Modeling the Progression of Chronic Kidney Disease Using the Multi-state Continuous Time Markov Model: A Case of Jimma University Medical Center

Abstract

Background: Chronic kidney disease (CKD) is a condition that decreases kidney function and can f inally leads to renal failure. The progression of CKD is a complex process with different intermediate events. This complex disease processes may be efficiently handled with a multi-state model rather than a simple survival model. Therefore, this study aims to model the progression of CKD using a continuous time multi-state Markov (MSM) model which evaluates the defined stages of the disease. Methods: This study is a retrospective cohort study of 194 CKD patients who were visited 1506 times in JUMC starting from february 2019 to february 2024. The CKD progression can be analyzed using the multi-state model to assess the effect of different risk factors on the transitions rates between each stages. The MSM model is employed to estimate the transition probabilities, transition intensity and sojourn time along with p-next probabilities between the stages of the underlying disease. Results: CKD is asymptomatic in its early stages, with only 15.9% of patients in stage 1, while 26.2% of patients are in stage 5. The transition probabilities of patients from any stable stages to worst stage are increasing over time, while the probabilities of remaining in the same stage is decreasing. The average duration patients spent in stages 1, 2, 3, and 4 before transiting to other stage was 4.33, 4.44, 5.79, and 4.57 months respectively. For transition from stage 3 to stage 4, serum creatnine, urea protein, sodium and hemoglobin were associated with risk of progression. Patients with diabetes were 2.58 times more likely to move from stage 1 to stage 2 than those with no diabetes (HR = 2.58, CI = 1.44, 4.62). The progression of CKD was significantly accelerated with predictor variables serum creatnine, urea protein, hemoglobin, sodium, and patient’s co-infected with diabetes, hypertension, cardiovascular disease and anemia. Conclusion: The mean sojourn time together with p-next probabilities in this study provides more perceptible parametric information of the multi-state continuous time model based on markov processes than transition intensity. This study concludes, chronic kidney disease predominantly affects an older, male, rural demographic patients; and is commonly accompanied by HTN, diabetes, CVD and anemia.