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Estimation of transition probabilities for diabetic patients using hidden Markov model | SpringerLink

Estimation of transition probabilities for diabetic patients using hidden Markov model


Diabetes is a common non-communicable disease affecting substantial proportion of adult population. This is true, especially in developing countries like India thereby posing a huge economic burden not only on the patient’s family but also on the nation as a whole. In this paper, we have employed a hidden Markov model to estimate the transition probabilities between three states of diabetes and applied it to real life data. A total of 184 Type 2 diabetic patients were included in this study. These patients are classified in different states on the basis of their available baseline value of Hemoglobin A1c (HbA1c). A HMM fits well to the data by capturing the misclassified states, and shows that the patients who had HbA1c ≥ 6.5% have minimum chance of recovery and substantially higher risk of complications. All the statistical analysis has been performed using the “Hidden Markov” package in R software.

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Fig. 1
Fig. 2



Hidden state


Observed state


Likelihood function


Initial state distribution

(S1, S2…SN):

Sequence of hidden state


Sequence of observed state


Transition probability matrix


Emission probability matrix

aij :

The probability of being in hidden state Sj at time (t + 1) given that the patient was in hidden state Si at time t

bjk :

The probability of being in observed state k at time t given that the patient was in hidden state Sj at time t


World Health Organization


Gestational diabetes mellitus


Hidden Markov model


Glycated hemoglobin


Standard deviation


Lower limit


Upper limit


Confidence interval


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Correspondence to Ankita Sharma.

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Varshney, M.K., Sharma, A., Goel, K. et al. Estimation of transition probabilities for diabetic patients using hidden Markov model. Int J Syst Assur Eng Manag 11, 329–334 (2020). https://doi.org/10.1007/s13198-020-00950-7

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  • Diabetes
  • HbA1c
  • Hidden Markov model (HMM)
  • Emission distribution
  • Goodness of fit