Individualized markers optimize class prediction of microarray data
© Pavlidis and Poirazi; licensee BioMed Central Ltd. 2006
Received: 11 April 2006
Accepted: 14 July 2006
Published: 14 July 2006
Identification of molecular markers for the classification of microarray data is a challenging task. Despite the evident dissimilarity in various characteristics of biological samples belonging to the same category, most of the marker – selection and classification methods do not consider this variability. In general, feature selection methods aim at identifying a common set of genes whose combined expression profiles can accurately predict the category of all samples. Here, we argue that this simplified approach is often unable to capture the complexity of a disease phenotype and we propose an alternative method that takes into account the individuality of each patient-sample.
Instead of using the same features for the classification of all samples, the proposed technique starts by creating a pool of informative gene-features. For each sample, the method selects a subset of these features whose expression profiles are most likely to accurately predict the sample's category. Different subsets are utilized for different samples and the outcomes are combined in a hierarchical framework for the classification of all samples. Moreover, this approach can innately identify subgroups of samples within a given class which share common feature sets thus highlighting the effect of individuality on gene expression.
In addition to high classification accuracy, the proposed method offers a more individualized approach for the identification of biological markers, which may help in better understanding the molecular background of a disease and emphasize the need for more flexible medical interventions.
discriminate between different disease types
predict the outcome of a disease
detect sub-categories or states of a disease
pin down independent and possibly unknown processes which are involved in the generation or the progression of a disease.
Several marker (or feature) selection methods have been used in gene expression studies utilizing microarray technology. Among these, filter methods in which the selection is independent from the optimization criteria of the classifier are most frequently used. Such methods have the advantage of being cost-effective and easy to implement which make them very attractive for microarray data experiments where the set of features is in the order of thousands. Frequently used filter methods include the two-sample t-test [14–22] Signal-to-Noise , TNoM , ICED  and the z-test  just to name a few. Wrapper methods on the other hand use similar criteria as the classifier in order to select optimal features thus maximizing classification capacity. Recursive Feature Elimination is an example of a wrapper method used on microarray data . A recent study  comparing the performance of filter vs. wrapper methods on microarray data showed that the latter achieve higher performance than the former but the improvement in performance is accompanied by a considerable cost in computational complexity. While a number of other feature selection methods have been used in microarray data, only the aforementioned filter methods are discussed as they are more relevant to the present work. All of these methods have a number of shortcomings that are particularly important when applied to microarray data. For example, a basic assumption of the t-test and Signal-to-Noise methods is that data follow a normal distribution, a postulation which is not always valid for microarray experiments. In fact, a recent publication  showed that a yeast gene expression dataset is better modeled by an alpha distribution (a = 1.3). The main difference between Signal-to-Noise and t-test is that the former gives a larger penalty to genes with high expression variance in both -as opposed to just one- classes. However, this kind of expression variability might be important for biological samples, where only a given condition may influence the expression of certain marker genes. The main drawback of these methods is that they both assume a global behavior of a marker gene across all samples of the same class, which is an oversimplified assumption for biological samples.
protein degradation and stability
immortalization and senescence
chemical and radiation- induced mutagenesis
the stress response (NIH-CE)
Samples belonging to the same class may have considerably different gene expression profiles. This variability is two-fold. First, each sample maybe best characterized by a (partially or entirely) different set of marker genes. Second, each sample maybe best characterized by a different expression range of a common set of gene features. To address this kind of variability, we construct a pool of genes, hereby termed "informative genes", each of which carries important information with respect to the categorization of some -but not necessarily all- samples. Each informative gene comprises of one or more "Consistent Expression Regions" (CERs) that accurately predict the category of certain samples (see Methods).
Variability among samples of the same class may indicate the existence of unknown subgroups that should be treated separately. The proposed method is particularly suitable for this kind of variability, as it has an innate property to identify subgroups based on their characterization by a common subset of genes or gene expression regions.
Results and discussion
Comparison of Proposed Method Performance against Existing Methods on Publicly Available Datasets. As shown in the table, the proposed method achieves a high classification performance on all datasets tested. In particular, the performance is superior to that of the referenced method in 3/6 datasets and matches that of the referenced method in the remaining 3 datasets. The last column shows the ratio of genes selected by both ours and the cross reference method over the total number of gene-features in the cross reference method. Abbreviations: S2N: Signal to Noise, CC: Correlation Coefficient, NA: Neighborhood Analysis, FA: Factor Analysis, 2-tail T: 2-Tail Student test, ER: Expression Ratio, K-NN: K-Nearest Neighbors. *Outlier samples for this dataset were omitted from the classification in both the reference and our method.
Cross Reference Method
4/4, 3/3, 8/8
AML vs. ALL leukemia results
Identification of AML sub-groups: "Failure" vs. "Success" discrimination
Identification of ALL sub-groups: B-cell vs. T-cell sample discrimination
ALL/MLL/AML leukemia results
Breast cancer results
Central Nervous System (CNS) results
The Central Nervous System data set  contains 60 biopsy samples taken from patients with various tumor types including medulloblastomas, primitive neuroectodermal tumours (PNETs), atypical teratoid/rhabdoid tumours (AT/RTs) and malignant gliomas. Samples were obtained before the patients received treatment, accompanied with clinical follow-up. Survivors are patients who are alive after treatment, while failures are those who succumbed to their disease. For a significance percentage p s = 2%, a total number of 443 genes (170, 82, 51 and 140, 1 st , 2 nd , 3 rd and 4 th order, respectively) were selected to discriminate between poor vs. good treatment outcome. When only first order genes were used in the classifier, the method achieved a performance of 44/60 correct classification. Notice that first order genes roughly resemble genes that are selected by Signal-to-Noise or t-test as done in the original publication, thus explaining the similar classification accuracy (47/60). However, using only higher order genes (n > 1) resulted in a significant improvement in discrimination accuracy with 55/60 correct class assignments. This improvement maybe be due to the complexity of the particular tumors that belong to at least four different categories, which can only be captured by more complex (higher order) gene features. Figure 6 in [Additional file 1] provides some supporting evidence for this hypothesis. As evident in the figure, the fraction of higher order genes among all selected features is consistently larger in the CNS as opposed to two other datasets (ALL/AML and Breast Cancer) in which the content of 1 st order genes is much bigger. The statistically significant presence of higher order genes in the CNS data along with the improved classification capacity achieved with these features suggests an important discriminatory and perhaps biological role. A list of six representative higher order genes selected in the CNS dataset is included in Table 4 of [Additional file 1].
Given a set of tissue-specific microarray experiments performed under different conditions, this work presents a new method for identifying genes that can explain or get affected by these conditions. Such informative genes are shown not only to accurately discriminate between different disease types or stages but also reveal the existence of known or new sub-groupings within a main category and pinpoint molecular mechanisms that are likely to support these groupings.
The utilization of higher order (multiple-region) genes often results in a significant improvement in discrimination performance. A nice example is the classification of Central Nervous System samples into two classes representing poor vs. good treatment outcome, where the utilization of higher order genes alone results in significantly higher accuracy compared to the use of first order genes. Note that first order (single-region) genes are similar to those detected by Signal-to-Noise, t-test or ICED methods as they often have a single-threshold for classification. It is likely however, that treatment outcome in these patients depends heavily on genes with a more complex expression pattern that differentially characterizes the heterogeneous group of CNS tumors used in this study. A comparison between AML/ALL Leukemia, Breast Cancer, and Central Nervous System datasets -all of which are performed using the same microarray chips – reveals several interesting differences in the number and order of selected genes. First order genes comprise nearly 70% of the total number of selected genes in both Breast Cancer and AML/ALL Leukemia datasets, but less than ~40% in the Central Nervous System dataset. On the contrary, more higher-order (4 th and 3 rd ) genes are selected in the Central Nervous System dataset as compared to the other two, supporting the hypothesis that treatment outcome for CNS tumor patients is characterized by complex gene expression patterns (see Figure 6 in [Additional file 1]). Moreover, a number of higher order genes selected by our method have been associated with CNS tumors and treatment outcome. Interesting examples include the gene encoding for CD70/CD27 ligand, the antiapoptotic gene seladin-1, the gene coding for the interleukin-1 receptor (IL1R1) and the gene coding for the Ser/Thr protein kinase CDK5 (see Table 4 in [Additional file 1]). CD70 is a member of the Tumor Necrosis Factor family which is highly expressed in human brain tumors  and was recently shown to play an immune stimulatory role -preventing tumor growth in vivo- that encourages its application in tumor immunotherapy . The interleukin-1 receptor (IL1R1) is a membrane protein which is variably expressed in different brain tumors  and has also been suggested to play a role in brain immunotherapy of astrocytomas . The antiapoptotic gene seladin-1, which is implicated in Alzheimer's disease and cholesterol metabolism, was also found to integrate cellular response to oncogenic and oxidative stress . This gene was recently found to be downregulated in adrenocortical adenomas and carcinomas  while its differential expression in pituitary adenomas has been suggested to associate with a different apoptotic response to somatostatin analogs . Cyclin dependent kinase 5 (CdK5) is a proline-direct protein kinase that is most active in the CNS and has been implicated in certain neurodegenerative diseases. It was recently shown to facilitate the progression of apoptosis by regulating the activity of the tumor suppressor protein p53 , the expression of which has been associated with poor prognosis in primary CNS diffuse large B-cell lymphoma . In addition, overexpression of both p53 and bcl-2 proteins has been associated with ominous prognosis in pediatric glioblastoma multiforme tumours . Taken together, these findings suggest that genes with heterogeneous expression detected by our method are not simply the result of technical or biological irrelevant variation but they can have an important biological role.
In conclusion, this work describes a new method for the identification of informative genes that takes into account inherent genetic variation in disease samples which may be characteristic of certain sub-groups within a disease category. This relatively simple approach, in conjunction with a committee voting classifier allows for improved class prediction as well as identification of interesting disease sub-groups. More importantly, our method allows the detection of marker genes that support these sub-groupings, thus possibly shedding some light on the underlying molecular mechanisms involved in disease related processes and providing a new tool that may facilitate efforts towards individualized medicine.
Identification of informative genes and construction of gene pool
The proposed algorithm uses a training set comprised of labeled samples belonging to two categories (0 or 1) to construct a pool of informative genes that exhibit Consistent Expression Regions (CERs). CERs are defined as the intervals enclosing the expression (sorted in ascending order) of a given gene in a significant number of training samples which belong to the same category. Examples of informative genes and associated CERs are shown in Figure 2. The consistency of a CER is given by the fraction of these majority samples in CER, normalized by the size of their respective category. Only genes with at least one CER whose consistency value is greater than a statistically defined threshold, p s , are used to construct the pool. The order of each informative gene with respect to a category (0 or 1) reflects the number of class-specific CERs it consists of (for more details about the estimation of consistency thresholds and gene orders see [Additional file 1]).
The outcome of this step is the identification of category-specific classifiers formed by expression regions in the profiles of selected genes as opposed to a single expression threshold defined by most existing feature selection methods. As a result, a gene exhibiting a class-specific CER can be used to reliably assign a label of the same class to any new sample in which its expression lies within the boundaries of this CER. Note that any informative gene can produce several different regional classifiers, according to its CER assortment.
The contribution of these thresholded expression regions could be twofold. First, their mapping to a limited sample number of the same class may provide insights about the complexity of a given disease category. For example, CERs of the same category may reflect differences in the order and/or extent that various cancer-associated molecular processes are utilized to induce qualitatively the same phenotype but with a different gene expression pattern. It is thus conceivable that CERs can detect subgroups within a single class. Second, the classification accuracy of these regions, which is overlooked by existing methods focusing on the expression profile of a gene as a whole, can be used to construct a potentially more powerful classifier that takes into account the individuality of different samples.
Class prediction using CERs and hierarchical clustering
To classify unseen samples into their respective categories, the method combines subsets of informative genes to form an aggregate classifier. For a two-class problem, the aggregate classifier consists of two -possibly overlapping- lists of informative genes. Each list consists of the set of informative genes that contain CERs specific to each class. If an informative gene contains at least two CERs, each corresponding to a different class (Figure 2), it serves as a classifier for both classes. For the categorization of each new sample the method proceeds as follows: first, the subsets of genes that are able to predict its category are retrieved from each class-specific list. Their respective CERs are then used to assign a class label to the new sample thus generating two lists of 0 and 1 votes, respectively. At this stage, the votes correspond to the informative genes containing the CER and not the CER itself. The procedure is repeated for all unseen samples and the class assignments for each sample are fed to a modified Manhattan distance to estimate dissimilarity scores between samples. Specifically, the distance between two samples a and b is defined as:
D(a, b) = T - C(a, b) (1)
where T is the total number of informative genes which constitute the aggregate classifier and C(a, b) is the number of genes that give the same vote (0 or 1) for both samples a and b. Alternatively, a similarity score between samples a and b is given by C(a, b). The determination of similarities between samples is graphically illustrated in Figure 3. Finally, the dissimilarity scores between all samples are fed in the publicly available phylogenetic software MEGA2  to build a hierarchical tree. The method's performance is measured as its discrimination capacity on the set of unseen samples.
Comparison to Entropy-based methods
Since the proposed method may sound similar to Entropy-based discretization methods frequently used in machine learning problems, we include a comparison between these two approaches.
In an information-based framework, Shannon's entropy  can be used for the evaluation of the information content of a given gene. The entropy of a particular k class input (k possible states) is given by the formula:
where p i corresponds to the probability of the state i. In the analysis presented here k equals 2, since all datasets were broken down to two-class discrimination problems.
Entropy-based methods consider all possible states (classes) of the input data in order to estimate discretization thresholds and identify informative genes. On the contrary, the method presented here detects genes whose expression within a well defined region consistently maps to a single class, without taking into account the remaining classes.
Entropy-based methods usually search for a single expression threshold that minimizes the entropy of a discretized gene. Although multi-interval discretization can be achieved with iterative application of entropy-based minimization methods , such an approach is of high computational cost. The basic idea of this method is to partition a range of real values into a number of disjoint intervals such that the entropy of the intervals is minimal. However, this method also considers minimization criteria that involve both classes for each interval.
Finally, the method presented here does not utilize any minimization criterion but searches for statistically significant homogeneous regions (CERs) in which no other state can occur as opposed to entropy-based methods where a few instances of other states are allowed.
Detection of sample sub-groups
Identification of sub-groups within a given disease class can be of major importance as it may pinpoint patient subcategories that respond differentially to a given treatment. To detect such sub-groups, the method utilizes informative genes that inherently separate a main class into two or more clusters by grouping different subsets of samples in different CERs. An example is given by gene VII in Figure 2, whose expression profile separates class 1 samples into two distinct sub-groups. Down-regulation of this gene is characteristic of the first while up-regulation is characteristic of the second sub-group. For the detection of within class sub-groups, the method combines all higher order informative genes (i.e. genes that contain more than one CER corresponding to the same class) or just a selected subset of them.
Using all genes with multiple single-class CERs
In this approach, all informative genes that contain at least two CERs specific to the same class (n > 1) are utilized. For each informative gene, samples that lie within different CERs are assigned to different sub-groups, using a voting scheme similar to that of the class prediction task. However, in contrast to the class prediction task, CERs of the same gene now offer a different vote which can take a value raging from 0 to the gene order. Resulting voting lists are then used along with the modified Manhattan distance to construct a dendrogram. This approach is particularly suitable for datasets in which the actual number of class categories is larger than originally suggested, as for example the classification of ALL/MLL/AML leukemia samples shown in Figure 6.
Using a tight set of genes
In the second approach, only genes of the same order are used to identify sample sub-groups (as shown in Figures 4 and 5). Reversely, the method identifies genes that support a pre-existing sub-clustering of samples. These sub-groups, which may be irrelevant to the original classification, are often supported by only a small -tight- set of genes. A tight set consists of same-order genes whose expression in the same -significantly large- set of samples is bounded by exactly one CER per gene. More importantly, their expression in the remaining samples must range over several other CERs. The reasoning for this second constraint is that a gene which clusters in one region samples that lie in various regions of other genes has a tendency to distract the grouping achieved by these genes and should thus be omitted from the set. Notice that this procedure is applied to each class separately and thus genes used are all specific to the same class. For a more detailed explanation regarding the construction of tight sets of genes, see [Additional file 1].
Comparison to bi-clustering methods
The approach described above for the identification of sample and gene subgroups is fundamentally different from existing bi-clustering methods. Bi-clustering methods allow for the identification of sets of genes that share compatible expression patterns across subsets of samples. These methods group samples and genes simultaneously. According to , if A is an expression matrix, with X genes and Y conditions then a ij represents the expression of gene i at condition j. I ⊂ X and J ⊂ Y denote a subset of genes and conditions respectively. The pair (I, J) specifies a submatrix A IJ or a bi-cluster A IJ and H(I, J) represents the following mean squared residue score:
In bi-clustering methods, selected genes within a bi-cluster must share similar expression profiles. In the proposed method these genes are only required to map approximately the same set of samples within a single CER, irrespectively of the expression values contained in this CER. We term these regions "significantly overlapping."
In addition to this similarity criterion, the proposed method demands that selected genes do not contain more than one significantly overlapping CER for a specific subset of samples. It is however possible to have several significantly overlapping CERs within the same subset of genes as long as they contain distinct subsets of samples. As a result, a set of genes containing two clusters of CERs can thus represent two different sample sub-groups.
The above criteria identify subsets of genes each of which group together a subset of samples in a single CER, irrespectively of co-expression constraints. If CERs were thought as independent features, the proposed method would resemble bi-clustering approaches except for the co-expression requirement which is not a prerequisite here.
We thank members of our lab for helpful discussions and comments on the manuscript. We thank Anastasis Oulas, Alkiviadis Simeonidis and Babis Papamanthou for their technical advice during the development of the algorithm. This work was supported by the EMBO Young Investigator Award (P. Poirazi.) and the IKY Foundation (P. Pavlides).
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