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

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.

Keywords

• Chronic kidney disease
• Hidden Markov model
• Glomerular filtration rate
• Transition intensity
• Mean sojourn time
• Viterbi algorithm