BACKGROUND
dna microarrays provide information about expression levels for thousands of genes simultaneously at the transcriptional level.
it is being applied to determine how global  differential transcription may affect biological systems.
the development of microarray technology has motivated interest in their use for disease research and diagnosis.
many studies have attempted to find disease-specific biomarkers, a small subset of genes that distinguish normal tissue from diseased tissue.
a wide variety of statistical methods have been applied to biomarker identification, including sparse logistic regression   <cit> , receiver operating characteristic  curve approach  <cit>  and gaussian process models  <cit> .
however, most of these focus on disease classification, while far fewer studies have been done to identify tissue biomarkers or genes with a tissue-restricted pattern of expression.
genes with a high level of expression in one tissue compared to other tissue types in the body are likely to have corresponding tissue-restricted functional annotation.
further, loss of the functional product encoded by these genes will frequently be associated with tissue pathology.
in general, the identification of tissue-specific biomarkers or genes with a tissue-restricted pattern of expression can provide important new insight into the biology of that tissue or the etiology/pathogenesis of diseases that impact that tissue.
quantiles are measures of relative standing.
for example, a student scoring at the τ th quantile on a standardized test means that he/she performs better than a proportion τ and worse than a proportion  of the reference group of students.
for any  <dig> <τ <  <dig>  f- <dig> = inf{x: f ≥ τ} is called the τ th quantile of the distribution f <cit> .
quantile regression as introduced by koenker and bassett  extends this idea to the estimation of conditional quantile functions modeling quantiles of the conditional distribution of the response variable as functions of observed covariates.
an ordinary least squares  regression models the relationship between covariates x and the conditional mean of the response variable y given x = x. however, covariates x often influence the whole distribution of y, not only the mean, thereby severely weakening ols  <cit> .
for example, a change in covariates may have an opposite effect on the high and low percentiles of y. unlike ols, quantile regression methods offer a mechanism for estimating models across the full range of conditional quantile functions given x = x. two models of quantile regression can be distinguished, depending on whether or not independent identically distributed  error terms are assumed.
we will call the model without assumption of iid error terms the non iid error model.
in linear quantile regression, if the slopes of the regression lines are different for different quantiles, then the non iid error model is more appropriate  <cit> .
recently, wang and he proposed a rank score test  <cit>  for detecting differential gene expression by modeling and analyzing the quantiles of gene intensity distributions through probe-level measurements.
though also based on the quantile regression idea, wang and he's method is otherwise not related to the approach presented here.
fold change has been widely used in microarray experiments to identify genes with different expression levels between two types of samples .
a cut off of 2-fold up or down regulation has been chosen to define differential expression in most published studies  <cit> .
however, the commonly used 2-fold change criterion does not take into account the magnitude of gene expression.
in this study, we propose an intensity-dependent linear quantile regression, using statistical and biological information to identify tissue-restricted patterns of gene expression.
we demonstrate our methods on the analysis of cdna microarray data to compare articular cartilage with ten different body tissues to identify genes with a cartilage-restricted pattern of expression representing potentially novel cartilage biomarkers.
chondrocytes are the only cell type in cartilage and they synthesize several proteins that are expressed in a highly tissue-restricted pattern, including type ii procollagen and aggrecan core protein.
screening for novel genes that have a cartilage-restricted pattern of expression can expand our understanding of chondrocyte function and potentially improve our understanding of important diseases that involve cartilage, such as arthritis.
RESULTS
implementation
after scanning, the median intensities adjusted for background intensities of each pair of spots were lowess  normalized for each individual slide.
the ma plot shows that the intensity dependent bias had been removed after lowess normalization  <cit>  .
because of some bad-flagged spots, the number of probesets available for analysis ranged from  <dig> in the cartilage/lung comparison to  <dig> in the cartilage/cerebellum comparison.
for each comparison, a piecewise nonparametric approach was used to reveal the relationship between percentiles of m and a, where m = log <dig>  and a = log <dig> rg with r representing the gene expression level in cartilage and g representing the gene expression level in one of the other  <dig> tissues.
the range of a was divided into  <dig> regions with a minimum of  <dig> probe sets and a maximum of  <dig> probe sets in each region.
the corresponding 1st, 5th, 10th, 20th, 50th, 80th, 90th, 95th, 99th percentiles of m were calculated for each region of a. scatter plots of the mean of a for each region and quantiles of m in the corresponding region were plotted.
for the cartilage versus bladder comparison , the scatter plot showed an approximate linear relationship between a and each of the considered conditional quantiles of m given a, with slight deviations from a linear relationship at the high intensities.
similar patterns were also observed in the other  <dig> tissue comparisons .
since the scatter plots for different quantiles were not parallel, the non iid error quantile regression model is more reasonable.
hence for each comparison, linear quantile regression  under the non iid error model  <cit>   was fitted to the data.
generally, the fit was good, except for small deviations at extreme high intensities .
the corresponding nine conditional percentiles  of m were estimated for each observed a. observed m was compared to the estimated nine conditional percentiles of m, and a cartilage specific z-score was calculated according to table  <dig>  the average z score and standard deviation were also calculated.
genes were considered potential cartilage biomarkers if the observed values for m were above the estimated 95th conditional percentile of m in all  <dig> of the cartilage/tissue comparisons analyzed .
transforming observed quantile of log <dig> into corresponding z-score
cartilage biomarkers identified
thirty-seven probe sets  were identified that exhibit expression above the 95th conditional quantile in all  <dig> of the cartilage/tissue comparisons analyzed .
of these,  <dig>  have existing annotation associated with cartilage including several well-established cartilage biomarkers .
blast hits for the remaining  <dig> probe sets  in which the cartilage-specificity score was at least  <dig>  in all  <dig> tissue comparisons have no reported sequence annotation associated with established functional roles in cartilage.
from table  <dig>  we can also see that the means of the z scores for these probe sets were high, with small standard deviations.
in contrast, six probe sets  exhibited expression levels below the 5th conditional quantile in all  <dig> of the cartilage/tissue comparisons analyzed .
these  <dig> probe sets represent the ones on this microarray  with consistently low relative gene expression in cartilage compared to the other tissue types studied.
with microarrays that contain probe sets for all genes in the genome of an organism, an analysis of the lowest quantiles should be useful in identifying genes with a near absence of expression in the reference tissue of interest.
cartilage-specificity scores for genes with existing functional annotation linked to cartilage and an established pattern of expression that is high in chondrocytes relative to many other cell types.
probe sets with high fold change but very low intensities should be excluded.
for example, a probe set might be reported with an intensity of  <dig> in bladder but  <dig> in cartilage, thus the fold change was  <dig>  however, if the intensity reading in cartilage is low, then we cannot reliably identify this kind of probe set as one that is exhibiting cartilage-specific expression.
for each chip, we calculate the 10th percentile of averaged log intensities, denoted as a*.
if a probe set's a value  was less than a*, we excluded it from the candidate list even when the m value  for this probe set was very large.
in other words, all  <dig> probe sets were selected from probe sets with values of a larger than a*.
for one of the ten comparisons , figure  <dig> illustrates that a for all  <dig> probe sets was larger than  <dig> and m was larger than  <dig> which implies that the intensity reading in cartilage was at least greater than  <dig> after lowess normalization.
similar ranges of a values for these  <dig> probe sets were found in the other  <dig> cartilage/tissue comparisons.
taking comp as an example in table  <dig>  we see that the intensity readings in cartilage were high and the relative expression differences between cartilage and each of the ten other tissues  were large.
similar ranges of intensity and relative expression differences were found with the other  <dig> probe sets.
therefore, data for these thirty-seven probe sets were interpreted as consistent with a cartilage-restricted pattern of expression.
expression intensity data for cartilage oligomeric matrix protein  across the  <dig> tissue comparisons examined.
in this study, cartilage-specific scores were used in place of percentiles of m .
we have compared cartilage with ten other body tissues and have identified  <dig> probe sets with expression all above the 95th percentile of m. however, with a larger number of tissue comparisons, the criterion of above the 95th percentile of m in all tissue comparisons may be too stringent to identify a cartilage-restricted expression pattern.
the idea of transforming percentiles of m into z-scores and then choosing probe sets with a high average z-score and low standard deviation makes the criterion more feasible to identify probe sets of interest.
one of the advantages of the standardized z-scores is that it is relatively simple to make adjustments that take the number of comparisons into account.
the appropriate cutoff for average z-score and standard deviation deserves further investigation.
due to the fact that genes were classified as cartilage-specific only when they showed high relative expression in all  <dig> tissue comparisons, the probability of falsely identifying a chance outlier as a cartilage-specific gene is rather low.
loguinov et al.
<cit>  distinguish five different circumstances represented by "outliers": a gene with higher individual variability than the majority of genes; an outlier by chance; a sporadic technical or biological outlier; a systematic technical outlier ; or a systematic biological outlier due to differential expression.
our result is based on limited biological replicates, so it is important to distinguish between differentially-expressed probe sets and the other four types of outliers.
we define genes as potential cartilage biomarkers if the observed values for m were above the estimated 95th conditional percentile of m in all  <dig> of the cartilage/tissue comparisons analyzed .
the probability that anyone of the thirty-seven probe sets identified would be due to the other four types of outliers in all  <dig> of cartilage/tissue comparisons is very small.
for example, if we assume that the probability of probe set being one of the other four types of outliers is 20% in one cartilage/tissue comparison, then the probability of this probe set being such an outlier in all  <dig> cartilage/tissue comparisons is  <dig> , which is  <dig> e- <dig>  a rather small value.
▪ feasibility and appropriateness of linear quantile regression
volcano plots, which consider both statistical tests of differences between sample types  and biological effects  are commonly used in microarray experiments to identify genes with different expression levels between two experimental groups.
with microarray experiments in which the design requires comparisons between many experimental groups, the number of biological replicates can be constrained by logistical variables.
for example, with the sample set analyzed in this study, the articular cartilage and eight of the comparative tissues were collected from a single donor while placental villous and testis samples were each collected from other donors.
the absence of biological replicates made statistical inference  of expression differences between cartilage and the other  <dig> tissues impossible.
in addition, a 2-fold change criterion does not take into account the varied magnitude of gene expression.
hence, quantile regression was used to determine quantiles of m conditional on a. microarray data consists of thousands of probe sets.
dividing the range of a into several regions still makes each region have enough probe sets  to calculate the quantiles of m. thus, the piecewise nonparametric method is feasible and appropriate to reveal the relationship between a and percentiles of m.
in this study, scatter plots showed percentiles above the 50th percentile of m  linearly increasing with a while percentiles below 50th percentiles of m  were linearly decreasing with a. hence, linear quantile regression with a linear term was fitted to the data.
expression levels above the 95th percentile were defined as cartilage-restricted expression.
thirty-seven probe sets were identified as exhibiting a cartilage-restricted pattern of expression.
within this group are widely recognized cartilage biomarkers, including genes encoding type ii procollagen and aggrecan core protein.
the presence of genes encoding these established cartilage biomarkers validate the linear quantile regression approach.
however, we recognize that the expression pattern for the remaining genes that currently lack established functional annotation linked to cartilage needs to be confirmed with additional studies.
simple linear regression  should not be applied to these data since different quantiles of m behave differently  and the iid error assumption  which is used in simple linear regression is obviously violated.
in figure 2d, at medium and high intensities, the 95th linear quantile regression line  was above the 95% confidence interval upper bound of the simple linear regression line .
as a result, the approach of fitting a linear regression and then calculating a 95% confidence interval of individual predicted values of m conditional on each a would lead to the false positive identification of cartilage-specific probe sets at medium and high intensities.
based on the m-a plots, one of the reviewers has suggested the following iterated logarithm approach for normalization.
let log2-log <dig> be m and +log2)/ <dig> be a to perform lowess normalization.
after normalization, for each comparison, linear quantile regression of m on a was fitted to the data.
<dig> probe sets were above the estimated 95% conditional percentile of m in all  <dig> tissue comparisons.
in contrast,  <dig> probe sets were above the estimated 95% conditional percentile of m in all  <dig> tissue comparisons using the originally proposed log transformation method.
there were  <dig> probe sets common in both approaches.
however, the iterated logarithm approach failed to identify  <dig> well-established cartilage biomarkers, which could be identified by the single log transformation approach.
one possible reason is that the iterated logarithm may not remove intensity-dependent bias as well as the single logarithm.
CONCLUSIONS
quantile regression is appropriate for the analysis of two color array experiments, especially for studies with only one replicate and hence highly limited quantifiable sources of experimental error.
we used a nonparametric approach to reveal the relationship between a and quantiles of m and then applied the appropriate quantile regression  to select genes with a high level of expression in specific tissue or tissue biomarkers.

 dna microarrays provide information about expression levels for thousands of genes simultaneously at the transcriptional level. it is being applied to determine how global differential transcription may affect biological systems. the development of microarray technology has motivated interest in their use for disease research and diagnosis. many studies have attempted to find disease-specific biomarkers, a small subset of genes that distinguish normal tissue from diseased tissue. a wide variety of statistical methods have been applied to biomarker identification, including sparse logistic regression, receiver operating characteristic curve approach and gaussian process models. however, most of these focus on disease classification, while far fewer studies have been done to identify tissue biomarkers or genes with a tissue-restricted pattern of expression. genes with a high level of expression in one tissue compared to other tissue types in the body are likely to have corresponding tissue-restricted functional annotation. further, loss of the functional product encoded by these genes will frequently be associated with tissue pathology. in general, the identification of tissue-specific biomarkers or genes with a tissue-restricted pattern of expression can provide important new insight into the biology of that tissue or the etiology/pathogenesis of diseases that impact that tissue. quantiles are measures of relative standing. for example, a student scoring at the τ th quantile on a standardized test means that he/she performs better than a proportion τ and worse than a proportion of the reference group of students. for any <τ < f- = inf{x: f ≥ τ} is called the τ th quantile of the distribution f. quantile regression as introduced by koenker and bassett extends this idea to the estimation of conditional quantile functions modeling quantiles of the conditional distribution of the response variable as functions of observed covariates. an ordinary least squares regression models the relationship between covariates x and the conditional mean of the response variable y given x = x. however, covariates x often influence the whole distribution of y, not only the mean, thereby severely weakening ols. for example, a change in covariates may have an opposite effect on the high and low percentiles of y. unlike ols, quantile regression methods offer a mechanism for estimating models across the full range of conditional quantile functions given x = x. two models of quantile regression can be distinguished, depending on whether or not independent identically distributed error terms are assumed. we will call the model without assumption of iid error terms the non iid error model. in linear quantile regression, if the slopes of the regression lines are different for different quantiles, then the non iid error model is more appropriate. recently, wang and he proposed a rank score test for detecting differential gene expression by modeling and analyzing the quantiles of gene intensity distributions through probe-level measurements. though also based on the quantile regression idea, wang and he's method is otherwise not related to the approach presented here. fold change has been widely used in microarray experiments to identify genes with different expression levels between two types of samples. a cut off of 2-fold up or down regulation has been chosen to define differential expression in most published studies. however, the commonly used 2-fold change criterion does not take into account the magnitude of gene expression. in this study, we propose an intensity-dependent linear quantile regression, using statistical and biological information to identify tissue-restricted patterns of gene expression. we demonstrate our methods on the analysis of cdna microarray data to compare articular cartilage with ten different body tissues to identify genes with a cartilage-restricted pattern of expression representing potentially novel cartilage biomarkers. chondrocytes are the only cell type in cartilage and they synthesize several proteins that are expressed in a highly tissue-restricted pattern, including type ii procollagen and aggrecan core protein. screening for novel genes that have a cartilage-restricted pattern of expression can expand our understanding of chondrocyte function and potentially improve our understanding of important diseases that involve cartilage, such as arthritis.  implementation after scanning, the median intensities adjusted for background intensities of each pair of spots were lowess normalized for each individual slide. the ma plot shows that the intensity dependent bias had been removed after lowess normalization. because of some bad-flagged spots, the number of probesets available for analysis ranged from in the cartilage/lung comparison to in the cartilage/cerebellum comparison. for each comparison, a piecewise nonparametric approach was used to reveal the relationship between percentiles of m and a, where m = log and a = log rg with r representing the gene expression level in cartilage and g representing the gene expression level in one of the other tissues. the range of a was divided into regions with a minimum of probe sets and a maximum of probe sets in each region. the corresponding 1st, 5th, 10th, 20th, 50th, 80th, 90th, 95th, 99th percentiles of m were calculated for each region of a. scatter plots of the mean of a for each region and quantiles of m in the corresponding region were plotted. for the cartilage versus bladder comparison, the scatter plot showed an approximate linear relationship between a and each of the considered conditional quantiles of m given a, with slight deviations from a linear relationship at the high intensities. similar patterns were also observed in the other tissue comparisons. since the scatter plots for different quantiles were not parallel, the non iid error quantile regression model is more reasonable. hence for each comparison, linear quantile regression under the non iid error model was fitted to the data. generally, the fit was good, except for small deviations at extreme high intensities. the corresponding nine conditional percentiles of m were estimated for each observed a. observed m was compared to the estimated nine conditional percentiles of m, and a cartilage specific z-score was calculated according to table the average z score and standard deviation were also calculated. genes were considered potential cartilage biomarkers if the observed values for m were above the estimated 95th conditional percentile of m in all of the cartilage/tissue comparisons analyzed. transforming observed quantile of log into corresponding z-score cartilage biomarkers identified thirty-seven probe sets were identified that exhibit expression above the 95th conditional quantile in all of the cartilage/tissue comparisons analyzed. of these, have existing annotation associated with cartilage including several well-established cartilage biomarkers. blast hits for the remaining probe sets in which the cartilage-specificity score was at least in all tissue comparisons have no reported sequence annotation associated with established functional roles in cartilage. from table we can also see that the means of the z scores for these probe sets were high, with small standard deviations. in contrast, six probe sets exhibited expression levels below the 5th conditional quantile in all of the cartilage/tissue comparisons analyzed. these probe sets represent the ones on this microarray with consistently low relative gene expression in cartilage compared to the other tissue types studied. with microarrays that contain probe sets for all genes in the genome of an organism, an analysis of the lowest quantiles should be useful in identifying genes with a near absence of expression in the reference tissue of interest. cartilage-specificity scores for genes with existing functional annotation linked to cartilage and an established pattern of expression that is high in chondrocytes relative to many other cell types. probe sets with high fold change but very low intensities should be excluded. for example, a probe set might be reported with an intensity of in bladder but in cartilage, thus the fold change was however, if the intensity reading in cartilage is low, then we cannot reliably identify this kind of probe set as one that is exhibiting cartilage-specific expression. for each chip, we calculate the 10th percentile of averaged log intensities, denoted as a*. if a probe set's a value was less than a*, we excluded it from the candidate list even when the m value for this probe set was very large. in other words, all probe sets were selected from probe sets with values of a larger than a*. for one of the ten comparisons, figure illustrates that a for all probe sets was larger than and m was larger than which implies that the intensity reading in cartilage was at least greater than after lowess normalization. similar ranges of a values for these probe sets were found in the other cartilage/tissue comparisons. taking comp as an example in table we see that the intensity readings in cartilage were high and the relative expression differences between cartilage and each of the ten other tissues were large. similar ranges of intensity and relative expression differences were found with the other probe sets. therefore, data for these thirty-seven probe sets were interpreted as consistent with a cartilage-restricted pattern of expression. expression intensity data for cartilage oligomeric matrix protein across the tissue comparisons examined. in this study, cartilage-specific scores were used in place of percentiles of m. we have compared cartilage with ten other body tissues and have identified probe sets with expression all above the 95th percentile of m. however, with a larger number of tissue comparisons, the criterion of above the 95th percentile of m in all tissue comparisons may be too stringent to identify a cartilage-restricted expression pattern. the idea of transforming percentiles of m into z-scores and then choosing probe sets with a high average z-score and low standard deviation makes the criterion more feasible to identify probe sets of interest. one of the advantages of the standardized z-scores is that it is relatively simple to make adjustments that take the number of comparisons into account. the appropriate cutoff for average z-score and standard deviation deserves further investigation. due to the fact that genes were classified as cartilage-specific only when they showed high relative expression in all tissue comparisons, the probability of falsely identifying a chance outlier as a cartilage-specific gene is rather low. loguinov et al. distinguish five different circumstances represented by "outliers": a gene with higher individual variability than the majority of genes; an outlier by chance; a sporadic technical or biological outlier; a systematic technical outlier; or a systematic biological outlier due to differential expression. our result is based on limited biological replicates, so it is important to distinguish between differentially-expressed probe sets and the other four types of outliers. we define genes as potential cartilage biomarkers if the observed values for m were above the estimated 95th conditional percentile of m in all of the cartilage/tissue comparisons analyzed. the probability that anyone of the thirty-seven probe sets identified would be due to the other four types of outliers in all of cartilage/tissue comparisons is very small. for example, if we assume that the probability of probe set being one of the other four types of outliers is 20% in one cartilage/tissue comparison, then the probability of this probe set being such an outlier in all cartilage/tissue comparisons is, which is e- a rather small value. ▪ feasibility and appropriateness of linear quantile regression volcano plots, which consider both statistical tests of differences between sample types and biological effects are commonly used in microarray experiments to identify genes with different expression levels between two experimental groups. with microarray experiments in which the design requires comparisons between many experimental groups, the number of biological replicates can be constrained by logistical variables. for example, with the sample set analyzed in this study, the articular cartilage and eight of the comparative tissues were collected from a single donor while placental villous and testis samples were each collected from other donors. the absence of biological replicates made statistical inference of expression differences between cartilage and the other tissues impossible. in addition, a 2-fold change criterion does not take into account the varied magnitude of gene expression. hence, quantile regression was used to determine quantiles of m conditional on a. microarray data consists of thousands of probe sets. dividing the range of a into several regions still makes each region have enough probe sets to calculate the quantiles of m. thus, the piecewise nonparametric method is feasible and appropriate to reveal the relationship between a and percentiles of m. in this study, scatter plots showed percentiles above the 50th percentile of m linearly increasing with a while percentiles below 50th percentiles of m were linearly decreasing with a. hence, linear quantile regression with a linear term was fitted to the data. expression levels above the 95th percentile were defined as cartilage-restricted expression. thirty-seven probe sets were identified as exhibiting a cartilage-restricted pattern of expression. within this group are widely recognized cartilage biomarkers, including genes encoding type ii procollagen and aggrecan core protein. the presence of genes encoding these established cartilage biomarkers validate the linear quantile regression approach. however, we recognize that the expression pattern for the remaining genes that currently lack established functional annotation linked to cartilage needs to be confirmed with additional studies. simple linear regression should not be applied to these data since different quantiles of m behave differently and the iid error assumption which is used in simple linear regression is obviously violated. in figure 2d, at medium and high intensities, the 95th linear quantile regression line was above the 95% confidence interval upper bound of the simple linear regression line. as a result, the approach of fitting a linear regression and then calculating a 95% confidence interval of individual predicted values of m conditional on each a would lead to the false positive identification of cartilage-specific probe sets at medium and high intensities. based on the m-a plots, one of the reviewers has suggested the following iterated logarithm approach for normalization. let log2-log be m and +log2)/ be a to perform lowess normalization. after normalization, for each comparison, linear quantile regression of m on a was fitted to the data. probe sets were above the estimated 95% conditional percentile of m in all tissue comparisons. in contrast, probe sets were above the estimated 95% conditional percentile of m in all tissue comparisons using the originally proposed log transformation method. there were probe sets common in both approaches. however, the iterated logarithm approach failed to identify well-established cartilage biomarkers, which could be identified by the single log transformation approach. one possible reason is that the iterated logarithm may not remove intensity-dependent bias as well as the single logarithm.  quantile regression is appropriate for the analysis of two color array experiments, especially for studies with only one replicate and hence highly limited quantifiable sources of experimental error. we used a nonparametric approach to reveal the relationship between a and quantiles of m and then applied the appropriate quantile regression to select genes with a high level of expression in specific tissue or tissue biomarkers. 
quantile regression is a promising method for the analysis of two color array experiments that compare multiple samples in the absence of biological replicates, thereby limiting quantifiable error. then we performed linear quantile regression to identify genes with a cartilage-restricted pattern of expression. related experiments can be done to identify tissue-restricted biomarkers, genes with a high level of expression in one tissue compared to other tissue types in the body. identification of biomarkers among thousands of genes arrayed for disease classification has been the subject of considerable research in recent years. these studies have focused on disease classification, comparing experimental groups of effected to normal patients. we determined cartilage specific z-scores based on the observed m to classify genes with z-scores ≥ in all ten cartilage/tissue comparisons as cartilage-specific genes. of these, have existing annotation associated with cartilage including several well-established cartilage biomarkers. thirty-seven probe sets were identified as cartilage biomarkers. we used a nonparametric approach to reveal the relationship between percentiles of m and a, where m is log and a is log with r representing the gene expression level in cartilage and g representing the gene expression level in one of the other tissues. in this study, cartilage was compared with ten other body tissues using a two color array experimental design.
 identification of biomarkers among thousands of genes arrayed for disease classification has been the subject of considerable research in recent years. these studies have focused on disease classification, comparing experimental groups of effected to normal patients. related experiments can be done to identify tissue-restricted biomarkers, genes with a high level of expression in one tissue compared to other tissue types in the body.  in this study, cartilage was compared with ten other body tissues using a two color array experimental design. thirty-seven probe sets were identified as cartilage biomarkers. of these, have existing annotation associated with cartilage including several well-established cartilage biomarkers. these genes comprise a useful database from which novel targets for cartilage biology research can be selected. we determined cartilage specific z-scores based on the observed m to classify genes with z-scores ≥ in all ten cartilage/tissue comparisons as cartilage-specific genes.  quantile regression is a promising method for the analysis of two color array experiments that compare multiple samples in the absence of biological replicates, thereby limiting quantifiable error. we used a nonparametric approach to reveal the relationship between percentiles of m and a, where m is log and a is log with r representing the gene expression level in cartilage and g representing the gene expression level in one of the other tissues. then we performed linear quantile regression to identify genes with a cartilage-restricted pattern of expression. 