1. Introduction

A DNA microarray technique allows to simultaneously observing the expression levels of thousands of genes during significant biological processes and across collections of related samples[1], microarray data applied to make possible drug and therapeutics improvement, disease diagnosis, and comprehensible basic cell biology. The datasets from microarray analysis enables the measurement of molecular signatures of diverse cells, becomes an important application of data mining, artificial intelligence and machine learning techniques to provide bioinformatics knowledge[2].

A few numbers of genes are highly related with diseases, these genes are called informative genes, which have expression pattern strongly correlated with the diseases. Byour the previous study[3], the subset of top ranked genes that gave the high classification accuracy was extracted by two techniques of Attribute selection technique, “Support Vector Machine-Recursive Feature Elimination (SVM-RFE) [4,5] and Information Gain Attribute Selection IGAS”[6]. 10 top ranked genes gave high classification accuracy by the most popular classifiers, which belong to six main categories, (1) Bayes classifiers ( Bayesian Network and Naive Bayes), (2) lazy classifier (K-nearest-neighbor), (3) rule base classifiers (PART and Decision Table, (4) function base classifiers (SVM and Artificial Neural networks ANN), (5) meta classifier ( AdaBoost(c4.5) and Baggin(c4.5)), (6) single Decision Tree (C4.5).

Gene networks, is a general class of gene nets where any set of genes may have connections. Theoretically genes that interact directly or indirectly may have the same or similar functions in the biological processes in which they are involved and together contribute to the related cancer diseases. The complicated relations between genes can be clearly represented using network theory[7, 8]. Thus Pearson’s correlation or Euclidean distance criterions are used to measure the similarity between genes for constructing genes network[9]. But Pearson’s correlation or Euclidean distance are not able to completely capture the relationship among all candidates genes expression profiles and lung cancer simultaneously[10, 11]. Therefore, to identify interactions between genes and to estimate the relationship between genes and lung cancer path analysis model is used.

The rest of this paper organized as follows: Section 2 describes path analysis problem and related materials. Section 3 describes lung cancer microarray dataset; Section 4 presents the proposed model to constructing genes network. Section 5 describes constructing genes network in practical. Section 6 analysis and discussions. Section 7 presents a comparison between single decision tree model and proposed path analysis model. Paper concluded in section 8.

2. Path Analysis Problem

Let X₁,X₂, . . . ,X_m be exogenous variables, correlated and have both direct and indirect effects (through endogenous variables X_m+1,X_m+2,…,X_n) on dependent variable Y.

Let M be the correlation coefficient matrix among these variable.

It is required to construct graph model G (Path diagram) depending on underlying relationship between these variables

Figure 1. An example of a general recursive causal system, (A) Illustration of possible relations among variables and output. (B) The result of significant variable

Path analysis function calculates the path coefficient between exogenous and endogenous variables, to predict the effect variables on the dependant variable Y.

An example of the different models of trait effects on output y is illustrated in figure 1. Figure 1 (A). shows a multiple regression model where each trait operates simultaneously on fitness y. Figure 1 (B). is the path analysis model showing four traits at four time periods.

From given or calculate correlation matrix the path coefficients can be compute for each path in the graph.

; n:number of variable,

Hence the target Y for one-headed arrow, “between” X₁ and X₂ in figure . 1A calculated as:

(1)

3. Lung Cancer Microarray Dataset

The dataset where used in this study primary lung cancer specimens, was collected from European Bioinformatics Institute (EBI) available onlinehttp://www.ebi.ac.uk/arrayexpress/experiments/E-GEOD-31908 , the dataset published on 2011-09-05, contains from 40 normal samples vs. 60 primary lung cancer. Each sample in the dataset contains from 22646 genes.

4. Proposed Model to Constructing Genes Network

As we mention above Microarray dataset contains thousand of genes unrelated with diseases, thus we can’t deal with a huge numbers of genes in single network, in addition to the redundant genes don’t provide any additional information, thus, for the simplicity we will dealing with microarray signature (most important genes).

The proposed genes network constructed as the follows:

1. Extract the microarray signature (subset of 10 top ranked genes) which ranked by information Gain Ratio (IGR) criterion.

2. Assign the gene that take higher IGR value as focal gene.

3. Calculate Pearson's correlation coefficient (PCC) between focal gene and each other genes, Only those genes with the absolute PCC value higher than (0.7) thresholds are linked to the focal gene.

4. Assign the gene that gave next IGR as focal gene. Return form 3.

Finally, a Directed networks are then created from these gene sets. In the network, a vertex set V = {g₁, g₂,…,g_i} represents the genes.

E = {{g_i, g_j} | g_i, g_j ϵ V ˄ |P_ij| T} is the edge set that represents the relationship between the genes, where T is the given threshold of PCC, and P_ij is the PCC value of g_i and g_j. Figure .2. shows the gene network.

Figure 2. Genes network generated from subset of top ranked genes (assigned as null path analysis model)

Figure 3. Standardized path coefficient among genes and lung cells state

5. Practical Constructing Genes Network

To extracting the subset of 10 top ranked genes according to information gain ratio criterion[3], ELBRAV algorithm[14, 15] was used. This subset of genes gave the higher classification accuracy on majority of cancerous microarray datasets.

Software package SPSS 16.0[16] was used to calculate the Pearson’s correlation to measure the similarity among genes and lung cancer “lung cells state”. Genes that have strong correlation coefficient have the same function and linked with same biological pathway[17]. Thus the genes those have Pearson’s correlation value greater than |0.7| are linked together. The 10-top ranked genes that extracted from the dataset labeled as being in the microarray. figure 3. shows the path diagram constructed based on Pearson’s correlation value. In the path diagram Figure 3.

6. Analysis and Discussion

Model Hypothesis

The genes network that generated from subset of top ranked genes assigned as null path analysis model.

The main objective here the question; is the genes network fit the subset of lung cancer microarray dataset?

Hypothesis Testing

To estimates the path coefficient (regression weights) for model (figure 2.) Maximum likelihood estimation function (MLF)[18] was used. The MLF exists in the AMOS (v16) software package[19], figure 3 shows standardized path coefficient among genes and lung cells state that calculated based on MLF.

6.1. Model Properties and Evaluation

The model (figure 3.) properties as the follows:

Number of variables (genes) (21), number of observed variables (11), number of unobserved variables (10), number of exogenous variables (11), number of endogenous variables (10).

Degrees of freedom: Number of distinct sample moments (66), number of distinct parameters to be estimated (41), thus degrees of freedom (25)

χ2 = 140.797, probability level = .000.

Goodness of Fit Index (GFI)[20] of the model GFI =0.821.

Root Mean Square Residual (RMR), RMR= 0.282.

Root Mean Square Error of Approximation (RMSEA) = 217.

Comparative Fit Index (CFI)[21], CFI > 0.894.

The model in figure 3. Contains several path coefficient values is not significantly different from zero at the p- value 0.05, these paths are organized in table 1.

Due to the path diagram in (figure 3.) contains several paths that are not significantly different from zero at the 0.05 p-value; the path diagram simplified by eliminating these paths and variables (genes) that insignificantly affected on lung cells state, the modified path diagram shown in figure. 4.

Table 1. Insignificant path coefficients for (model in figure 3.), where SE (Standard Error of Regression Weight), CR Critical ratio for regression weight) and P (Probability Value) Direct path Estimate SE CR P 231411_at<---228536_at 0.043 0.112 0.381 0.703 231411_at<---227682_at 0.175 0.099 1.769 0.077 244470_at<---227682_at 0.182 0.12 1.521 0.128 LungCellsState<---227682_at 0.053 0.12 0.442 0.658 LungCellsState<---225813_at 0.095 0.118 0.807 0.419 LungCellsState<---225721_at 0.054 0.082 0.66 0.509 LungCellsState<---225720_at 0.191 0.103 1.864 0.062 LungCellsState<---242809_at 0.155 0.091 1.712 0.087 LungCellsState<---231411_at -0.047 0.113 -0.418 0.676 LungCellsState<---228536_at -0.003 0.126 -0.022 0.983 LungCellsState<---244470_at 0.069 0.086 0.804 0.421 225813_at<---225720_at 0.078 0.098 0.797 0.426

The path coefficients of the simplified path diagram were re-estimated as it’s shown in figure . 5. Its notice from figure 5. all variables (genes) are significantly affected among each other, as well as on lung cells state. Also the goodness of the simplified model (figure 5.) is GFI=0.832 (better than the original model). The path coefficients (regression weights) for path diagram (figure 5.) Organized in table ‎2, table 3 presents the total effects in the model figure 5.

Table 2. Standardization path coefficients for path diagram Figure 5 Direct path Estimate SE CR P 228536_at<---242809_at 0.355 0.068 5.251 *** 225813_at<---242809_at 0.495 0.064 7.789 *** 227682_at<---225162_at 0.213 0.046 4.647 *** 229163_at<---225162_at 0.656 0.076 8.601 *** LungCellsState<---225162_at 0.221 0.069 3.22 0.001 LungCellsState<---229163_at 0.297 0.069 4.318 *** LungCellsState<---225720_at 0.304 0.06 5.093 *** LungCellsState<---242809_at 0.214 0.059 3.653 *** 227682_at<---228536_at 0.244 0.068 3.593 *** 225813_at<---227682_at 0.365 0.08 4.582 *** 225720_at<---228536_at 0.642 0.078 8.231 *** 228536_at<---225813_at 0.555 0.076 7.31 *** 227682_at<---225720_at 0.509 0.065 7.877 ***

Table 3. Insignificant path coefficients for (model in Fig.4.), where SE (Standard Error of Regression Weight), CR Critical ratio for regression weight) and P (Probability Value 242809_at 225162_at 225720_at 225813_at 228536_at 227682_at 229163_at 225720_at 0.48 0.03 0.08 0.40 0.77 0.15 0 225813_at 0.64 0.09 0.21 0.13 0.24 0.42 0 228536_at 0.71 0.05 0.12 0.69 0.13 0.23 0 227682_at 0.41 0.24 0.58 0.36 0.65 0.13 0 229163_at 0 0.66 0 0 0 0 0 LungCellsState 0.35 0.43 0.33 0.12 0.22 0.05 0.3

In summary: the genes network that generated from subset of top ranked genes is fit the data with GFI =0.821, also we simplified the genes network by eliminating insignificant path coefficient, the resulted simplified model fit the subset of the dataset GFI =0.832 and better than the original model.

From two models the interaction between candidate genes were estimated and the standardization path coefficient reflect the quantitative of these interaction.

7. Single Decision Tree Model vs. Proposed Path Analysis Model

In addition to path analysis model measure the effect of variables (genes) on the target variable (Lung cell stat) also it can used as classification model as shown in the comparative below.

The output of traditional classification model such as single decision tree (c4.5) is a set of roles that partition the dataset according to higher informative attribute. Tested samples are classified according to these roles. As shown in the real practical example Figure 5.

Figure 6. the microarray dataset is the input of the C4.5 classifier, the output is set of rules, in testing stage tested samples are input of rules, and the output is category of the new samples.

Figure 4. Path diagram resulted after simplified model (Figure 2)

Figure 5. Real example of decision tree model

Figure 6. Path analysis model classifier

In Path analysis model the gene network firstly constructed from correlated and interacted genes. Path analysis model allows estimating the path coefficient of all paths in the model and visualizing these effects.

The value of path analysis model in addition to estimate the regression weights of all paths simultaneously, its work as a classifier by convert the output (target) value into domain between[0 and1] that represent probability of the target value belong to one of category. Figure 5. shows path analysis model as classifier.

Lung cell state calculated as equation (5) for the path analysis model in Figure 4. and as equation (6) for path analysis model in Figure 5.

(5)

(6)

By Applying the Logistic regression to obtain the probability if new samples are tumor or normal

(7)

The path analysis modeling gave 95% by the model (figure 3) and model (figure 5) vs. 90% accuracy obtained by single decision tree model (Figure 4). And it’s useful to mention, samples that incorrect classified were the same in two path analysis models (figure 3) and (figure 4) So, in this case path analysis modeling can be used as attribute reduction.

8. Conclusions

We presented new approach to predict genes inference based on gene-gene interaction network that constructed from gene expression data. To elucidate this approach, a real lung cancer microarray dataset was used.

In this approach, information gain ratio attribute evaluation is used to extract the signature of cancerous microarray dataset, and Pearson’s correlation criterion was used to measure the similarity between genes to construct genes network according to the strength correlation between focal gene and other candidate genes, where the high correlated genes linked together and theoretically do the same genes function. In addition to, estimate the effect of each gene on lung cancer (path coefficient) using path analysis model.

The value of this approach is that it not only tackles the measurement problem by path analysis but also provides a visualization of the relation among genes. In addition to its ease of use, this approach effectively addresses the genes reduction problem. For instance; the genes that gave approximately equal information gain ratio value or Pearson’s correlation value, not gave the same path coefficient on lung cancer using path analysis model, due to in the genes reduction methods or correlation methods dealing with each gene and the disease label individually but path analysis modeling analysis all genes simultaneously.

Path analysis modeling can be used as classifier but it is need additional steps, such as data standardization and logistic regression function. In this case path analysis modeling gave the probability of the target (class label) belong to one class, this is additional advantage of path analysis modeling vs. other classification modeling, where path analysis in this study gave 95% classification accuracy vs. 90% that given by C4.5.

This approach provides path diagram that explains the direct and indirect effect of each gene on lung cancer and shows the genes that provide significantly and insignificantly effect on lung cancer, maximum likelihood estimation function is used to calculate the path coefficients, and the proposed path diagram fit the subset of the microarray dataset, hypothesis testing were used to measure the goodness of the proposed path diagram, where the Goodness of Fit Index (GFI) was ≥ 0.832.