A Multi-State Markov Model for the Progression of Chronic Kidney Disease

Abstract

Objective: The main goal of this study is to develop a stochastic model for the progression of Chronic Kidney Disease (CKD) into different stages based on estimated Glomerular Filtration Rate (eGFR). Material and Methods: The present study is a retrospective study of 117 patients suffering from CKD during the period March 2006 to October 2016. The prognostic factors such as gender, age, body mass index, diabetes, hypertension, hemoglobin, urea, serum creatinine, albumin and duration of the disease were recorded for each patient. We have applied the continuous time homogeneous multistate model based on Markov processes. The deterioration of disease is continuous in time and the probability of transition from one state to another state depends on the length of time and is independent of time on which transition takes place. Also, Cox proportional hazard model has been used to examine the effects of prognostic factors on the transition rates. Results: The probabilities of staying in the same state in first five years i.e. stage 1, stage2, stage 3, stage 4 and stage 5 are 0.6126, 0.5508, 0.5631, 0.0596 and 1 respectively. The probabilities of moving to the next state are also computed for first five and ten years. The prognostic factors age, hypertension, diabetes, hemoglobin, urea, serum creatinine are significant factors for the progression of CKD into different stages. Conclusions: The mean sojourn times along with p-next probabilities provide more intuitive parametric information of continuous time multistate model based on Markov processes than crude transition intensities.