eISSN: 2345-4202  
J Nephropharmacol. 2019;8(1):7-7.
doi:10.15171/npj.2019.07

Original

On the estimation of misclassification probabilities of chronic kidney disease using continuous time hidden Markov models 

Gurprit Grover 1, Alka Sabharwal 2, Shrawan Kumar 2 * , Arpan Kumar Thakur 1

1 Department of Statistics, University of Delhi. Delhi, India
2 Department of Statistics, Kirori Mal College, University of Delhi, Delhi, India
*Corresponding author: Shrawan Kumar, Email: Email: shrawan.kmc@gmail.com

Abstract

Introduction: The severity of chronic kidney disease (CKD) is reflected in the form of stages of CKD and can be decided on the basis of estimated glomerular filtration rate (eGFR). The computation of eFGR may have computational and measurement errors which may lead to misclassification of stages.

Objectives: Estimation of transition rates, mean sojourn times, probabilities of misclassification of stages and odds ratios for misclassification probabilities.

Patients and Methods: The retrospective data of 117 patients suffering from CKD during the period March 2006 to October 2016 is used. Hidden Markov model (HMM) with continuous time has been developed to present the course of progression of CKD into various stages.

Results: Under the HMM, the estimated transition intensity corresponding to transition from stage 1 to stage 2 is 0.0405 and reverse transition intensities are zero. The estimated mean sojourn time corresponding to stage 1, stage 2, stage 3 and stage 4 are 15.923 years, 11.976 years, 7.936 years and 2.890 years respectively. The probability of a CKD patient with stage 1 of disease will be misclassified as a patient of stage 2 is 0.211. The odds ratios for misclassification probabilities in the presence of prognostic factors are computed. The probability of misclassification corresponding to the observed stage 2 given the true stage 1 for females is approximately 3.8 times more than that of males.

Conclusion: For CKD having progression in stages, the HMM is an appropriate model to draw the course of progression of the disease.

Implication for health policy/practice/research/medical education:

CKD is asymptomatic in its early stages and the determination of stage may be erroneous due to other prognostic factors which may lead to misclassification of stages. Medical practitioners should consider all the factors while screening a patient before declaring the stage of the disease.

Please cite this paper as: Grover G, Sabharwal A, Kumar S, Thakur AK. On the estimation of misclassification probabilities of chronic kidney disease using continuous time hidden Markov models. J Nephropharmacol. 2019;8(1):e07. DOI: 10.15171/ npj.2019.07

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Submitted: 08 Jul 2018

Accepted: 08 Oct 2018
First published online: 10 Nov 2018
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