BACKGROUND
the rna molecule plays a critical role in transferring information encoded in the genome  to the many different forms of proteins.
after extracting rna from cells by various methods, scientists are provided with a direct measure of cellular activity using gene expression measurement techniques.
among these, real-time pcr and dna microarrays are the most widely used techniques.
importance of integrity
rna is a thermodynamically stable molecule, which is, however, rapidly digested in the presence of the nearly ubiquitous rnase enzymes.
as a result, shorter fragments of rna commonly occur in a sample, which can potentially compromise results of downstream applications  <cit> .
in order to evaluate the degree of degradation, electrophoretic methods have been applied that separate the samples according to the size of the comprised molecules.
historically, rna integrity is evaluated using agarose gel electrophoresis stained with ethidium bromide, which produces a certain banding pattern  <cit> .
typically, gel images show two bands comprising the 28s and 18s ribosomal rna  species and other bands where smaller rna species are located.
rna is considered of high quality when the ratio of 28s:18s bands is about  <dig>  and higher.
since this approach relies on human interpretation of gel images, it is subjective, hardly comparable from one lab to another, and the resulting data cannot be processed digitally.
towards an automated approach
in  <dig>  the agilent  <dig> bioanalyzer was introduced for the separation of dna, rna, and protein samples.
it has since become a mainstream technique for the analysis of rna samples.
the bioanalyzer is an automated bio-analytical device using microfluidics technology that provides eletrophoretic separations in an automated and reproducible manner  <cit> .
tiny amounts of rna samples are separated in the channels of the microfabricated chips according to their molecular weight and subsequently detected via laser-induced fluorescence detection.
the result is visualized as an electropherogram where the amount of measured fluorescence correlates with the amount of rna of a given size.
since data are produced in a digital format, they can be easily re-processed to allow additional calculations based on the acquired raw data.
when first released, the biosizing software calculated the ratio of the two ribosomal bands, following the commonly used approach for rna integrity assessment.
however, although assessing rna quality with the bioanalyzer proves to be far superior to the slab gel based approach, the usage of ribosomal ratio for rna quality assessment has several shortcomings.
in many cases, ribosomal ratios showed only weak correlation with rna integrity  <cit>  and more in-depth analysis of the electrophoretic traces requires expert knowledge and is of a subjective nature.
to provide a tool for standardization of rna quality control, a user-independent, automated and reliable procedure was developed.
in this study we present a software algorithm that allows the calculation of an rna integrity number .
the algorithm was developed using methods from information theory to rank features according to their information content and using a bayesian approach to train and select a prediction model on the basis of artificial neural networks.
an overview of the application scenario is summarized schematically in figure  <dig>
techniques for measuring rna integrity
for microcapillary electrophoresis, the agilent  <dig> bioanalyzer was used in conjunction with the rna  <dig> nano and the rna  <dig> pico labchip kits.
this bio-analytical device is based on a combination of microfluidic chips, voltage-induced size separation in gel filled channels and laser-induced fluorescence  detection on a miniaturized scale  <cit> .
twelve samples can be processed sequentially while consuming only very small amounts of each sample.
rna molecules are stained with an intercalating dye and detected by means of lif.
data are archived automatically and available as electropherograms, gel-like images, as well as in tabular format.
figure  <dig> shows example electropherograms of different rna samples displaying varying rna integrity levels.
visual inspection of the electrophoretic traces reveals that progressing degradation entails a decrease of signal intensities for the two ribosomal bands in conjunction with an increase of shorter fragments, i.e.
an elevated baseline between the two ribosomal bands and below the 18s band.
integrity measures for rna
the degradation process of rna is only partly understood since it is dependent on the type of rnase that is present and is often combined with fragmentation processes.
also, the quality of rna in a given experiment can vary extensively from one extraction to another and needs to be under constant surveillance.
using precise analytical instrumentation such as the agilent  <dig> bioanalyzer, human experts are capable of distinguishing rna samples of different quality by examining electrophoretic traces and assigning integrity values or integrity categories  <cit> .
note that the degradation of rna is a continuous process, which implies that there are no natural integrity categories.
in this situation, machine learning methods can be applied to data from experimental measurements to learn an implicit model of rna integrity in order to achieve a user-independent method for assigning integrity values.
that is, the algorithm extracts the relationship between characteristics of the measurement, or features, and the expert-assigned categories.
traditionally, a simple model evaluating the 28s to 18s rrna ratio has been used as a criterion for rna quality.
if not restricted to very specific rna types this model has been shown to be insufficient for a general rna integrity prediction  <cit> .
an adaptive approach can be applied to solve this prediction task when based on a large collection of samples.
in general, an approach applied to this kind of task comprises at least the following basic steps, which are described in more detail below in the method section:
<dig>  data labeling and preprocessing
<dig>  extracting features from the electropherogram
<dig>  selecting an appropriate feature combination
<dig>  training prediction models and selecting the most promising model
RESULTS
sample preparation and data basis
total rna was obtained from various tissues and different organisms mainly human, rat, and mouse.
all samples were analyzed on the agilent  <dig> bioanalyzer.
for the development of the algorithm a large set of data files was kindly provided by the resource center for genome research  <cit>  as well as by agilent.
the overall number of samples in the database totals  <dig>  about 30% of the samples are of known origin from human, mouse and rat extracted from liver, kidney, colon, spleen, brain, heart and placenta.
the origin of the remaining samples was not traceable, but is known to be of mammalian cells or cell lines.
for the development of the algorithm, it was important to include samples of all degradation stages into the database.
the final data set included many intact as well as almost completely degraded rna samples .
partially degraded rna samples were less common but still sufficient in number.
furthermore, the data set comprised different sample concentrations and different extraction methods.
to some extent anomalies were found in the data set as well.
this provided a realistic collection of input data containing a representative basis for all stages of rna degradation.
applying our method described below to the data basis yields a sorted list of features, which was used to construct feature spaces for training regression models.
furthermore, results are given for models based on features proposed in the literature.
finally, we show the correlation of the rin with the outcome of real-time pcr experiments.
feature selection
the total rna ratio was selected as first feature covering 79% of the entropy of the categorical values.
the next two features contribute information about the 28s-region: 28s peak height and the 28s area ratio.
the fourth feature compares the 18s and 28s area to the area of the fast region.
feature  <dig> is the value of a linear regression at the end point of the fast region, whereas the next feature reflects the amount of detected fragments in the fast region.
then, the presence or absence of the 18s peak is selected, which enables the model to distinguish between weaker and stronger degradation.
the last feature gives the relation of the overall mean value to the median value.
since the mean value is sensitive to large peaks it carries information about totally degraded rna or about abnormalities like spikes.
table  <dig> summarizes the results of the feature selection process.
an interpretation of these features from a biological point of view is given in the discussion and an overview of all features is given in the additional files .
model training
based on the sorted list of features we trained neural networks as regression models and systematically increased the number of hidden neurons from  <dig> to  <dig>  until the model evidence decreased clearly.
furthermore, we varied the feature space as described in the previous section.
we observed maximal model evidence using  <dig> to  <dig> features with  <dig> to  <dig> neurons in the hidden layer.
the values are averaged over the results of a 10-fold cross-validation procedure .
as expected, the model evidence is strongly negatively correlated with the generalization error , which shows that the model evidence is a sensible model selection criterion .
we selected the topology using  <dig> features and  <dig> hidden neurons as the most probable model and performed the final training on the whole training data set.
the log value for the evidence of the final model was slightly higher compared to the values during cross validation , whereas the generalization error was stable .
the cross validation error was observed to be a good estimate for the generalization error on the test data.
the feature selection procedure provides in each step the local optimal additional feature, which will not necessarily lead to the globally best combination.
in the later iteration steps, several candidate features provide the same gain in information about the target and there is some randomness in the final selection.
explorative searching for the best combination is intractable because of the computational costs of the combinatorial search.
in an additional, manual optimization step application knowledge was used to substitute some features by plausible alternatives.
feature  <dig> and  <dig> were replaced by the area ratio in the fast region .
additionally the marker height was selected.
in the normalized electropherogram, the marker height allows to detect strongly degraded samples, because it is the only part of the signal which differs from the background noise.
this combination also has a relative mi value of  <dig> , but the best model with  <dig> hidden neurons had a log value for the evidence of - <dig>  it reaches a cross-validation error of  <dig>  and a test error of  <dig> , which is slightly better compared to the results from figure  <dig>  both models perform equally well, the later one was chosen for the final implementation in the expert software for the sake of simplicity.
finally, we evaluated regression models for a subset of  <dig> samples on two different feature spaces: the 28s/18s ratio, and the feature computed by the degradometer software  <cit> .
table  <dig> shows that the rin model is based on a feature space, with higher information content than the other two models.
model evidences indicate that using a single feature results in a lower posterior probability of the model.
this is again consistent with the generalization performance of the models.
the error of rin model is forty times lower compared to 28s/18s-model and about twenty times lower compared the degradometer based model if all samples are considered.
if the samples that are labeled black by the degradometer software are removed from the data set , the relative mi value increases to  <dig> , the evidence reaches a value of - <dig>  whereas the cross validation error is at  <dig> , which is still four times higher than for the rin model.
model evaluation
if a model is supposed to extract a relationship from experimental data, it is helpful for the model evaluation to explore the data in the most important two dimensions, as well as to check for large error values which correspond to categorical misclassifications.
furthermore, the model prediction can be cross-checked against control parameters of follow-up experiments, like rt-pcr.
visualization of decision boundaries
the 2d-visualization of total rna ratio and 28s peak height shows, that we can clearly separate high integrity values from low integrity values.
the categories form clusters in this space.
however, as mentioned in the previous section, the borderline between categories is not sharp, which is due to the fact that degradation is a continuous process.
categorical misclassifications
simple features like the ribosomal ratio which cover only one aspect of the degradation process tend to have larger errors for certain groups of experiments.
that is, they cannot distinguish very well between the categories.
it is very useful to check, that only a few experiments are interchanged over more than one categorical border, that is, the model covers all aspects of the degradation process.
misclassifications are measured by receiver operating characteristics  for distinguishing electropherograms from different groups of categories, whereas the value of the area under the roc-curve  is a balanced measure for the classification error.
we briefly and informally describe how a roc curve is constructed.
the electropherograms are sorted into a ordered list according to the integrity measure estimated by the model.
for a fixed classification task, a roc curve is constructed as exemplarily described in the following for the task of distinguishing electropherograms of category  <dig> from all other categories: walk through the sorted list in descending order.
in each step check if the considered item is in category  <dig> or not according to the original expert label.
if it is true, draw a line fragment in vertical direction, if it is false draw it in horizontal direction.
perfect separation of category  <dig> from the others would imply that the roc curve shoots up vertically on the y-axis to the maximal value, before the first horizontal step is taken.
random assignment of electropherograms would result in a roc curve that corresponds to a diagonal line from the origin to the right top corner.
a roc curve gives a balanced measure of the model performance by integrating over all possible classification borders.
each border corresponds to a specific ratio of sensitivity to specifity, i.e.
a specific point on the roc curve.
several electropherograms are interchanged between the adjacent categories  <dig> and  <dig> , which is natural due to the noise in label assignment step.
very rarely are assignments from electropherograms from category  <dig> to category  <dig> or less .
only  <dig> electropherogram is interchanged between category  <dig> and category  <dig> .
computing the auc value for all other sensible groups of categories shows that categorical misclassifications are seldom observed.
the average auc-value is  <dig>  with a standard deviation of  <dig> .
table  <dig> summarizes the categorical errors over all possible sets of experiments.
correlation with the outcome of experiments
correlation of rin values with downstream experiments is of critical importance.
on the one hand, a good correlation will demonstrate the validity of this approach.
on the other hand, it allows determination of threshold values in order to get meaningful downstream data.
for two-color microarray experiments, this could mean for example that the two input samples should not differ by more than a given number of rin classes, while the lowest acceptable rin can be determined as well.
in the present study, rin values as well as ribosomal ratios were correlated with real-time pcr data.
a detailed description of the sample types and extraction methods as well of the entire experimental setup has been published previously  <cit> .
in short, a gene score was calculated based on the average apparent expression level of  <dig> different housekeeping genes  as measured by real-time pcr.
please note that in this experiment, differences in the apparent gene expression levels are induced by progressing degradation of the rna string material.
figure  <dig> shows the plot of the average apparent gene expression on a logarithmic scale against the rin.
immediately  <dig> cluster of data appear corresponding to high gene expression  with a high rin value and low gene expression  with a low rin value.
on the other hand, the ribosomal ratio exhibits only a weak correlation with the experimentally observed gene expression level .
the rin allows for a straightforward separation in positives and negatives, whereas the ribosomal ratio would reject many more experiments than necessary.
the historical value of  <dig>  would reject about  <dig> experiments of good quality and a value of  <dig>  results in about  <dig> false negatives.
discussion
because of the critical influence of rna integrity on downstream experiments, there is a strong need for a reliable, reproducible, and standardized approach to classify the quality of rna samples.
the long time standard consisting in a 28s to 18s peak ratio of  <dig>  was shown to provide only weak correlation with rna integrity.
the agilent  <dig> bioanalyzer, a bio-analytical device based on a combination of microfluidics, microcapillary electrophoresis, and fluorescence detection, provides a platform to record the size distribution of molecules, e.g., rna, in a digital format.
since this approach is highly reproducible and automated, it provides the basis for an automated, user-independent, and reproducible approach to evaluate the integrity of rna samples using a software algorithm.
for the development of the rna integrity number algorithm, a total of  <dig> rna samples from various sources and of different degradation states was analyzed.
after assigning the samples to  <dig> different categories ranging from  <dig>  to  <dig> , methods from information theory were applied to calculate features describing the curve of the electropherogram.
in the following step, features were selected for further processing that showed high information content about the task to distinguish the  <dig> categories.
these features were then taken as input variables for a model-training step.
here, using a bayesian learning approach to select the most probable model, several models were trained utilizing artificial neural networks and the best was chosen for prediction of previously unseen test data.
the result produced by this procedure is an algorithm called rna integrity number .
analysis of the rin model
the rin algorithm is based on a selection of features that contribute information about the rna integrity.
it is obvious, that a single feature is hardly sufficient for a universal integrity measure.
moreover, a combination of different features covers several aspects of the measurement and is more robust against noise in the signal .
to understand why the features were selected and to enhance the confidence for application specialists it is important, to give an interpretation of the features:
<dig>  the total rna ratio measures the fraction of the area in the region of 18s and 28s compared to the total area under the curve and reflects the proportion of large molecules compared to smaller ones.
it has large values for categories  <dig> to  <dig>
<dig>  the height of the 28s peak contributes additional information about the state of the degradation process, i.e.
during degradation, the 28s band disappears faster than the 18s band.
therefore, it allows detection of a beginning degradation.
it has largest values for categories  <dig> and  <dig>  and zero values for categories  <dig> to  <dig>
<dig>  the fast area ratio reflects how far the degradation proceeded and has typically larger values for the categories  <dig> to  <dig>
<dig>  the marker height has large values for categories  <dig> and  <dig> and small values for all other categories since short degradation products will overlap with the lower marker.
comparing the approaches
using a single simple feature to judge rna integrity was already shown to be insufficient  <cit> .
while focusing on one aspect of the electropherogram allows for a rough orientation about the integrity, it is still subjective to a high degree.
linear models based on these features show a mean squared error that is four to sixty times higher  than compared to the proposed approach.
the reason for this tremendous difference lies in the fact, that neither the 28s/18s ratio nor the degradation factor reflect all properties of the rna degradation process.
for example, several samples of integrity category  <dig> are labeled black from the degradometer software as they have low signal intensities.
this happened for 42% of the samples under consideration, which are all samples that were under investigation for microarray experiments.
the degradation factor contains similar information as the fast area ratio, which reflects typical characteristics of categories  <dig> to  <dig>  the high ribosomal ratio is useful to detect a certain amount of high quality samples, but the categorization is not valid for all of them.
using several features which complement one another and allow for a non-linear weighting of these features allowed to reduce the error to a minimum value which is in the order of the natural noise in the target data.
the noise results from using a categorical grid for a continues process as well as from a few abnormalities.
interestingly, almost no interchanges over more than one categorical border are observed.
thus, the classification errors appear almost only at the borderline between two categories, which was also difficult for humans to decide, when labeling the data.
availability of the rin model
the agilent  <dig> bioanalyzer system software can be downloaded from agilent's webpage .
version b.
<dig>  and later will allow for measurement reviews  including the calculation of the rna integrity number  <cit> .
up-to-date information about the rin-project can be found at the rin web site  <cit> .
CONCLUSIONS
this article investigates an automated procedure for extracting features from signal measurements, selecting suitable subsets of features and extracting a functional relationship to target labels of experiments.
we demonstrated that the application of the methodology to a large collection of electrophoretic rna measurements recorded with an agilent  <dig> bioanalyzer provides a predictive model for rna integrity, the rin.
the generalization error is as low as the natural noise in the target values and apparently lower than for ribosomal ratios.
our results show the importance of taking characteristics of several regions of the recorded electropherogram into account in order to get a robust and reliable prediction of rna integrity, furthermore, it was demonstrated that the rin can be correlated with the outcome of downstream experiments, i.e.
by performing this quality assessment step users can prevent themselves from erroneous results and loss of money and resources.
we conclude, that the rna integrity number is an important tool in conducting valid gene expression measurement experiments as real-time pcr or dna microarray, that is already widely and successfully used since the release of the β-version.
it is largely free from instrument and concentration variability, thereby facilitating the comparison of samples between different labs.
for example, the rin can be assigned to a rna sample before shipping from a lab and the same quality control can be performed in a user-independent way at the destination lab.

 the rna molecule plays a critical role in transferring information encoded in the genome to the many different forms of proteins. after extracting rna from cells by various methods, scientists are provided with a direct measure of cellular activity using gene expression measurement techniques. among these, real-time pcr and dna microarrays are the most widely used techniques. importance of integrity rna is a thermodynamically stable molecule, which is, however, rapidly digested in the presence of the nearly ubiquitous rnase enzymes. as a result, shorter fragments of rna commonly occur in a sample, which can potentially compromise results of downstream applications. in order to evaluate the degree of degradation, electrophoretic methods have been applied that separate the samples according to the size of the comprised molecules. historically, rna integrity is evaluated using agarose gel electrophoresis stained with ethidium bromide, which produces a certain banding pattern. typically, gel images show two bands comprising the 28s and 18s ribosomal rna species and other bands where smaller rna species are located. rna is considered of high quality when the ratio of 28s:18s bands is about and higher. since this approach relies on human interpretation of gel images, it is subjective, hardly comparable from one lab to another, and the resulting data cannot be processed digitally. towards an automated approach in the agilent bioanalyzer was introduced for the separation of dna, rna, and protein samples. it has since become a mainstream technique for the analysis of rna samples. the bioanalyzer is an automated bio-analytical device using microfluidics technology that provides eletrophoretic separations in an automated and reproducible manner. tiny amounts of rna samples are separated in the channels of the microfabricated chips according to their molecular weight and subsequently detected via laser-induced fluorescence detection. the result is visualized as an electropherogram where the amount of measured fluorescence correlates with the amount of rna of a given size. since data are produced in a digital format, they can be easily re-processed to allow additional calculations based on the acquired raw data. when first released, the biosizing software calculated the ratio of the two ribosomal bands, following the commonly used approach for rna integrity assessment. however, although assessing rna quality with the bioanalyzer proves to be far superior to the slab gel based approach, the usage of ribosomal ratio for rna quality assessment has several shortcomings. in many cases, ribosomal ratios showed only weak correlation with rna integrity and more in-depth analysis of the electrophoretic traces requires expert knowledge and is of a subjective nature. to provide a tool for standardization of rna quality control, a user-independent, automated and reliable procedure was developed. in this study we present a software algorithm that allows the calculation of an rna integrity number. the algorithm was developed using methods from information theory to rank features according to their information content and using a bayesian approach to train and select a prediction model on the basis of artificial neural networks. an overview of the application scenario is summarized schematically in figure techniques for measuring rna integrity for microcapillary electrophoresis, the agilent bioanalyzer was used in conjunction with the rna nano and the rna pico labchip kits. this bio-analytical device is based on a combination of microfluidic chips, voltage-induced size separation in gel filled channels and laser-induced fluorescence detection on a miniaturized scale. twelve samples can be processed sequentially while consuming only very small amounts of each sample. rna molecules are stained with an intercalating dye and detected by means of lif. data are archived automatically and available as electropherograms, gel-like images, as well as in tabular format. figure shows example electropherograms of different rna samples displaying varying rna integrity levels. visual inspection of the electrophoretic traces reveals that progressing degradation entails a decrease of signal intensities for the two ribosomal bands in conjunction with an increase of shorter fragments, i.e. an elevated baseline between the two ribosomal bands and below the 18s band. integrity measures for rna the degradation process of rna is only partly understood since it is dependent on the type of rnase that is present and is often combined with fragmentation processes. also, the quality of rna in a given experiment can vary extensively from one extraction to another and needs to be under constant surveillance. using precise analytical instrumentation such as the agilent bioanalyzer, human experts are capable of distinguishing rna samples of different quality by examining electrophoretic traces and assigning integrity values or integrity categories. note that the degradation of rna is a continuous process, which implies that there are no natural integrity categories. in this situation, machine learning methods can be applied to data from experimental measurements to learn an implicit model of rna integrity in order to achieve a user-independent method for assigning integrity values. that is, the algorithm extracts the relationship between characteristics of the measurement, or features, and the expert-assigned categories. traditionally, a simple model evaluating the 28s to 18s rrna ratio has been used as a criterion for rna quality. if not restricted to very specific rna types this model has been shown to be insufficient for a general rna integrity prediction. an adaptive approach can be applied to solve this prediction task when based on a large collection of samples. in general, an approach applied to this kind of task comprises at least the following basic steps, which are described in more detail below in the method section: data labeling and preprocessing extracting features from the electropherogram selecting an appropriate feature combination training prediction models and selecting the most promising model  sample preparation and data basis total rna was obtained from various tissues and different organisms mainly human, rat, and mouse. all samples were analyzed on the agilent bioanalyzer. for the development of the algorithm a large set of data files was kindly provided by the resource center for genome research as well as by agilent. the overall number of samples in the database totals about 30% of the samples are of known origin from human, mouse and rat extracted from liver, kidney, colon, spleen, brain, heart and placenta. the origin of the remaining samples was not traceable, but is known to be of mammalian cells or cell lines. for the development of the algorithm, it was important to include samples of all degradation stages into the database. the final data set included many intact as well as almost completely degraded rna samples. partially degraded rna samples were less common but still sufficient in number. furthermore, the data set comprised different sample concentrations and different extraction methods. to some extent anomalies were found in the data set as well. this provided a realistic collection of input data containing a representative basis for all stages of rna degradation. applying our method described below to the data basis yields a sorted list of features, which was used to construct feature spaces for training regression models. furthermore, results are given for models based on features proposed in the literature. finally, we show the correlation of the rin with the outcome of real-time pcr experiments. feature selection the total rna ratio was selected as first feature covering 79% of the entropy of the categorical values. the next two features contribute information about the 28s-region: 28s peak height and the 28s area ratio. the fourth feature compares the 18s and 28s area to the area of the fast region. feature is the value of a linear regression at the end point of the fast region, whereas the next feature reflects the amount of detected fragments in the fast region. then, the presence or absence of the 18s peak is selected, which enables the model to distinguish between weaker and stronger degradation. the last feature gives the relation of the overall mean value to the median value. since the mean value is sensitive to large peaks it carries information about totally degraded rna or about abnormalities like spikes. table summarizes the results of the feature selection process. an interpretation of these features from a biological point of view is given in the discussion and an overview of all features is given in the additional files. model training based on the sorted list of features we trained neural networks as regression models and systematically increased the number of hidden neurons from to until the model evidence decreased clearly. furthermore, we varied the feature space as described in the previous section. we observed maximal model evidence using to features with to neurons in the hidden layer. the values are averaged over the results of a 10-fold cross-validation procedure. as expected, the model evidence is strongly negatively correlated with the generalization error, which shows that the model evidence is a sensible model selection criterion. we selected the topology using features and hidden neurons as the most probable model and performed the final training on the whole training data set. the log value for the evidence of the final model was slightly higher compared to the values during cross validation, whereas the generalization error was stable. the cross validation error was observed to be a good estimate for the generalization error on the test data. the feature selection procedure provides in each step the local optimal additional feature, which will not necessarily lead to the globally best combination. in the later iteration steps, several candidate features provide the same gain in information about the target and there is some randomness in the final selection. explorative searching for the best combination is intractable because of the computational costs of the combinatorial search. in an additional, manual optimization step application knowledge was used to substitute some features by plausible alternatives. feature and were replaced by the area ratio in the fast region. additionally the marker height was selected. in the normalized electropherogram, the marker height allows to detect strongly degraded samples, because it is the only part of the signal which differs from the background noise. this combination also has a relative mi value of, but the best model with hidden neurons had a log value for the evidence of - it reaches a cross-validation error of and a test error of, which is slightly better compared to the results from figure both models perform equally well, the later one was chosen for the final implementation in the expert software for the sake of simplicity. finally, we evaluated regression models for a subset of samples on two different feature spaces: the 28s/18s ratio, and the feature computed by the degradometer software. table shows that the rin model is based on a feature space, with higher information content than the other two models. model evidences indicate that using a single feature results in a lower posterior probability of the model. this is again consistent with the generalization performance of the models. the error of rin model is forty times lower compared to 28s/18s-model and about twenty times lower compared the degradometer based model if all samples are considered. if the samples that are labeled black by the degradometer software are removed from the data set, the relative mi value increases to, the evidence reaches a value of - whereas the cross validation error is at, which is still four times higher than for the rin model. model evaluation if a model is supposed to extract a relationship from experimental data, it is helpful for the model evaluation to explore the data in the most important two dimensions, as well as to check for large error values which correspond to categorical misclassifications. furthermore, the model prediction can be cross-checked against control parameters of follow-up experiments, like rt-pcr. visualization of decision boundaries the 2d-visualization of total rna ratio and 28s peak height shows, that we can clearly separate high integrity values from low integrity values. the categories form clusters in this space. however, as mentioned in the previous section, the borderline between categories is not sharp, which is due to the fact that degradation is a continuous process. categorical misclassifications simple features like the ribosomal ratio which cover only one aspect of the degradation process tend to have larger errors for certain groups of experiments. that is, they cannot distinguish very well between the categories. it is very useful to check, that only a few experiments are interchanged over more than one categorical border, that is, the model covers all aspects of the degradation process. misclassifications are measured by receiver operating characteristics for distinguishing electropherograms from different groups of categories, whereas the value of the area under the roc-curve is a balanced measure for the classification error. we briefly and informally describe how a roc curve is constructed. the electropherograms are sorted into a ordered list according to the integrity measure estimated by the model. for a fixed classification task, a roc curve is constructed as exemplarily described in the following for the task of distinguishing electropherograms of category from all other categories: walk through the sorted list in descending order. in each step check if the considered item is in category or not according to the original expert label. if it is true, draw a line fragment in vertical direction, if it is false draw it in horizontal direction. perfect separation of category from the others would imply that the roc curve shoots up vertically on the y-axis to the maximal value, before the first horizontal step is taken. random assignment of electropherograms would result in a roc curve that corresponds to a diagonal line from the origin to the right top corner. a roc curve gives a balanced measure of the model performance by integrating over all possible classification borders. each border corresponds to a specific ratio of sensitivity to specifity, i.e. a specific point on the roc curve. several electropherograms are interchanged between the adjacent categories and, which is natural due to the noise in label assignment step. very rarely are assignments from electropherograms from category to category or less. only electropherogram is interchanged between category and category. computing the auc value for all other sensible groups of categories shows that categorical misclassifications are seldom observed. the average auc-value is with a standard deviation of. table summarizes the categorical errors over all possible sets of experiments. correlation with the outcome of experiments correlation of rin values with downstream experiments is of critical importance. on the one hand, a good correlation will demonstrate the validity of this approach. on the other hand, it allows determination of threshold values in order to get meaningful downstream data. for two-color microarray experiments, this could mean for example that the two input samples should not differ by more than a given number of rin classes, while the lowest acceptable rin can be determined as well. in the present study, rin values as well as ribosomal ratios were correlated with real-time pcr data. a detailed description of the sample types and extraction methods as well of the entire experimental setup has been published previously. in short, a gene score was calculated based on the average apparent expression level of different housekeeping genes as measured by real-time pcr. please note that in this experiment, differences in the apparent gene expression levels are induced by progressing degradation of the rna string material. figure shows the plot of the average apparent gene expression on a logarithmic scale against the rin. immediately cluster of data appear corresponding to high gene expression with a high rin value and low gene expression with a low rin value. on the other hand, the ribosomal ratio exhibits only a weak correlation with the experimentally observed gene expression level. the rin allows for a straightforward separation in positives and negatives, whereas the ribosomal ratio would reject many more experiments than necessary. the historical value of would reject about experiments of good quality and a value of results in about false negatives. discussion because of the critical influence of rna integrity on downstream experiments, there is a strong need for a reliable, reproducible, and standardized approach to classify the quality of rna samples. the long time standard consisting in a 28s to 18s peak ratio of was shown to provide only weak correlation with rna integrity. the agilent bioanalyzer, a bio-analytical device based on a combination of microfluidics, microcapillary electrophoresis, and fluorescence detection, provides a platform to record the size distribution of molecules, e.g., rna, in a digital format. since this approach is highly reproducible and automated, it provides the basis for an automated, user-independent, and reproducible approach to evaluate the integrity of rna samples using a software algorithm. for the development of the rna integrity number algorithm, a total of rna samples from various sources and of different degradation states was analyzed. after assigning the samples to different categories ranging from to, methods from information theory were applied to calculate features describing the curve of the electropherogram. in the following step, features were selected for further processing that showed high information content about the task to distinguish the categories. these features were then taken as input variables for a model-training step. here, using a bayesian learning approach to select the most probable model, several models were trained utilizing artificial neural networks and the best was chosen for prediction of previously unseen test data. the result produced by this procedure is an algorithm called rna integrity number. analysis of the rin model the rin algorithm is based on a selection of features that contribute information about the rna integrity. it is obvious, that a single feature is hardly sufficient for a universal integrity measure. moreover, a combination of different features covers several aspects of the measurement and is more robust against noise in the signal. to understand why the features were selected and to enhance the confidence for application specialists it is important, to give an interpretation of the features: the total rna ratio measures the fraction of the area in the region of 18s and 28s compared to the total area under the curve and reflects the proportion of large molecules compared to smaller ones. it has large values for categories to the height of the 28s peak contributes additional information about the state of the degradation process, i.e. during degradation, the 28s band disappears faster than the 18s band. therefore, it allows detection of a beginning degradation. it has largest values for categories and and zero values for categories to the fast area ratio reflects how far the degradation proceeded and has typically larger values for the categories to the marker height has large values for categories and and small values for all other categories since short degradation products will overlap with the lower marker. comparing the approaches using a single simple feature to judge rna integrity was already shown to be insufficient. while focusing on one aspect of the electropherogram allows for a rough orientation about the integrity, it is still subjective to a high degree. linear models based on these features show a mean squared error that is four to sixty times higher than compared to the proposed approach. the reason for this tremendous difference lies in the fact, that neither the 28s/18s ratio nor the degradation factor reflect all properties of the rna degradation process. for example, several samples of integrity category are labeled black from the degradometer software as they have low signal intensities. this happened for 42% of the samples under consideration, which are all samples that were under investigation for microarray experiments. the degradation factor contains similar information as the fast area ratio, which reflects typical characteristics of categories to the high ribosomal ratio is useful to detect a certain amount of high quality samples, but the categorization is not valid for all of them. using several features which complement one another and allow for a non-linear weighting of these features allowed to reduce the error to a minimum value which is in the order of the natural noise in the target data. the noise results from using a categorical grid for a continues process as well as from a few abnormalities. interestingly, almost no interchanges over more than one categorical border are observed. thus, the classification errors appear almost only at the borderline between two categories, which was also difficult for humans to decide, when labeling the data. availability of the rin model the agilent bioanalyzer system software can be downloaded from agilent's webpage. version b. and later will allow for measurement reviews including the calculation of the rna integrity number. up-to-date information about the rin-project can be found at the rin web site.  this article investigates an automated procedure for extracting features from signal measurements, selecting suitable subsets of features and extracting a functional relationship to target labels of experiments. we demonstrated that the application of the methodology to a large collection of electrophoretic rna measurements recorded with an agilent bioanalyzer provides a predictive model for rna integrity, the rin. the generalization error is as low as the natural noise in the target values and apparently lower than for ribosomal ratios. our results show the importance of taking characteristics of several regions of the recorded electropherogram into account in order to get a robust and reliable prediction of rna integrity, furthermore, it was demonstrated that the rin can be correlated with the outcome of downstream experiments, i.e. by performing this quality assessment step users can prevent themselves from erroneous results and loss of money and resources. we conclude, that the rna integrity number is an important tool in conducting valid gene expression measurement experiments as real-time pcr or dna microarray, that is already widely and successfully used since the release of the β-version. it is largely free from instrument and concentration variability, thereby facilitating the comparison of samples between different labs. for example, the rin can be assigned to a rna sample before shipping from a lab and the same quality control can be performed in a user-independent way at the destination lab. 
the resulting algorithm is a user-independent, automated and reliable procedure for standardization of rna quality control that allows the calculation of an rna integrity number. this approach is applied to a large collection of electrophoretic rna measurements recorded with an agilent bioanalyzer to extract an algorithm that describes rna integrity. our results show the importance of taking characteristics of several regions of the recorded electropherogram into account in order to get a robust and reliable prediction of rna integrity, especially if compared to traditional methods. the integrity of rna molecules is of paramount importance for experiments that try to reflect the snapshot of gene expression at the moment of rna extraction. a method is introduced that automatically selects features from signal measurements and constructs regression models based on a bayesian learning technique. until recently, there has been no reliable standard for estimating the integrity of rna samples and the ratio of 28s:18s ribosomal rna, the common measure for this purpose, has been shown to be inconsistent. the advent of microcapillary electrophoretic rna separation provides the basis for an automated high-throughput approach, in order to estimate the integrity of rna samples in an unambiguous way.
 the integrity of rna molecules is of paramount importance for experiments that try to reflect the snapshot of gene expression at the moment of rna extraction. until recently, there has been no reliable standard for estimating the integrity of rna samples and the ratio of 28s:18s ribosomal rna, the common measure for this purpose, has been shown to be inconsistent. the advent of microcapillary electrophoretic rna separation provides the basis for an automated high-throughput approach, in order to estimate the integrity of rna samples in an unambiguous way. methods a method is introduced that automatically selects features from signal measurements and constructs regression models based on a bayesian learning technique. feature spaces of different dimensionality are compared in the bayesian framework, which allows selecting a final feature combination corresponding to models with high posterior probability.  this approach is applied to a large collection of electrophoretic rna measurements recorded with an agilent bioanalyzer to extract an algorithm that describes rna integrity. the resulting algorithm is a user-independent, automated and reliable procedure for standardization of rna quality control that allows the calculation of an rna integrity number.  our results show the importance of taking characteristics of several regions of the recorded electropherogram into account in order to get a robust and reliable prediction of rna integrity, especially if compared to traditional methods. 