A fuzzy linear regression model for identifying risk factors of coronary heart disease*

Coronary heart disease is a major cause of morbidity and mortality in the modern society. Many risk factors for coronary heart disease have been discussed and identified by medical fraternity. However, the magnitudes of risk factors, particularly in predicting the disease are remained unknown and inconclusive. The purpose of this study was to develop fuzzy regression prediction model and to investigate the contribution of risk factors that affect coronary heart disease based on the knowledge of flexibility of individual’s risk habits and risk factors. Four risk factors, namely body mass index, cholesterol reading, systolic blood pressure and serum fasting glucose level were identified and investigated using the matrix-driven multivariate fuzzy linear regression model. One hundred and thirty patients’ data supplied by a government funded university hospital in Peninsular Malaysia were tested using the matrix-based fuzzy regression model. Apart from coefficients of the regression equation, variations in risk of coronary heart disease caused by the risk factors were investigated using coefficient of determination with flexibility of αcuts of the model. Finally, the performance of the regression model was measured using the area under receiver operating characteristic curve analysis and a comparative analysis. The analyses indicate that body mass index was the dominant and the strongest predictor to the likelihood of developing coronary heart disease. The multiple risk factors did contribute to the coronary heart disease, but the model was not sensitive to the flexibility of α-cuts. The areas under receiver operating characteristic curves for all predictors were greater than 0.7 indicate that the fuzzy regression model was reliable. This investigation is not only affirms the numerous adverse effects of the risk factors to coronary heart disease but also provides evidence on the feasibility of using the flexibility of fuzzy numbers for obtaining fuzzy linear regression model.