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Estimation of transition probabilities for diabetic patients using hidden Markov model

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Abstract

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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Abbreviations

S:

Hidden state

V:

Observed state

L:

Likelihood function

π:

Initial state distribution

(S1, S2…SN):

Sequence of hidden state

(V1,V2…Vm):

Sequence of observed state

A:

Transition probability matrix

B:

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

WHO:

World Health Organization

GDM:

Gestational diabetes mellitus

HMM:

Hidden Markov model

HbA1c:

Glycated hemoglobin

SD:

Standard deviation

L:

Lower limit

U:

Upper limit

CI:

Confidence interval

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Authors and Affiliations

  1. Department of Statistics, Hindu College, University of Delhi, New Delhi, India

    Manoj Kumar Varshney

  2. Department of Statistics, Faculty of Mathematical Sciences, University of Delhi, New Delhi, India

    Ankita Sharma, Komal Goel & Gurprit Grover

  3. Department of Statistics, Lady Shri Ram College, University of Delhi, New Delhi, India

    Vajala Ravi

Authors
  1. Manoj Kumar Varshney
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  2. Ankita Sharma
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  3. Komal Goel
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  4. Vajala Ravi
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  5. Gurprit Grover
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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 (Suppl 2), 329–334 (2020). https://doi.org/10.1007/s13198-020-00950-7

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  • DOI: https://doi.org/10.1007/s13198-020-00950-7

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