American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2018, 6(5), 186-200
DOI: 10.12691/ajams-6-5-3
Open AccessArticle

Modelling Diabetes Mellitus among Adult Kenyan Population Using Artificial Neural Network

Pius Miri Ng’ang’a1, , Antony Waititu Gichuhi2, Antony Wanjoya2 and Thomas Mageto2

1Population and Social Statistics, Kenya National Bureau of Statistics, Nairobi, Kenya

2Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

Pub. Date: October 07, 2018

Cite this paper:
Pius Miri Ng’ang’a, Antony Waititu Gichuhi, Antony Wanjoya and Thomas Mageto. Modelling Diabetes Mellitus among Adult Kenyan Population Using Artificial Neural Network. American Journal of Applied Mathematics and Statistics. 2018; 6(5):186-200. doi: 10.12691/ajams-6-5-3


Artificial Neural Network (ANN) is a parallel connection of a set of nodes called neurons which mimic biological neural system. Statistically, ANN represents a class of non-parametric models which is capable of approximating a non-linear function by a composition of low dimensional ridge functions. This study aimed at modeling diabetes mellitus among adult Kenyan population using 2015 stepwise survey data from Kenya National Bureau of Statistics. Data analysis was carried out using R statistical software version 3.5.0. Among the input variables Age, Sex, Alcoholic status, Sugar consumption, Physical Inactivity, Obesity status, Systolic and Diastolic blood pressure had a significant relationship with diabetic status at 5% level of significance. A multi layered feed-forward neural network with a back propagation algorithm and a logistic activation function was used. Considering a parsimonious model, the model selected had the eight input variables with two neurons in the hidden layer since it gave a minimum MSE of 0.0580 reported. 75% of data was used for training while 25% was used for testing. The sensitivity of the trained network was reported as 75% while specificity was 94.29%. The overall accuracy of the model was 84.64% . This implied that the model could correctly classify an individual as either diabetic or not with an accuracy rate of 84.64%. A 10-fold cross validation was carried out and an average MSE of 0.0686 reported. Kolmogorov-Smirnov test of normality was carried out and at 5% level of significance, for most parameter estimates, we failed to reject the null hypothesis and concluded that the network parameter estimates were asymptotically normal and consistent. With a good choice of risk factors for diabetes, neural network structures could be successfully used to accurately model diabetes melitus among Kenyan adult population.

artificial neural network diabetes mellitus activation function asymptotic normality accuracy

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[1]  World Health Organization. Global Report on Diabetes, WHO Press, Geneva, 2006, page 6.
[2]  Zainab A, et al. Using Neural Network to predict the Hypertension. International Journal of Scientific Development and Research, 2(2): 35-38, 2017.
[3]  Ripley, B. D. Pattern Recognition and Neural Networks, Oxford Press, London, 1996.
[4]  Robert, S. “Artificial Intelligence: its use in Medical Diagnosis”, The Journal of Nuclear Medicine, 34 (3): 510-514, 1993.
[5]  Flury, B., & Riedwyl, H.Multivariate statistics: A practical approach. London: Chapman and Hall,1999.
[6]  Press, S. J.,&Wilson, S. “Choosing between logistic regression and discriminant analysis”, Journal of the American Statistical Association, 73(364): 699-705, 1978.
[7]  Hosmer, D. W., & Lemeshow, S. Applied logistic regression. New York: Wiley Series, 1989.
[8]  Buntine, W. L., & Weigend, A. S. “Bayesian Back-propagation”, Complex Systems, 5(6):603-643, 1991.
[9]  Menard, S. Applied logistic regression analysis, series: Quantitative applications in the social sciences. Thousand Oaks, CA: Sage, 1993.
[10]  Myers, R. H. Classical and modern regression with applications (2nd edition). PWS-KENT Publishing Company, Boston, Massachusetts, 1990.
[11]  Neter, J., Li, W., Nachtsheim, C.J., & Kutner, M. H. Applied linear statistical models (5th edition), McGraw-Hill/Irwin, New York, 2005.
[12]  Snedecor, G. W., & Cochran, W. G. Statistical methods (7th edition). Ames, IA: The Iowa State University Press, 1980.
[13]  Razi M.A.,& Athappilly, K. . A comparative predictive analysis of neural networks (NNs), nonlinear regression and classification and regression tree (CART) models. Expert Systems with Applications , 29(1): 69-74, 2005.
[14]  Zhang, G., Patuwo B.E., & Hu, M.Y. “Forecasting with artificial neural networks: The state of the art”, International Journal of Forecasting, 14(1): 35-62, 1998.
[15]  Cybenko, G. “Approximation by superpositions of a sigmoidal function”. Mathematics of Controls Signals and Systems, 2(4): 303-314, 1989.
[16]  Funahashi, K. “On the approximate realization of continuous mappings by neural networks”. Neural Networks, 2(3): 183-192, 1989.
[17]  Hornik, K., Stichcombe, M., & White H. “Multilayer feedforward networks are universal approximators”. Neural Networks, (2): 359-366, 1989.
[18]  Hornik, K. “Approximation capabilities of multilayer feed- forward networks”. Neural Networks, 4(2): 251-257, 1991.
[19]  Irie, B., & Miyake, S. “Capabilities of three-layered perceptrons,In: Proceedings of the IEEE Second International Conference on Neural Networks, July 1988, San Diego, California USA.
[20]  Dybowski, R., & Gant,V. Clinical Applications of Artificial Neural Networks, Cambridge University Press, London, 2007.
[21]  Szolovits, P., Patil,S., & Schwartz, W. “Artificial Intelligence in Medical Diagnosis.”, Annals of Internal Medicine, 108(1): 80-87, 1988.
[22]  Bradley, B. “Finding Biomarkers is Getting Easier”, Ecotoxicology, 21(3): 631-636, 2012.
[23]  Baxt, W.G. “Use of an artificial neural network for the diagnosis of myocardial infarction”. Annals of Internal Medicine, 115(11): 843-848, 1991.
[24]  Jayalakshmi, T., & Santhakumaran A. “A novel classification method for classification of diabetes mellitus using artificial neural networks”, In: International Conference on Data Storage and Data Engineering, February, 2010, Bangalore, India.
[25]  Swanson, N. R., & White, H. “A model-selection approach to assessing the information in the term structure using linear models and artificial neural networks”, Journal of Business Economic Statistics, 13(3): 265-275, 1995.
[26]  Olaniyi E. O, & Adnan K. “Onset Diabetes Diagnosis Using Artificial Neural Network”, International Journal of Scientific & Engineering Research, 5(10): 754-759, 2014.
[27]  Adeyemo, A & Akinwonmi, A. “On the Diagnosis of Diabetes Mellitus Using Artificial Neural Network Models”. African Journal of Computing & ICT, 4(1):1-8, 2011.
[28]  Rajib D, V. Bajpai, G. Gandhi & B. Dey. “Application of artificial neural network technique for diagnosing diabetes mellitus”, In:2008 IEEE Region 10 Colloquium and the Third ICIIS, 8-10 December, 2008, Kharagpur, INDIA.
[29]  Chan K, Ling S, Dillon T, & Nguyen H. “Diagnosis of hypoglycemic episodes using a neural network based rule discovery system”, Expert System Applications. 38(8): 9799-9808, 2011.
[30]  Kenya National Bureau of Statistics. Kenya STEPwise Survey For Non Communicable Diseases Risk Factors KNBS, MOH and WHO, Nairobi, page 137-140, 2015.
[31]  Agresti, A. An Introduction to Categorical Data Analysis (2nd edition). New York: Wiley Series, 2007.
[32]  Amato F, et al. “Artificial neural networks in medical diagnosis”. Journal of Applied Biomedicine, 11(2): 47-58, 2013.
[33]  Intrator, O., & Intrator, N. “Interpreting Neural Networks Results: A simulation study”, Computational Statistics and Data Analysis, 37(3): 373-393, 2001.
[34]  Waititu, A.G. Nonparametric Change point Analysis for Bernoulli Random Variables Based on Neural Networks, Phd Thesis, Kaiserslautern University, Germany. (, 2008.
[35]  White, H. “Some Asymptotic Results for Learning in Single Hidden-Layer Feedforward Network Models”, Journal of the American Statistical Association, 84(408): 1003-1013, 1989.
[36]  Warner, B., & Misra, M. “Understanding neural networks as statistical tools”, The American Statistician, 50(4), 284-293, 1996.
[37]  Sussmann, H. J. “Uniqueness of the weights for minimal feed-forward nets with a given input-output map”,Neural Networks, 5(4): 589-593, 1992.
[38]  Hwang, J. T., & Ding, A. A. “Prediction intervals for artificial neural networks”. Journal of American Statistical Association, 92(438): 748-757, 1997.
[39]  Berger, V., & Zhou, Y. “Kolmogorov Smirnov test: Overview”. In Wiley statsref: Statistics reference online. New York: John Wiley & Sons, Ltd.
[40]  Rissanen, J. “Stochastic complexity and modeling”, Annals of Statistics, 14(3): 1080-1100, 1986.
[41]  Haykin, S. Neural Networks and Learning Machines (3rd edition). New Jersey: Pearson Education, 2009.
[42]  Muhammad, A. R., & Kuriakose, A. “A comparative predictive analysis of neural networks (NNs), nonlinear regression and classification and regression tree (CART) models”, Expert Systems with Applications, 29(1): 65-74, 2005.
[43]  Temurtas, H., Yumusak, N., & Temurtas F. “A comparative study on diabetes disease diagnosis using neural networks”, Expert System Applications, 36(4): 8610-8615, 2009.
[44]  White, H. Artificial neural networks: Approximation and learning theory. Oxford: Basil Blackwell, 1992.