the separate states 'on' and 'off'.
the probability of a gene being 'on' is obtained from the posterior probability using this weibull-normal mixture distribution.
we examine the advantage of our method over the detection call of mas <dig> using the data sets of human genome u <dig> provided by affymetrix.
we implement our proposed methods of microarray analysis to explore candidate genes involved in neuroblastoma prognosis.
the symbol x denotes the number of pairs in a probe set satisfying pm >mm :x = #{j|pmj >mmj, j =  <dig>  ⋯, j}, where j is the number of probe pairs in a probe set.
RESULTS
estimation of weibull-normal density function
the results of applying the weibull-normal mixture model to the human genome u <dig> data sets are shown in figure  <dig>  the estimated parameter vector was  = , where μ and α denote location and power parameters of the weibull distribution, ξ denotes mixture rate of 'off' genes, and σ <dig> denotes the variance of the normal distribution.
figure 3a shows a comparison of the fitted weibull-normal distribution with two components  to the empirical distribution.
figure 3b shows the corresponding density function and its components.
we defined the gene state as 'on' if x ≥  <dig> and 'off' if x ≤  <dig>  the vertical dotted lines in figures 3a and 3b correspond to x =  <dig>
comparison between mas <dig> calls and 'on/off' calls usingspike-in genes
the mas <dig> method also provides a qualitative evaluation by calling gene expression present , marginal , or absent  for each probe set in determining whether the measured transcript is detected or not detected.
however, there is an important difference between a gene being 'off' and a call of 'absent'.
in the cases of figure 2b- <dig> and 2c- <dig>  for example, the probe sets were called 'absent' whereas their states were determined to be 'on'.
to make the detection call, the mas <dig> method uses a nonparametric statistical test  under the null hypothesis that pms and mms have the same distribution  <cit> .
the mas <dig> method attempts to identify truly expressed genes with certainty.
exclusion probes that are called 'absent' can result in many false negatives and loss of a large amount of information, especially with genes that switch between 'on' and 'off' with different phenotypes.
on the other hand, our method seeks to correctly identify 'off' genes using an order relationship between pm and mm measures.
we compared 'on/off' calls with the mas <dig> calls using spike-in genes of the human genome u <dig> data sets.
the spike-in genes with  <dig> pm concentration were used as negative controls .
the spike-in genes with more than  <dig>  pm concentration were used as positive controls .
a cutoff point dividing gene states into 'on' and 'off' was determined as the minimum value of x that contains as small an 'off' component as possible using the fitted weibull-normal distribution .
the value x =  <dig> was obtained as the cutoff point and is shown by the vertical dotted lines in figures 3a and 3b.
table  <dig> shows the distribution of number of p/m/a calls by mas <dig> and number of on/off genes for each concentration of spike-in genes.
as is shown in table  <dig>  mas <dig> calls generated many false negatives  compared to 'on/off' calls .
'on/off' calls generated  <dig> % false positives, although less than 4%  is desirable.
the sensitivities of the 'on/off' and mas <dig> methods are shown in figure  <dig>  the 'on/off' and mas <dig> methods require at least  <dig>  pm and  <dig>  pm of spike-in genes to achieve around 80% sensitivity, respectively.
identification of candidate genes for predicting neuroblastoma prognosis
neuroblastoma is one of the most common solid tumors in childhood.
its prognosis varies remarkably, ranging from spontaneous regression to fatal progression  <cit> .
we call these outcomes 'favorable' and 'unfavorable', respectively.
it is well known that mycn amplification strongly correlates with adverse outcome in neuroblastoma  <cit> .
nevertheless, whether mycn expression is truly predictive of neuroblastoma outcome remains controversial  <cit> .
we examined the relationship between mycn expression and clinical outcomes.
a scatter diagram of x  versus expression intensity of mycn is shown in figure  <dig> for each neuroblastoma case.
pink points represent cases with unfavorable outcome and blue points represent those with favorable outcome.
a cross-tabulation of state of mycn being 'on/off' and outcome  is also shown in figure  <dig>  where we define the gene state as 'on' if x ≥  <dig> and 'off' if x ≤  <dig> according to the fit of the weibull-normal model.
the state of mycn is uniformly 'off' in the favorable group but variable--either 'on' or 'off'--in the unfavorable group, suggesting that mycn being 'on' is sufficient for unfavorable outcome and that genes other than mycn are associated with poor prognosis.
we then introduce a new notation, 'or_on' type gene, which shows the logical relationship between multiple genes and binary phenotypes.
results of applying the weibull-normal mixture model to  <dig> cases of neuroblastoma with favorable outcome and  <dig> cases with unfavorable outcome are shown in figures 6a and 6b, respectively.
the estimated parameter vectors for favorable and unfavorable groups were  =  and , respectively, where μ and α denote location and power parameters of the weibull distribution, ξ denotes mixture rate of 'off' genes, and σ <dig> denotes the variance of the normal distribution.
figures 6a- <dig> and 6b- <dig> show the fitted weibull-normal distribution with two components  and the empirical distribution.
figures 6a- <dig> and 6b- <dig> show the corresponding density functions and their components.
the cutoff point dividing genes into 'on' and 'off' states, x =  <dig>  is denoted by the vertical dotted lines in figures 6a and 6b.
we set out to identify or_on type genes involved in neuroblastoma prognosis using the estimate of the probability of a gene being 'on' or 'off' .
a hundred genes were selected as candidates from a total of  <dig>  genes.
the five genes identified as candidate genes involved in neuroblastoma progression were: mycn , npw , slc30a <dig> , mycnos , and mycn* .
mycn and mycn* are the same genes detected by different probes.
mycnos and slc30a <dig> were confirmed to be correlated with the status of expression of mycn in neuroblastoma  <cit> .
for each of the selected genes, the probability of being 'on' in the favorable group, that in the unfavorable group, and the difference in probability of being 'on' between the unfavorable and favorable groups and its ranking, are listed in table  <dig>
to assess the advantage of the 'on/off' method, we calculated 'relative difference' statistics for the difference of average of gene expression intensities between favorable and unfavorable groups .
for each of the selected genes, average expression intensities obtained by the rma methods and their standard errors in the favorable and unfavorable groups, as well as the ranking of 'relative difference' statistics in descending order, are listed in table  <dig>  accordingly, the or_on type genes are difficult to select based on the ranking of gene expression intensities.
the method based on the 'on/off' state of a gene performs better than the method based on gene expression intensity.
real-time rt-pcr was employed to verify whether the four distinct selected genes were or_on type genes.
gene-expression features obtained by microarray data analysis and ct values from real-time rt-pcr for each of these genes are shown in figures 7a-d. the displayed features are scatter diagrams of x and expression intensity , parallel box plots of ct values in real-time rt-pcr for three groups -- favorable, unfavorable 'on', and unfavorable 'off'  -- and parallel box plots of ct values from real-time rt-pcr of gapdh according to the same three groups.
as mentioned above, the state of a gene was defined as 'on' if x ≥  <dig> and 'off' if x ≤  <dig>  average ct value was significantly lower in the unfavorable_on group compared with that in the favorable and unfavorable_off groups.
this confirms that the selected genes were not expressed in the favorable and unfavorable_off groups but were in the unfavorable_on group.
discussion
mas <dig> p/m/a calls are based on a nonparametric statistical test, in which the default state of a gene is 'absent'.
therefore, it inevitably yields many false negatives which, we think, is its main disadvantage.
for example, birc <dig> , also called survivin, which is a human gene that is a member of the inhibitor of apoptosis  family, is expressed at high levels in most human tumors but is completely absent in terminally differentiated cells  <cit> .
figure  <dig> shows a diagram of x and expression rma intensities of birc <dig> for each neuroblastoma case.
birk <dig> was judged as 'on' in all of the  <dig> cases by our method but  <dig> cases, which are circled in figure  <dig>  were classified as 'absent' by mas <dig>  as is shown in table  <dig> or figure  <dig>  'on/off' calls generated few false negatives compared to mas <dig> calls.
although the poor separation of 'on' and 'off' components of the weibull-normal mixture would result in false positives or negatives, we think that it is due to a limitation of microarray performance.
in this study, we only identified genes that switched 'on' and 'off' between phenotypes using an indicator based on the probability of being 'on'.
of course, some genes exhibit differences between phenotypes in terms of their quantitative expression intensities, going from normal to abnormally increased or decreased.
for example, birc <dig> was judged as 'on' in all cases and, in addition, 'on' with 'abnormally increased intensity' predicted poor diagnosis  except for one case that had been detected by mass-screening at stage i followed by radical resection.
we further explored the genes whose intensity levels changed quantitatively from normal to abnormal between two different phenotypes, such as birc <dig>  by calculating the likelihoods under the null hypothesis that gene expression intensities obey a normal distribution.
as a result, more than a thousand genes were selected as candidates.
a method to create a gene expression barcode - genes expected to be expressed are coded with ones and those expected to be unexpressed are coded with zeros - was developed by zilliox and irizarry  <cit> .
furthermore, an algorithm for estimating expression states was described by mccall et al.
<cit> .
they state that the magnitude of the unexpressed observed intensities differs among genes; accordingly the distribution of observed intensities must be estimated for each gene.
their method therefore requires a large database of observed intensities across many different tissues.
we consider it natural that the magnitude of the unexpressed observed intensities differs by gene because unexpressed observed intensities include gene dependent cross-hybridization.
on the other hand, our method can correct gene dependent cross-hybridizations by using mm probes.
therefore, it is unnecessary to be concerned with differences in distribution of unexpressed observed intensities among genes.
several tens of samples are enough to estimate it.
another characteristic of our method is robustness, because it is based on the order relationship between pm and mm values.
our assumptions are just  the expected pm value is larger than that of the mm value when a gene is expressed, and  the expected pm value equals that of the mm value when a gene is unexpressed.
although availability of mm probes may be in doubt  <cit> , our approach provides good justification for the use of mms.
CONCLUSIONS
the qualitative evaluation 'probability of a gene being expressed' provides a useful indicator for improving the performance of microarray data analysis.
when expression intensity of a gene is not high, it is difficult to determine its real intensity after removing non-specific binding.
especially in this case, 'probability of a gene being expressed' gives useful qualitative information complementing its true intensity.
in regards to a practical problem in expression array analysis, genes that switch between 'on' and 'off' with different phenotypes can be found with greater confidence.
our proposed method of estimating 'probability of a gene being expressed' is robust because it is not based on expression intensities but rather is based on the order relationship between pm and mm values.

 microarray technology is a high-throughput method for measuring the expression levels of thousand of genes simultaneously. recent completion of the microarray quality control project ensures intra-platform consistency across test sites as well as a high level of inter-platform concordance. as a result, microarrays are increasingly being used in the medical and biological fields as a powerful tool for disease diagnosis, identifying biomarkers, and studying gene function. however, observed intensities combine non-specific bindings including cross-hybridization or stray signals, which is a major disadvantage of microarray data. the affymetrix genechip microarray, in which oligonucleotides of bp are used to probe genes, is designed to include measures that allow the evaluation of non-specific hybridization. each gene will be represented by 11~ pairs of olligonucleotides referred to as a probe set. each of the probe pairs in a probe set consists of a perfect match and a mismatch probe. the pm probes are designed to bind perfectly to the gene of interest and the mm probes are created by changing the middle base to disrupt the bulk of specific hybridization. however, opinions vary regarding the usefulness of mm measures. background correction algorithms for the affymetrix genechip microarray may be classified into two groups: those that use mm measures and those that do not and its modified version, pm-only gc-rma ). rma and mas are representative algorithms used for background correction. with the rma method, only pm is used to obtain a corrected intensity. mas was originally provided as a default measure by affymetrix, in which pms are corrected by subtracting mms, but many researchers pointed out that direct subtraction of mm from pm is unlikely to be useful. the preprocessing step affects the stochastic properties of the final statistical summaries. biologists who want to analyze microarray data might be bewildered with the availability of so many preprocessing procedures with varying results. biologically, it is likely that not all observed intensities are associated with expressed genes -- that is, many of those are associated with unexpressed genes, of which measured values simply express noise due to non-specific binding, cross-hybridization, or stray signal. it has been reported that only 30-40% of the genes -- around - genes in total -- are expressed in human cell lines in vitro. identifying probe sets associated with un-expressed genes would allow the subsequent statistical analysis to be carried out with greater efficiency. for example, in an analysis aimed at finding differentially expressed genes, filtering out these probe sets prior to analysis contributed to a decreased number of false discoveries. in previous work, we proposed a mathematical model based on the assumption that a gene has two separate functional states -'on' means a gene is really expressed and'off' means a gene is un-expressed - for identifying differentially expressed genes between two cell types. furthermore, we proposed to identify'off' genes using an order relationship between pm and mm measures using affymetrix genechip probe level data. we applied the'on/off' model to real medical or biological data and obtained meaningful results. in this study, we propose to quantify a gene as being expressed using a weibull-normal mixture distribution with two components corresponding to the separate states'on' and'off'. the probability of a gene being'on' is obtained from the posterior probability using this weibull-normal mixture distribution. we examine the advantage of our method over the detection call of mas using the data sets of human genome u provided by affymetrix. we implement our proposed methods of microarray analysis to explore candidate genes involved in neuroblastoma prognosis. the symbol x denotes the number of pairs in a probe set satisfying pm >mm:x = #{j|pmj >mmj, j = ⋯, j}, where j is the number of probe pairs in a probe set.  estimation of weibull-normal density function the results of applying the weibull-normal mixture model to the human genome u data sets are shown in figure the estimated parameter vector was =, where μ and α denote location and power parameters of the weibull distribution, ξ denotes mixture rate of'off' genes, and σ denotes the variance of the normal distribution. figure 3a shows a comparison of the fitted weibull-normal distribution with two components to the empirical distribution. figure 3b shows the corresponding density function and its components. we defined the gene state as'on' if x ≥ and'off' if x ≤ the vertical dotted lines in figures 3a and 3b correspond to x = comparison between mas calls and'on/off' calls usingspike-in genes the mas method also provides a qualitative evaluation by calling gene expression present, marginal, or absent for each probe set in determining whether the measured transcript is detected or not detected. however, there is an important difference between a gene being'off' and a call of'absent'. in the cases of figure 2b- and 2c- for example, the probe sets were called'absent' whereas their states were determined to be'on'. to make the detection call, the mas method uses a nonparametric statistical test under the null hypothesis that pms and mms have the same distribution. the mas method attempts to identify truly expressed genes with certainty. exclusion probes that are called'absent' can result in many false negatives and loss of a large amount of information, especially with genes that switch between'on' and'off' with different phenotypes. on the other hand, our method seeks to correctly identify'off' genes using an order relationship between pm and mm measures. we compared'on/off' calls with the mas calls using spike-in genes of the human genome u data sets. the spike-in genes with pm concentration were used as negative controls. the spike-in genes with more than pm concentration were used as positive controls. a cutoff point dividing gene states into'on' and'off' was determined as the minimum value of x that contains as small an'off' component as possible using the fitted weibull-normal distribution. the value x = was obtained as the cutoff point and is shown by the vertical dotted lines in figures 3a and 3b. table shows the distribution of number of p/m/a calls by mas and number of on/off genes for each concentration of spike-in genes. as is shown in table mas calls generated many false negatives compared to'on/off' calls.'on/off' calls generated % false positives, although less than 4% is desirable. the sensitivities of the'on/off' and mas methods are shown in figure the'on/off' and mas methods require at least pm and pm of spike-in genes to achieve around 80% sensitivity, respectively. identification of candidate genes for predicting neuroblastoma prognosis neuroblastoma is one of the most common solid tumors in childhood. its prognosis varies remarkably, ranging from spontaneous regression to fatal progression. we call these outcomes'favorable' and'unfavorable', respectively. it is well known that mycn amplification strongly correlates with adverse outcome in neuroblastoma. nevertheless, whether mycn expression is truly predictive of neuroblastoma outcome remains controversial. we examined the relationship between mycn expression and clinical outcomes. a scatter diagram of x versus expression intensity of mycn is shown in figure for each neuroblastoma case. pink points represent cases with unfavorable outcome and blue points represent those with favorable outcome. a cross-tabulation of state of mycn being'on/off' and outcome is also shown in figure where we define the gene state as'on' if x ≥ and'off' if x ≤ according to the fit of the weibull-normal model. the state of mycn is uniformly'off' in the favorable group but variable--either'on' or'off'--in the unfavorable group, suggesting that mycn being'on' is sufficient for unfavorable outcome and that genes other than mycn are associated with poor prognosis. we then introduce a new notation,'or_on' type gene, which shows the logical relationship between multiple genes and binary phenotypes. results of applying the weibull-normal mixture model to cases of neuroblastoma with favorable outcome and cases with unfavorable outcome are shown in figures 6a and 6b, respectively. the estimated parameter vectors for favorable and unfavorable groups were = and, respectively, where μ and α denote location and power parameters of the weibull distribution, ξ denotes mixture rate of'off' genes, and σ denotes the variance of the normal distribution. figures 6a- and 6b- show the fitted weibull-normal distribution with two components and the empirical distribution. figures 6a- and 6b- show the corresponding density functions and their components. the cutoff point dividing genes into'on' and'off' states, x = is denoted by the vertical dotted lines in figures 6a and 6b. we set out to identify or_on type genes involved in neuroblastoma prognosis using the estimate of the probability of a gene being'on' or'off'. a hundred genes were selected as candidates from a total of genes. the five genes identified as candidate genes involved in neuroblastoma progression were: mycn, npw, slc30a, mycnos, and mycn*. mycn and mycn* are the same genes detected by different probes. mycnos and slc30a were confirmed to be correlated with the status of expression of mycn in neuroblastoma. for each of the selected genes, the probability of being'on' in the favorable group, that in the unfavorable group, and the difference in probability of being'on' between the unfavorable and favorable groups and its ranking, are listed in table to assess the advantage of the'on/off' method, we calculated'relative difference' statistics for the difference of average of gene expression intensities between favorable and unfavorable groups. for each of the selected genes, average expression intensities obtained by the rma methods and their standard errors in the favorable and unfavorable groups, as well as the ranking of'relative difference' statistics in descending order, are listed in table accordingly, the or_on type genes are difficult to select based on the ranking of gene expression intensities. the method based on the'on/off' state of a gene performs better than the method based on gene expression intensity. real-time rt-pcr was employed to verify whether the four distinct selected genes were or_on type genes. gene-expression features obtained by microarray data analysis and ct values from real-time rt-pcr for each of these genes are shown in figures 7a-d. the displayed features are scatter diagrams of x and expression intensity, parallel box plots of ct values in real-time rt-pcr for three groups -- favorable, unfavorable'on', and unfavorable'off' -- and parallel box plots of ct values from real-time rt-pcr of gapdh according to the same three groups. as mentioned above, the state of a gene was defined as'on' if x ≥ and'off' if x ≤ average ct value was significantly lower in the unfavorable_on group compared with that in the favorable and unfavorable_off groups. this confirms that the selected genes were not expressed in the favorable and unfavorable_off groups but were in the unfavorable_on group. discussion mas p/m/a calls are based on a nonparametric statistical test, in which the default state of a gene is'absent'. therefore, it inevitably yields many false negatives which, we think, is its main disadvantage. for example, birc, also called survivin, which is a human gene that is a member of the inhibitor of apoptosis family, is expressed at high levels in most human tumors but is completely absent in terminally differentiated cells. figure shows a diagram of x and expression rma intensities of birc for each neuroblastoma case. birk was judged as'on' in all of the cases by our method but cases, which are circled in figure were classified as'absent' by mas as is shown in table or figure'on/off' calls generated few false negatives compared to mas calls. although the poor separation of'on' and'off' components of the weibull-normal mixture would result in false positives or negatives, we think that it is due to a limitation of microarray performance. in this study, we only identified genes that switched'on' and'off' between phenotypes using an indicator based on the probability of being'on'. of course, some genes exhibit differences between phenotypes in terms of their quantitative expression intensities, going from normal to abnormally increased or decreased. for example, birc was judged as'on' in all cases and, in addition,'on' with'abnormally increased intensity' predicted poor diagnosis except for one case that had been detected by mass-screening at stage i followed by radical resection. we further explored the genes whose intensity levels changed quantitatively from normal to abnormal between two different phenotypes, such as birc by calculating the likelihoods under the null hypothesis that gene expression intensities obey a normal distribution. as a result, more than a thousand genes were selected as candidates. a method to create a gene expression barcode - genes expected to be expressed are coded with ones and those expected to be unexpressed are coded with zeros - was developed by zilliox and irizarry. furthermore, an algorithm for estimating expression states was described by mccall et al.. they state that the magnitude of the unexpressed observed intensities differs among genes; accordingly the distribution of observed intensities must be estimated for each gene. their method therefore requires a large database of observed intensities across many different tissues. we consider it natural that the magnitude of the unexpressed observed intensities differs by gene because unexpressed observed intensities include gene dependent cross-hybridization. on the other hand, our method can correct gene dependent cross-hybridizations by using mm probes. therefore, it is unnecessary to be concerned with differences in distribution of unexpressed observed intensities among genes. several tens of samples are enough to estimate it. another characteristic of our method is robustness, because it is based on the order relationship between pm and mm values. our assumptions are just the expected pm value is larger than that of the mm value when a gene is expressed, and the expected pm value equals that of the mm value when a gene is unexpressed. although availability of mm probes may be in doubt, our approach provides good justification for the use of mms.  the qualitative evaluation'probability of a gene being expressed' provides a useful indicator for improving the performance of microarray data analysis. when expression intensity of a gene is not high, it is difficult to determine its real intensity after removing non-specific binding. especially in this case,'probability of a gene being expressed' gives useful qualitative information complementing its true intensity. in regards to a practical problem in expression array analysis, genes that switch between'on' and'off' with different phenotypes can be found with greater confidence. our proposed method of estimating'probability of a gene being expressed' is robust because it is not based on expression intensities but rather is based on the order relationship between pm and mm values. 
we assume two functional states of a gene - expressed or unexpressed - and propose a robust method to estimate gene expression states using an order relationship between pm and mm measures. microarray technology is a high-throughput method for measuring the expression levels of thousand of genes simultaneously. it should be noted that not all observed intensities are associated with expressed genes and many of those are associated with unexpressed genes, of which measured values express mere noise due to non-specific binding, cross-hybridization, or stray signals. the observed intensities combine a non-specific binding, which is a major disadvantage with microarray data. the implicit assumption that all genes are expressed leads to poor performance of microarray data analyses. the proposed qualitative evaluation,'probability of a gene being expressed', is a useful indicator for improving microarray data analysis. we identified the candidate genes for which expression states differed when compared between two outcomes. expression states - expressed or unexpressed - correspond to the most fundamental gene function'on' and'off', which can lead to biologically meaningful results. the affymetrix genechip assigned a mismatch probe with the intention of measuring non-specific binding, but various opinions exist regarding usefulness of mm measures. the usefulness of'probability of a gene being expressed' is illustrated through an exploration of candidate genes involved in neuroblastoma prognosis.
 microarray technology is a high-throughput method for measuring the expression levels of thousand of genes simultaneously. the observed intensities combine a non-specific binding, which is a major disadvantage with microarray data. the affymetrix genechip assigned a mismatch probe with the intention of measuring non-specific binding, but various opinions exist regarding usefulness of mm measures. it should be noted that not all observed intensities are associated with expressed genes and many of those are associated with unexpressed genes, of which measured values express mere noise due to non-specific binding, cross-hybridization, or stray signals. the implicit assumption that all genes are expressed leads to poor performance of microarray data analyses. we assume two functional states of a gene - expressed or unexpressed - and propose a robust method to estimate gene expression states using an order relationship between pm and mm measures.  an indicator'probability of a gene being expressed' was obtained using the number of probe pairs within a probe set where the pm measure exceeds the mm measure. we examined the validity of the proposed indicator using human genome u data sets provided by affymetrix. the usefulness of'probability of a gene being expressed' is illustrated through an exploration of candidate genes involved in neuroblastoma prognosis. we identified the candidate genes for which expression states differed when compared between two outcomes. the validity of this result was subsequently confirmed by quantitative rt-pcr.  the proposed qualitative evaluation,'probability of a gene being expressed', is a useful indicator for improving microarray data analysis. it is useful to reduce the number of false discoveries. expression states - expressed or unexpressed - correspond to the most fundamental gene function'on' and'off', which can lead to biologically meaningful results. 