MATERIAL AND METHODS

This is a cross-sectional study aimed at measuring the application of logistic regression using Adaptive LASSO in studying the association between different genes and prostate cancer. Required information were downloaded from ncbi.nlm.nih.gov website, GEO gene expression data sets. Here, a prostate cancer gene expression dataset with [HG_U95B] Affymetrix Human Genome U95B Array platform was used. A total of 167 subjects participated among whom 76 subjects were unaffected and the rest were affected. Also, 12,620 genes were analyzed. Thus, the prostate cancer gene expression dataset dimension was 12,620 x 167.

Since data obtained from the matrix of microarray technology for prostate cancer data are raw data and require pre-processing to be used, various statistical methods, called normalization, were performed to remove or minimize some of the unwanted changes brought about by biases and laboratory or technical inconsistencies. Then, they were imputed for missing values and filtering methods were used to remove large-scale data effects. Quantiles were used in this method; values less than the first quarter and larger than the third quarter were excluded. Using filtering method, the number of examined genes was reduced to 3,145. To select the most important and significant features used in stratification, the next step was to select important variables which were allowed to participate in stratification. In order to be able to identify significant genes, data scale should be reduced. PLS method was used for reducing data dimensions. PLS model was conducted because of having large scale and correlated data. PLS-DA regression was used for gene expression. Adaptive LASSO method was employed for stratification of important genes in prostate cancer. To modify and conduct primary measures on the dataset, SPSS software version 22 was used. To fit the models and draw the diagrams R software version 3.3.1 and penalty specific packages were used. Finally, the results were analyzed using ROC analysis and gene ontology annotation.

FINDINGS

PLS-DA model fitting for selecting important variables in stratification analysis
After normalization, the goal was to select important variables in stratification. Thus, according to PLS-DA model, variables with p-value <0.01 were included (n=1700) (p-value calculation for Variable Importance in the Projection index). Figure 1 shows variables’ significance based on their P-values.

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Figure 1: The importance of studied genes using PLS-DA model fitting

The Application of Lasso Adaptive Regression Model for the studied data Regularization Parameter Estimation
To find the best regularization parameter, 47 different modes are regulated for 47 Lasso adaptive regressions with estimated regularization parameter so as to find the best for the best value (Figure 2).

Click here for Figure 2: Regularization parameter estimation in 47 different modes

Then, adaptive Lasso regression model with estimated regularization parameter was carried out on the study dataset based on which the variables were stratified. Accuracy of area under the ROC curve was 0.99 (95% CI:0.97-0.99) (Figure 3).

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Figure 3: ROC curve obtained from stratification based on adaptive Lasso regression model with estimated regularization parameter

Biovalidation of data from stratification of prostate cancer gene expression data
In order to properly measure predicted models for stratification of prostrate cancer gene expression data using Gene Ontology (GO), it was determined that, based on a specific GO interpretation in different models, whether the set of genes obtained from stratification are significant or not. The most significant GO terms used to describe the identified genes at P-value<0.05 are shown. Stratification rate of the studied models were between 76 to 89% (Table 1).

Table 1: GO analysis of prostate cancer gene expression data

DISCUSSION

Medical studies in recent years, and especially after the publication of information about sequencing the human genome project, have experienced a new field that opens promising ways for researchers to identify and treat incurable diseases, such as cancer. Yet, unlike medical data collected in earlier studies where researchers have been dealing with a small number of variables, the new field of cellular and molecular Medicine is faced with a very high volume of information which is being produced by laboratory-based methods and techniques.

One of the most efficient methods to extract genetic information is microarray method which has given researchers very high potential for extracting huge volumes of information instantaneously and according to arbitrary conditions. It is one of the most controversial scientific topics in the field of computational methods, management methods, and analysis of this type of data. Given the researchers’ goal of using microarray techniques in data mining, which is understanding the function of genes in cell activities, computational methods related to this area, known as stratification methods, are also more important and one of the most important questions which have been raised on the use of these methods was to identify the method or methods with proper function of gene stratification. Adaptive Lasso regression was evaluated in different conditions.

The best value estimated for regularization parameter in 47 different modes was 3.79, with 99% accuracy and CI between 97%-99% for area under the ROC curve which was a very suitable model with more acceptable performance than other values estimated for regularization parameter. Tibshirani investigated the effect of 8 variables on prostate specific antigen using data from the prostate cancer in analysis of Lasso model performance and its comparison with least squares method and the best subset. Results showed equality of the best subset and Lasso and both introduced 3 variables as influential ones(10). He also used penalized model, for the first time in 1997, for survival analysis and variable selection in Cox model. Using Lasso method, he studied the effect of 6 variables on survival time of patients with lung cancer(11).

Li and Fan (2001) introduced 3 features for a good penalty model, i.e. unbiasedness, sparsity and continuity. As Lasso model may lead to over-estimation with big penalty coefficient, it is not unbiased in all conditions. Techniques, such as ridge regression, lack sparsity features, as well, because it has not the potential of excluding insignificant variables from the model. Also, criteria such as Akaike criterion (for variable selection) or the best subset method lack the third feature because of instability in variable selection. Yet, given these 3 features, Fan proposed a penalty function called Smoothly Clipped Absolute Deviation (SCAD). The major difference between SCAD and Lasso is that the former considers fixed penalties for coefficients bigger than a. Considering 7.3 as an optimum value for “a” resulted in SCAD method notation solely with subscript(12).

Efron et al. (2004) introduced least angle regression. Inspired by forward selection, in each step of this method, only one variable can be entered. The advantage of Least Angle Regression (LARS) is that, with a simple modification and no need for complex mathematical algorithms, all estimates may be calculated using Lasso(13).

Zou and Hastie (2005) used elastic net and blood cancer data to identify genetic factors affecting cancer and predict its types (I or II) by these genes. They used blood cancer data of 7,129 genes selected by t1000 gene statistics which had the highest significance level. Sample sizes of training data and test were 38 and 34, respectively(14).
Huang et al. (2008) compared Lasso and iterative Lasso (adaptive Lasso with reverse weight of Lasso coefficients) using breast cancer data. At first, they selected 500 genes with the largest absolute values of correlation coefficients and obtained missed values using median values. Then, Leave-one-out cross validation (LOOCV) method was used to calculate prediction error. The obtained results suggested more sparsity of the model proposed by iterative Lasso so that it selected only 22 genes while Lasso selected 42 genes with the same function(15).

Raeisi Shahraki et al. (2016) used Lasso and adaptive Lasso to identify genes affecting bladder cancer. In this study, with sample size of 48, expression of 22 different genes in peripheral blood of people with bladder cancer was compared with control group using logistic regression, Lasso, and adaptive Lasso so as to identify genes which can increase or decrease the risk of bladder cancer. The first notable point was that Lasso and adaptive Lasso methods could be fitted to data, despite high correlation between some variables, by considering all 22 variables; however, logistic regression was not able to converge even by taking one third of variables into account. By controlling the multicollinearity, adaptive Lasso method was well fitted to data and estimated coefficients with a very high accuracy and low error. The model proposed by this method was a reliable model with many other optimal features such as reliability, compatibility, predictability, sparsity, and ideal flexibility(16).

Due to massive amounts of gene expression data, which is an important characteristic of this study, results obtained from various studies showed that all the previous research has been conducted on a limited number of genes. Since 1996, introduction of microarray technology in simultaneous expression of thousands of genes revolutionized analysis of genes so as not to limit gene analysis to few number of genes. Considering that microarray knowledge is used in this study, various models are predicted and compared, final results are evaluated using ROC analysis and validation of gene ontology, and the most appropriate stratification method is carried out to identify significant genes, it is not so much similar to previous studies.

CONCLUSION

Based on the results of this study, in gene expression data, where there are both linear and large scale data, techniques such as adaptive Lasso provide higher performance in stratification aid diagnosis of effective genes.

Acknowledgment:
This research is derived from a thesis approved by deputy of research at Kermanshah University of Medical Science numbered 95072.