Insulin Chart Prediction for Diabetic Patients Using Hidden Markov Model (HMM)

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1 Insulin Chart Prediction for Diabetic Patients Using Hidden Markov Model (HMM) Ravindra Nath a Department of Computer Science and Engineering, University Institute of Engineering and Technology, Chattrapati Shahuji Maharaj University, Kanpur, Uttar Pradesh, India rnkatiyar@gmail.com Renu Jain b Department of Computer Science and Engineering, University Institute of Engineering and Technology, Chattrapati Shahuji Maharaj University, Kanpur, Uttar Pradesh, India jainrenu@gmail.com Abstract- Diabetic patients need to take insulin before every meal. The doctors have to decide insulin doses for every patient according to the patient s previous records of doses and sugar levels measured at regular intervals. This paper proposes a Hidden Markov Model to predict the insulin chart for a patient and uses Simulated Annealing search algorithm to efficiently implement the model. The one month chart maintained by the patient has been used to train the model and the prediction for next few days is done on the basis of the trained data. Our university medical doctor was very pleased to see to the result obtained. Keywords: Hidden Markov Model (HMM), Randomized Algorithm (RA), Simulated Annealing [SA], Diabetes patient chart prediction[dpcp]. I. INTRODUCTION Hidden Markov Model has various applications in the area of speech recognition, bioinformatics [11][12][15][16], climatology and acoustics [26][11], etc.. In addition to this HMM has been applied for prediction problems like stock marketing [2][3][4], forecasting, etc. Mostly two types of problems occur in these research areas while modeling as Hidden Markov Model. First, the training problem to optimize the model parameters and second, the prediction problem using training sequence. Out of many probabilistic models, HMM Model is most popular due to its mathematical foundation of HMM learning problem. In this paper, we have taken the application of medical science, i.e preparation of insulin chart for Diabetic patients. We have used HMM model to predict the insulin chart taking the data of a diabetic patient. HMM learning problem is solved using randomized search Algorithms. We have used Simulated Annealing as a randomized algorithm. Training is done taking one month s chart maintained by the patient. Simulated Annealing [5][6][22] is a randomized search method that can perform global search within the defined searching space giving local maxima or global maxima. In our previous paper [7][8][9][10], we solved HMM learning problem modeled for dice using different randomized search algorithms. In this paper, insulin chart prediction is modeled as HMM and HMM Learning problem is solved using Simulated Annealing algorithm. Experimental results show that SA evaluates HMM parameters quite fast and accurately on the basis of previous data giving good prediction results. The organization of the paper is as follows. Section 2 briefly describes the data set taken. Section 3 explains HMM and section 4 explains in detail the HMM model used and results obtained. Section 5 is about results and discussions. II. DATA SET INFORMATION The data set used in this paper was taken from called UCI Repository. Diabetics patient records can be obtained from two sources: an automatic electronic recording device and paper records. The automatic device has an internal clock to timestamp events, whereas paper records provide "logical time" slots (breakfast, lunch, dinner, bedtime). Diabetic files consist of four fields per record. (1) Date in MM-DD-YYYY format (2) Time in XX:YY format (3) Code (4) Value. The Code field is deciphered as follows: 33 = Regular insulin dose, 34 = NPH insulin dose, 35 = Ultralente insulin dose, 48 = Unspecified blood glucose measurement, 57 = Unspecified blood glucose measurement etc. We have taken two month s data (insulin chart) for code 33 i. e. Regular insulin dose of a patient. Assuming first month s data as training data, next one month chart is

2 predicted and compared with the actual data. III. THE HIDDEN MARKOV MODEL (HMM) HMM is a probabilistic model useful for finite state stochastic sequence structures. Stochastic sequences are called observation sequences, i.e. O = O 1 O 2,., O T, where T is the length of the observed sequence. HMM with N states (S 1, S 2...S N ) can be characterized by a set of parameters (A, B, ) is called the model of HMM λ = (A, B, ) In order to characterize an HMM completely, following elements are needed [1][4][5][6][13] N: The number of states in the model M: The number of distinct observation symbols M per state A: The state transition probability distribution A = { a }, a p q s q S ) ij ij ( t j t 1 i B: The observation symbol probability distribution in state j B = b k) P( V at t q S ) j ( k t j : The initial state distribution P q S ) i ( 1 i The Three main problems of HMM are: Evaluation problem, Decoding problem, and Learning problem. (1) Evaluation problem: Compute P (O λ), the probability of the observation sequence O = O 1 O 2 O 3 O T, given the model λ = (A, B, ). (2) Decoding problem: Uncover the hidden part of the model i.e. find the optimal state sequence, for the given observation sequences O = O 1 O 2 O 3 O T, given the model λ = (A, B, ). (3) Learning problem: model parameters (A, B, ) are adjusted such that P (O λ) is maximized. In this paper, we have considered the third problem of HMM i.e. the learning problem or training problem and tried to solve it. IV. HIDDEN MORKOV MODEL FOR A DIABETES PATIENT To completely define a problem of HMM we need to define three probabilities: state transition probabilities, observation symbols probabilities and initial state probabilities. It was observed that a patient takes the medicine at Breakfast (08:00), Lunch (12:00), Dinner (18:00), and Bedtime (22:00) or morning, noon, evening and night, and the amount of insulin (code=33) varies from value 2 to 11. The dataset contains 4 values per day corresponding to 4 slots i.e. breakfast, lunch, dinner and bedtime. We have taken these four slots as four states where S 1 corresponds to breakfast, S 2 corresponds to lunch, S 3 corresponds to dinner and S 4 corresponds to bedtime. In addition to this, we have taken 10 observation symbols on the basis of insulin dose values given to the patient. Table 1 shows the actual amount of insulin give to the patient for few days. Date Code Breakfast Lunch Dinner Bed Time 21-Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr May May May May May May May May May Table 1: Actual input of doses for one month Further, whole one month s data was divided into slots of three days and training is done taking three days data repeatedly. For training, Simulated Annealing algorithm is used and at the end of the process, a model λ is obtained. Hence, our model λ has four states (S 1, S 2 S 3 and S 4 ) and we assume that the patient starts his doses from morning, i.e. there is a very high probability that the

3 patient will be in state 1. So we take initial probability as: = [ ] After examining the patient s previous data, we roughly initialize the state transition probabilities and symbol emitting probabilities generating initial A = a ij and B = B j (k) as follows: A=a ij =[ ] B= b j (k)= [ ] The observation sequence for first three days will be: O = [o 1 o 2 o 3 o 4 o 5 o 6 o 7 o 8 o 9 o 10 o 11 o 12 ] Taking the initial model, we keep training using Simulated Annealing[21][22][23] method for every three days, get a model λ 10 and then it is again trained taking all the previous observation sequences getting a λ Final Taking λ Final as model, observation sequence is predicted by matching P (O λ) values with previous model values. V. PREDICTION After training the HMM model [18], the procedure can be described as for the predicting the observation sequence. For predicting O i+1 we use P(O i λ final ) (O i is i th the obseravation sequence) to find those events which have closest P(O i λ final ) value. If we assume there are two closest values O k1 and O k2 ; then we evaluate two possible predicting values O p1 = O i + (O k1+1 O k1 ) and O p2 = O i + (O k2+1 O k2 ). For example for predicting O 11, we use the following steps; (a) For predicting O 11, we found P (O 4 /λ final ) and P(O 8 /λ final ) where are the closest observation sequences. (b) We find the differences of O 5 - O 4 and O 9 - O 8, and then these differences are added to O 10 giving two predicted observation sequences O p1 and O p2. Predicted Observation (O p1 = ) and (O p2 = ) (c) We again evaluate the P(O p1 λ Final ) and P(O p2 λ Final ) values, and O p2 chosen because it is observed that P(O p2 λ Final ) is higher value than P(O p1 λ Final ). Therefore O p2 observation sequence because the predicted sequence. Similarly using step a, b and c we predict O P11, O P12, O P13, O P14 and O P15 as follows. O P11 = O P12 = O P13 = O P14 = O P15 = Actual observation sequences are Oa 11, Oa 12, O a13, O a14 and O a15 are as follows O a11 = O a12 = O a13 = O a14 = O a15 = Actual Data Predictable Data Bed Bed Date code Breakfast Lunch Dinner Time Breakfast Lunch Dinner Time 21-May May May May May May May May May May May Jun Jun Jun Jun

4 Table1: Comparison between actual data and predicted Data 20 Actual doses Predicted doses Dose of insulin Number of days * 4 Graph1: Graph between Actual doses and Predicted doses for fifteen days. Does of Insulin Actual doses Predicted doses Number of days * 4 Graph2: Graph between actual doses and predicted doses for five days. V. RESULTS AND DISCUSSION In this study, we have taken the problem of predicting insulin chart for diabetic patients. Graph1 and Graph2 show the comparison between predicted data and actual data and it can be observed that results are very encouraging. We have discussed our results with our University medical doctor Dr. Chaman Kumar; he was very enthusiastic to see the results. To start with, the results obtained can be very useful to guide the junior doctors who prepare the complete chart for the patients. However, we need to make it user friendly before it can be tested in actual practice by the doctors. We are using simulated annealing algorithm to solve HMM learning problem which makes the whole computation very fast in comparison to the Baum Welch algorithm. We would like to compare the results by implementing other randomized algorithms. ACKNOWLEDGMENT The authors of the paper are highly grateful to Dr. Chaman Kumar (MBBS, MD) CSJM University Kanpur For discussing the results with us and encouraging us to do more work in this direction. VI. REFERENCES [1] Rabiner L.R. A tutorial on HMM and Selected Applications in Speech Recognition", Proceedings of the IEEE, Vol. 77, NO. 2, P [2] Md. Rafiul Hassan and Baikunth Nath Stock Market Forecasting using HMM: A New Approch,Proceeding of 2005 International Conference on Intelligent systems design and Applications(ISDA 05 ), [3] Behrooz Nobakht, Cart-Edward Joseph and Babak Loni Stock market Analysis and predection Using HMM LIACS. [4] R. Sundararajan, Stock market trend and predection using Markov models RTCSP 09, Department of ECE, Amrita Vishwa vidyapeeth, Coimbatore. [5] S. Kwong,C.W. Chau, K.F. Man, K.S. Tang Optimization of HMM topology and its model parameters by genetic algorithm, Pattern recognitions 34 (2001) [6] The Metropolis Algorithm, Statistical Systems and Simulated Annealing [7] Ravindra Nath, and Renu Jain, CpG sequence Identification using HMM and randomized search Algorithms, IRNet-Inernational Conference on computer science and IT Applications (CSIT ) New Delhi. [8] Ravindra Nath, and Renu Jain Parameter Estimation of Hidden Markov Models (HMM) using go with the Winner Algorithms,

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