Colorectal cancer (CRC) is a type of cancer in the large intestine (colon), the lower part of our digestive system. Most cases of colon cancer begin as small non-cancerous clumps of cells called adenomatous polyps. The aim of this quantitative study is to identify the determinants of patient who have colorectal cancer symptoms in general hospital. The sample study included 180 patients who have colorectal cancer aged above 21 years old and received treatment at general hospital in Kuala Lumpur, Malaysia. Secondary data were obtained through doctors and nurses using cluster sampling. Based on the results of multiple linear regressions (MLR), 11 predictor variables were significant to predict tumour size of colorectal cancer. The statistical measurement error used were mean square error (MSE), root mean square error values (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE)

Azmi, N. A. H. M.

Hamzah, N. S. A.

Nasibov, E. N.

Rusiman, M. S.

Shafi, M. A.

English

Journals of Universiti Tun Hussein Onn Malaysia (UTHM)

Journal of Science and Technology, Vol. 8 No. 2 (2016) p. 1-5  *Corresponding author: saifulah@uthm.edu.my 2016 UTHM Publisher. All right reserved. penerbit.uthm.edu.my/ojs/index.php/jst   1 The use of Linear Statistical Model to Predict Tumour Size of Colorectal Cancer   M. A. Shafi1, M. S. Rusiman1*, N. S. A. Hamzah1, E. N. Nasibov2, N. A. H. M. Azmi1  1Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, 86400, Batu Pahat,    Johor, Malaysia. 2Department of Computer Science, Faculty of Science, Dokuz Eylul University 35160 Buca, Izmir, Turkey   1. Introduction  The types of cancer in medical record reach more than 100 different diseases. One of the top three of cancer diseases faced by patient includes colorectal cancer (CRC). CRC is the most common cancer in Malaysia by 13.2% compared to the Western Countries [1,2,3]. It is noticeable that this cancer has been spreading in Malaysia during recent decades. In Malaysia, generally among citizens above 50 years’ old diagnosed with colorectal cancer, there are more male cases than female cases [4,5,6]. It contributes to higher demand of bed’s patient due to neoplasm. Neoplasms may have begun with no cancer then malignant (cancer). They are also called as a tumour [3]. At present, the cause of colorectal cancer is not completely understood and nonspecific. It may involve numerous risk factors which contribute to developing colorectal cancer. The common factors identified amongst patients are age, polyps, family history, diet, tobacco and body weight [7]. Moreover, causes of CRC typically include gastric, ovarian, small bowel and others. The stages of CRC are based on the size of tumour developed by patient. Physical examination, biopsy and imaging test are the process of finding out the size of tumour. Colorectal cancer has four stages which are stage I and II that are called as earlier stage, while stage III and IV are called final stage. Publicly known, stage I means the condition where the cancer is kept to the inner wall of the colon, stage II means the cancer has blow-out through the wall of the colon, stage III means cancer has blow-out the blood vessel until lymph node and stage IV means the cancer has blow-out to other organs. The stages of CRC play an important factor in determining treatment options [7,8]. The guidelines to reduce and prevent development of colorectal cancer among individuals were introduced in 2017. It discussed about the screening to detection of cancer, radiotherapy to kill cancer cells and treatment or surgery of colorectal cancer. Unfortunately, less than 40% of individuals in their early stages take immediate action and keep in mind about the risk of colorectal cancer [2,5].  However, the awareness of colorectal cancer screening in Malaysia is still lower than other cancer, especially cervical cancer. This probably gives higher impact to patients in an advance stage [9].   1.1 Background of regression  Regression analysis is statistical methodology that utilizes the relationship between two or more quantitative variables. The outcome of the variables can be predicted based on data in regression analysis. This methodology can be applied in Abstract: Colorectal cancer (CRC) is a type of cancer in the large intestine (colon), the lower part of our digestive system. Most cases of colon cancer begin as small non-cancerous clumps of cells called adenomatous polyps. The aim of this quantitative study is to identify the determinants of patient who have colorectal cancer symptoms in general hospital. The sample study included 180 patients who have colorectal cancer aged above 21 years old and received treatment at general hospital in Kuala Lumpur, Malaysia. Secondary data were obtained through doctors and nurses using cluster sampling. Based on the results of multiple linear regressions (MLR), 11 predictor variables were significant to predict tumour size of colorectal cancer. The statistical measurement error used were mean square error (MSE), root mean square error values (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE).  Keywords: Multiple Linear Regression, mean square error (MSE), root mean square error values (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE).  Journal of Science and Technology, Vol. 8 No. 2 (2016) p. 1-5     2 business analysis, social analysis, biological sciences and other disciplines [10]. A few examples of applications are; (i) sales of product can be predicted through relationship between sales and amount of profit, (ii) the performance of employee can be predicted through relationship between worker performance and attitude test and (iii) the length of time stay in shopping mall can be predict by relationship between the money spending and buy items. All these applications show that the main objective in regression analysis is predicting. Recently, there are many models used by researchers in regression analysis such as multiple linear regression (MLR), logic model, fuzzy regression and others. There are many researchers studied about predicting tumour size of colorectal cancer of patients using fuzzy linear regression [1,11,12,13].   1.2 Aim of study  The aims of this study are to identify which determinants give the higher impact to develop colorectal cancer stages and to determine whether MLR is a good model to predict tumour size of colorectal cancer by statistical measurement error such as mean square error (MSE), root mean square error values (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE).   2. Material and Method 2.1 Material  The data of this study is defined as the patients aged from 21 until 90 years old who show symptoms and suffer from colon cancer in any of the four stages and are receiving treatment at general hospital, Kuala Lumpur. The patients include male and female from various ethnics.   2.2 Method  In this study, MLR model are used toward CRC data. There are some conditions and assumptions that need to be determined first. Before using the MLR model, the model should fulfill the early assumptions such as normality test and multicollinearity.  Multiple linear regression model is stated as follow,       Yi   =  0 + 1Xi1 + 2Xi2 + …kXik + )( i        (1)   where: Yi is the value of dependent variable Β0, β1, β2 and βj are parameters Xi is a known as independent variables i = 1,……, n  The function for least squares method is,          S(0, 1, 2, …,k)    =  S() = djj12       or  T  From (1),      () = Y-X Then,           S() = (Y- X)T (Y- X)                       = YTY- 2TXTY + TXTX   (2)  In order to minimize S(), we have to differentiate S() with respect to  where ββ ˆS is equal to 0,                        ββ ˆS   =  022  XβXYX TT   Hence, the least squares estimator is,   β̂  = (XTX) 1 XTY                                      (3)  The values fit by the equation β0 + β1xi1 + ... + βixi are denoted as i, and the residuals ei are equal to yi- ŷ, the difference between the observed and fitted values [10].    3. Results 3.1 Assumption of MLR  The data of this study tested for three assumptions and all the assumptions were satisfied and trustworthy. The results are shown in Table 1, Figure 1 and Figure 2.  a) The constant variance of residual  Scatter plot was used to identify a condition variance of residual using SPSS software. The points on the Figure 1 appeared to be randomly Journal of Science and Technology, Vol. 8 No. 2 (2016) p. 1-5     3 scattered and shows no pattern. It can be assumed that the variance in the error terms is constant. The first assumption is satisfied.   Figure 1 Scatter plot of constant variance  b)   The residual of normality distributed  To test the normality, this study used Q-Q plot by tumour size variable (dependent variable) to determine the shape/trend that follows the normal distribution. The Q-Q plot in Figure 2 shows that the data are in straight line. This indicates that the data are normal and the assumption is satisfied.   Figure 2 Scatter plot of constant variance  c)    Multicollinearity checking  Table 1 shows that the tolerance values are less than 0.99 and all VIF values are less than 10. This indicates that the multicollinearity among independent variables do not exist.   Table 1  Coefficients of tolerance values, VIF and eigen values for actual data  Variable Tolerance VIF Eigen value (Constant)     18.145 Gender 0.864 1.158 0.731 Age (years) 0.860 1.163 0.672 Ethnic Group 0.876 1.141 0.578 ICD 10 Site 0.845 1.183 0.519 TNM Staging 0.856 1.168 0.474 Family History 0.840 1.190 0.468 Crohn's Disease 0.869 1.151 0.418 Polyp 0.863 1.158 0.354 History of cancer 0.787 1.271 0.334 Endometrial 0.877 1.141 0.313 Gastric 0.858 1.166 0.287 Small bowel 0.843 1.186 0.281 Hepatobiliary 0.891 1.123 0.249 Urinary tract 0.844 1.185 0.245 Ovarian 0.83 1.205 0.221 Other cancer 0.839 1.192 0.189 Intestinal Obstruction 0.847 1.181 0.171 Colorectal 0.841 1.19 0.154 weight loss 0.854 1.171 0.119 diarrhea 0.843 1.186 0.095 blood stool 0.886 1.129 0.043 anemia 0.867 1.154 0.076 abdominal 0.787 1.27 0.012   3.2 Analysis of multiple linear regression  Majority of researchers in medical health will use MLR model to predict the tumour size of colorectal cancer (CRC). This study also applied MLR model toward CRC data. There are 25 predictor variables and tumour  size of colorectal cancer as a response or dependent variables. The results in Table 2 showed that 11 predictor variables were significant toward tumour  size. All the significant variables are age at diagnosis, icd10 site, TNM staging, family history, Crohn’s disease, history of cancer, gastric, ovarian, intestinal obstruction, anemia and abdominal. The MLR model is shown as below:     Journal of Science and Technology, Vol. 8 No. 2 (2016) p. 1-5     4 Ŷ = 76.056 + 0.421 age + 3.459 icd10 + 0.961 TNM Staging – 16.738 family history + 5.035 Crohn’s disease + 5.557 history of cancer – 6.517 gastric + 12.865 ovarian – 4.350 intestinal obstruction – 7.943 anemia – 3.994 abdominal.  Table 2  Summary of parameter estimation multiple linear regression model  Independent variables Beta (β) Sig. Value (Constant) 76.056 *0.000 Gender 1.977 0.286 Age at diagnosis (years) -0.421 *0.000 Ethnic Group 2.231 0.114 ICD 10 Site 3.459 *0.027 TNM Staging 0.961 *0.040 Family History -16.738 *0.000 Diabetes Mellitus 0.832 0.679 Crohn's Disease 5.035 *0.012 Ulcerative colitis 1.508 0.432 Polyp -1.577 0.396 History of cancer 5.557 *0.007 Endometrial -0.869 0.648 Gastric -6.517 *0.001 Small bowel -3.33 0.087 Hepatobiliary -1.047 0.589 Urinary tract 2.597 0.176 Ovarian 12.865 *0.000 Other cancer 3.248 0.084 Intestinal Obstruction -4.35 *0.022 Colorectal 1.227 0.511 Weight loss 3.063 0.1 Diarrhea 0.75 0.695 Anemia -7.943 *0.003 Blood stool -2.158 0.233 Abdominal -3.994 *0.038 *Significant at 0.05  The summarization of measurement errors value is shown in Table 3.  Table 3 Result of statistical measurement error in MLR  3.3 Summary of results  In order to predict the tumor size of colorectal cancer and its significant determinants, this study performed multiple linear regressions (in mm). From the model, there are 11 predictor variables were significant to predict the size of tumor .   4. Conclusion and Discussions  This study applied MLR model to analyze the data. The MSE, RMSE, MAE and MAPE had been used to measure the effectiveness of the model in predicting the tumor size of colorectal cancer, based on the factor and causes of colorectal cancer. Only 11 independent variables are significant in this study and ovarian give the higher chances to develop CRC among patient by 12.865. The variable includes are age, icd10, TNM staging, crohn’s disease, history of cancer and ovarian are directly proportional to the tumor size. The rest of variables are inversely proportional to the tumor size.   Acknowledgements   This research work is supported by FRGS (Fundamental Research Grant Scheme) grant (Vot 1498), Ministry of Higher Education, Malaysia.   References  [1] M.A.B. Shafi, M.S.B. Rusiman, N.S.H.C. Yusof, (2014). “Determinants status of patient after receiving treatment at Intensive Care Unit: A case study in Johor Bahru,” 2014 International Conference on Computer Communications and Control Technology (I4CT), pp. 80 – 82. [2] R.T. Greenlee, M.B. Hill-Harmon, T. Murray, S. Bolden, P.A. Wingo, (2001). “Cancer Statistic, ” CA cancer J Clin, vol. 51, pp. 15-36. [3] Health indicator, Ministry of health, Malaysia. (2010). “Indicators for Monitoring and Evaluation of Strategy Health for All,” Ministry of Health, Malaysia. [4] M.S. Haerian, B.S. Haerian, H. Rooki (2009). “Comparison of Survival between Patients with Hereditary Non Polyposis Colorectal Cancer (HNPCC) and Sporadic Colorectal Cancer,” Asian Pac J Cancer Prev., vol. 10, pp. 497-500. [5] C.K. Kong, A.C. Roslani, C.W. Law, S.K.D. Law SKD, K. Arumugam (2010). “Impact Of Socio-Economic Class On Colorectal Cancer Patient Model MSE RMSE MAE MAPE Multiple linear regression (MLR)  129.558  11.3826  10.349  20.798 Journal of Science and Technology, Vol. 8 No. 2 (2016) p. 1-5     5 Outcomes in Kuala Lumpur And Kuching, Malaysia’’. Asian Pasific J Cancer Prev, vol. 11, pp. 969-74 [6] B. Monghimi-dehkordi, A. Safaee (2012). “An Overview of Colorectal Cancer Survival Rates and Prognosis in Asia’’. World J Gastrointestinal Oncol, vol. 4, pp. 71. [7] Malaysian Oncological Society Novartis Corporation (Malaysia). (2007). The Lancet Oncology, vol. 8, pp. 773-783. [8] Q.M. Akhtar, M. Raj and J. Menon. (2012). “Screening for Colorectal Cancer in Malaysia Consensus/ Clinical Practice Guidelines’’. Academy of Medicine, Malaysia, pp. 2-12. [9] K.L. Goh, F.K. Quek, G.T.S. Yeo (2005). “Colorectal Cancer In Asians: A Demographic And Anatomic Survey In Malaysian Patients Undergoing Colonoscopy’’. Aliment Pharmachol Ther, vol. 22, pp. 859-64. [10] M.H. Kutner, C.J. Nachtsheim, (2004). Applied Linear Statistical Models. Fifth edition, Mc Graw Hill. [11] M.A. Shafi, M.S. Rusiman (2015). “Status of Patient After Receiving Treatment Using Multinomial Logistic Regression at Intensive Care Unit in Johor’’.  Australian Journal of Basic and Applied Sciences, 9(8) Special 2015, pp 29-34 [12] M.A. Shafi, M.S. Rusiman (2015). “The Use of Fuzzy Linear Regression Models for Tumor Size in Colorectal Cancer in Hospital Of Malaysia’’. Applied Mathematical Sciences, vol. 56, pp. 2749-2759. [13] M.A. Shafi, M.S. Rusiman (2015). “The Effective Model of Linear Regressions for Colorectal Cancer Stages in General Hospital: A Case Study in Kuala Lumpur’’. Australian Journal of Basic and Applied Sciences, Vol. 9, pp 7-10    

The use of Linear Statistical Model to Predict Tumour Size of Colorectal Cancer

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The use of Linear Statistical Model to Predict Tumour Size of Colorectal Cancer

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