Identification of Marker Genes for Cancer Based on Microarrays Using a Computational Biology Approach

Abstract

Rapid advances in gene expression microarray technology have enabled to discover molecular markers used for cancer diagnosis, prognosis, and prediction. One computational challenge with using microarray data analysis to create cancer classifiers is how to effectively deal with microarray data which are composed of high-dimensional attributes (p) and low-dimensional instances (n). Gene selection and classifier construction are two key issues concerned with this topics. In this article, we reviewed major methods for computational identification of cancer marker genes. We concluded that simple methods should be preferred to complicated ones for their interpretability and applicability.

1 Introduction

Recent advances in microarray technology have made it feasible to rapidly measure the expression levels of tens of thousands of genes in a single experiment at a reasonable expense [1]. By measuring gene expression levels related to normal and tumor samples, investigators can discover molecular markers to be used for cancer diagnosis, prognosis, and prediction. Since the pioneering work of Golub et al. in applying gene expression monitoring by DNA microarray to cancer classification [2], the use of microarray technology to identify marker genes for cancer has been a hot topics in both computational and biomedical science [2–8].

Microarray data are concerned with two major issues. First, they contain a large amount of noise in gene expression data measured. Second, compared with the measured quantities of gene expression levels in experiments, the numbers of samples are severely limited. These issues bring about serious challenges for accurate identification of marker genes for cancer diagnosis and prediction. To address these issues, a substantial number of data process strategies have been investigated. These strategies are generally concerned with data normalization, feature selection and classifier construction. Actually, so many strategies have emerged that one often feels dazzled when tries to make a proper choice among them. Although there is no a unified standard in evaluation of classification methods, some basic criteria are recognized which are based on computational cost, classification accuracy and acceptance of classification models in medical applications.

2 Data Normalization

Data normalization is used to remove systematic variation in microarray experiments that may hamper proper comparisons of gene expression levels. This step is crucial to identification of marker genes as it seriously affects the subsequent analysis results. An excellent review of microarray data normalization has been given by Quackenbush [9]. The often-used normalization methods include global normalization using the global median of log intensity ratios, intensity dependent linear normalization, intensity dependent nonlinear normalization using a LOWESS curve etc [10]. In [10], the authors suggest that intensity-dependent normalization performs better than global normalization methods, and that linear and nonlinear normalization methods perform similarly by analysis of 36 cDNA microarrays of 3,840 genes obtained in an experiment to search for changes in gene expression profiles during neuronal differentiation of cortical stem cells. Dual-channel data is normalized within each array, whereas single-channel data is normalized relative to a designated reference array. There are many software tools which provide microarray data normalization methods. For example, in BRB-ArrayTools, there are four normalization methods: median normalization, housekeeping gene normalization, lowess normalization and print-tip group normalization, among which the median normalization and housekeeping gene normalization options are available for both single-channel and dual-channel data while the lowess normalization and print-tip group normalization options are available only for dual-channel data. The software can be freely downloaded from the website: http://linus.nci.nih.gov/BRB-ArrayTools.html.

3 Feature Selection

Feature selection, i.e., gene selection in microarray data, is an important step for identification of marker genes. Because the number of genes is large in a microarray data, it is tricky to select proper genes for cancer classification.

3.1 Feature Select Methods

In machine learning and data mining, the often-used feature selection methods include t-statistics, Wilcoxon-Mann-Whitney (WMW) statistics, chi-square, information gain (or information entropy) and Relief-F method etc.

The t-statistics and WMW statistics are two types of simple feature selection methods. The t-statistics measure was first used by Golub et al. to measure the class predictability of genes for two-class problems [2, 11]. Both t-statistics and WMW-statistics were used for gene selection by Dudoit et al and showed good classification performance [12].

The chi-square (χ²) method evaluates features individually by measuring their chi-squared statistic with respect to the classes [13]. The χ² value of an attribute a is defined as follows:

$${\chi }^2(a)=\sum _{v\in V}\sum _{i=1}^n\frac{{[A_i(a=v)-E_i(a=v)]}^2}{E_i(a=v)},$$

where V is the set of possible values for a, n the number of classes, A_i(a = v) the number of samples in the ith class with a = v, and E_i(a = v) the expected value of A_i(a = v) ; E_i(a = v) = P(a = v)P(c_i)N, where P(a = v) is the probability of a = v, P(c_i) the probability of one sample labeled with the ith class, and N the total number of samples.

Information Gain [14] method selects the attribute with highest information gain, which measures the difference between the prior uncertainty and expected posterior uncertainty caused by attributes. The information gain by branching on an attribute a is defined as:

$${\mathit{Info}}_{-}\mathit{Gain}(S,a)=E(S)-\sum _{i=1}^n\frac{S_i}{S}E(S_i),$$

where E(S) is the entropy before split, ${\displaystyle \sum _{i=1}^n}\frac{S_i}{S}E(S_i)$ the weighted entropy after split, and {S₁, S₂, …, S_n} the partition of sample set S by a values.

Symmetric uncertainty method compensates for information gain’s bias towards features with more values. It is defined as:

$$SU(X,Y)=2\frac{IG(X\mid Y)}{H(X)+H(Y)},$$

where H(X) and H(Y) are the entropy of attribute X and Y respectively, and IG(X | Y) =H(X)−H(X | Y) (H(X | Y) is the conditional entropy of X given Y), represents additional information about X provided by attribute Y. The entropy and conditional entropy are respectively defined as:

$$H(X)=-\sum _{i}P(x_i){log}_2(P(x_i)),$$

$$H(X\mid Y)=-\sum _{j}P(y_j)\sum _{i}P(x_i\mid y_j){log}_2(P(x_i\mid y_j)).$$

The values of symmetric uncertainty lie between 0 and 1. A value of 1 indicates that knowing the values of either attribute completely predicts the values of the other; a value of 0 indicates that X and Y are independent.

Relief-F method estimates the quality of features according to how well their values distinguish between examples that are near to each other. Specifically, it tries to find a good estimate of the following probability to assign as the weight for each feature a [15]: w_a = P(different value of a | different class) − P(different value of a | same class). Differing from the majority of the heuristic measures for estimating the quality of the attributes assume the conditional independence of the attributes and are therefore less appropriate in problems which possibly involve much feature interaction. Relief algorithms (including Relief-F) do not make this assumption and therefore are efficient in estimating the quality of attributes in problems with strong dependencies between attributes [16].

In [17], the authors developed a feature selection method based on a soft-computing approach. The α depended degree was defined and utilized as the basis for gene selection. The α depended degree of an attribute subset P by the decision attribute D was defined as ${\gamma }_P(D,\alpha )=\frac{\mid {\text{POS}}_P(D,\alpha )\mid }{\mid U\mid }$, where 0 ≤ α ≤ 1, $\mid {\text{POS}}_P(D,\alpha )\mid =\mid \underset{X\in U/R(D)}{\cup }\mathit{pos}(P,X,\alpha )\mid$ and pos(P,X,α) = ∪ {Y ∈ U/R(P) | |Y∩X|/|Y|≥α;}. When α equals to 1, the α depended degree contracts to the depended degree, an essential concept in rough set theory [18]. In [19], the authors compared the proposed feature selection method with the established methods: the depended degree, chi-square, information gain, Relief-F and symmetric uncertainty, and showed that the method was superior or comparable to the compared methods.

3.2 Wrapper vs. Filter

In the wrapper approach, the feature selection algorithm exists as a wrapper around the induction algorithm. In the other words, the feature selection algorithm searches for a good feature subset using the induction algorithm itself as part of the function evaluating feature subsets [20]. In contrast, the filter method selects features independently of any induction algorithm. In the other worlds, the filter method ignores the effects of the selected feature subset on the performance of the induction algorithm. As a result, the filter method is much faster than the wrapper method. Because microarray data contain a huge number of features (genes), the filter method is more suitable for microarray data [21].

3.3 Univariate vs. Multivariate

The univariate gene selection method evaluates the importance of each gene individually, while the multivariate gene selection method evaluates the importance of a group of genes. Obviously, the multivariate gene selection method is much more complicated than univariate gene selection method in that the former involves combinatorial searches through the space of possible feature subsets [22]. Due to a large number of genes contained in microarray data, only simplified multivariate gene selection methods are feasible [23–31]. Although the univariate feature selection approach is simple compared to the complex multivariate feature selection approaches, the former often outperformed the latter [12, 22, 32].

3.4 Number of Genes vs. Classification Performance

Although a large literature on the development and validation of predictive classifiers has emerged, most of the classifiers developed have involved complex models containing numerous genes [5, 33–38]. This has limited the interpretability of the classifiers and therefore hampered their applicability as diagnostic tools. Actually, many studies have revealed that classifiers could be developed containing few genes that provided classification accuracy comparable to that achieved by more complex models, e.g., in [3, 24, 31, 39–41], the authors explored the use of one or two genes to perform tumor classifications. They reported that the classification performance based on the one or two genes was often comparable to those based on many genes. For example, Table 1 shows that the single gene and two-gene classifiers have comparable performance to more complex classifiers in most cases examined [40–41]. It should be noted that the DLDA, k-NN, SVM and RF used a large number of genes for constructing the classifiers in most of the eleven datasets (see Table 2 in [40]).

Table 1.

Comparison of classification accuracy (%)

Method Dataset	SGC-t	SGC-W	TGC-1	TGC-2	TSP	DLDA	k-NN	SVM	RF
Melanoma [44]	97	96	97	96	99	97	97	97	97
Breast Cancer 1 [45]	63	69	64	64	75	61	53	52	43
Brain Cancer [7]	80	77	77	75	77	65	73	60	70
Breast Cancer 2 [46]	58	50	82	78	47	73	67	73	67
Gastric Tumor [47]	89	80	89	88	91	81	96	97	95
Lung Cancer 1 [48]	98	95	98	100	95	95	98	98	98
Lung Cancer 2 [3]	93	93	93	93	97	99	99	99	99
Lymphoma [8]	74	71	59	60	57	66	52	59	57
Myeloma [49]	68	67	68	54	71	75	78	74	79
Pancreatic Cancer [50]	69	90	71	73	90	63	61	65	55
Prostate Cancer [6]	89	89	89	90	81	78	93	93	93

Note:

1 SGC-t: Single Gene Classifier with the t-test gene selection method.

2 SGC-W: Single Gene Classifier with the WMW gene selection method.

3 TGC-1: Two Gene Classifier Type 1.

4 TGC-1: Two Gene Classifier Type 2.

5 TSP: Top-Scoring Pair(s) (TSP) classifier.

6 DLDA: Diagonal Linear Discriminant Analysis.

7 k-NN: k-Nearest Neighbor (k=3).

8 SVM: Support Vector Machines.

9 RF: Random Forest.

10 Leave-one-out cross validation (LOOCV) results are presented.

4 Construction of Classification Rules

Many different classification rules have been proposed for high dimensional predictive classification including Support Vector Machines (SVM), Diagonal Linear Discriminant Analysis (DLDA), Artificial Neural Network (ANN), Bayesian, k-Nearest Neighbor (k-NN), Nearest Centroid (NC), Decision Tree (DT), Random Forest (RF), Rough Set (RS) [42], Emerging Pattern (EP) [43] etc. Among these classifiers, SVM, DA, ANN, GA, NB and k-NN produce “black-box” models, in which class predication is often based on abstract mathematical formulae which are difficult to interpret. In contrast, DT, RS and EP produce “white-box” models, which often implement classification by giving explicit rules. The “white-box” models have an advantage over the “black-box” models when applied to identification of marker genes for cancer based on microarrays for they are more understandable so as to be easily accepted by biologists and clinicians.

4.1 “Black-box” models

An SVM views input data as two sets of vectors in an n-dimensional space, and constructs a separating hyperplane in that space, one which maximizes the margin between the two data sets. The SVM method has been widely used in molecular classification of cancer [35, 51–53].

The Bayesian classifier is a probabilistic algorithm based on Bayes’ rule and the simple assumption that the feature values are conditionally independent given the class. Given a new sample observation, the classifier assigns it to the class with the maximum conditional probability estimate. Many investigators have used the Bayesian classifier to analyze gene expression [54–57].

k-NN is an instance-based classifier. The classifier decides the class label of a new testing sample by the majority class of its k closest neighbors based on their Euclidean distance. Compared with SVM and Bayesian classifiers, k-NN is simpler while has comparable performance in classification of cancer based on gene expression data [12]. ANN has also been used for classification of cancer based on gene expression data [58–59]. Although ANN has been widely applied in biomedical fields [60–63], its utility in gene expression data is relatively unpopular due to complex of the method.

“White-box” models

DT is the rule-based classifier with non-leaf nodes representing selected attributes and leaf nodes showing classification outcomes. Every path from the root to a leaf node reflects a classification rule [14]. Some investigators have applied the method to cancer-related gene expression data [38, 64].

Rough sets is a data-analysis method originally proposed by Pawlak in the early 1980s [18], has evolved into a widely accepted machine-learning and data-mining method [42]. In [17, 39, 65–68], rough sets method was applied for cancer classification and prediction based on gene expression profiling.

The EP model developed by Li and Wong was also a “White-box” model by which they implemented classification by giving “IF-THEN”-like rules [43, 69–70]. This type of classification rules was simple, clear and efficient.

In [39, 41, 71], the authors simply constructed the classification rule based on cut-points for the expression levels of a single gene or gene pairs selected. For example, if a single gene g is selected and the expression level of the gene in the sample s is no more than T, then the sample is assigned to the class c₁; otherwise the sample is assigned to the class c₂, i.e., “E(g, s) ≤ T => C(s)=c₁; E(g, s) > T => C(s)=c₂”; or a direction-reversed classification is produced, i.e., “E(g, s) ≤ T => C(s)=c₂; E(g, s) > T => C(s)=c₁”. Here T is the optimal cut point for gene g. The authors found the optimal cut point by using the entropy-based discretization method [72]. Obviously, this type of classification rules is simple, explicit and may be more suitable for clinical application.

Concluding Remarks

Expression profiling of marker genes for cancer can be used to develop classifiers of prognosis or sensitivity to particular treatments. However, one serious drawback of most existing methods for identification of cancer-related genes based on microarrays is that too many genes are ultimately selected for the classification of cancer, thereby hampering the interpretability of the models. Moreover, classification models based on numerous genes can also be more difficult to transfer to clinical application. Actually, it is often difficult to identify marker genes for cancer when a large cluster of genes are used to build classifiers because it is not easy to gauge which gene is essential in determining a cancerous class. In fact, some classifiers composed of very few genes can perform well. For example, Geman et al. developed the top-scoring pair(s) (TSP) classifier which classified gene expression profiles using a comparison-based approach [31]. The TSP classifier had better or comparable performance relative to multi-gene classifiers and has gained popularity [64, 73–77].

Classifier rules are often classified into two categories: “black-box” and “white-box” models. Compared with the “black-box” models, the “white-box” models are clearer, simpler and equally or even more efficient, and therefore are more inclined to be accepted in clinical applications.