Multistate Markov model for predicting the natural disease progression of type 2 diabetes based on hemoglobin A1c

Abstract

Introduction: Type 2 diabetes is a common non-communicable disease, especially in developing countries like India, posing a huge economic burden on the family and nation as a whole. It is a chronic metabolic disorder in which prevalence has been increasing steadily all over the world. In studies of many chronic medical conditions, the health status of a patient may be characterized using a finite number of disease states. The multi-state Markov model is a useful way to describe states of a disease over time. In this research article, we have illustrated the usefulness of multistate Markov models in the analysis of follow-up of diabetes. The valuable information provided by the hemoglobin A1c (HbA1c) test has rendered it as a reliable biomarker for the diagnosis and prognosis of diabetes. Objectives: The main purpose of this study is to assess the importance and significance of HbA1c as a useful disease marker for type 2 diabetes by using a three-state Markov model. Patients and Methods: A total of 246 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 HbA1c. HbA1c repeated after every 1 year for consecutive four years. Based on ranges of HbA1c, three transient states (4 ≤ HbA1C ≤ 5.6, 5.7 ≤ HbA1C ≤ 6.4 and HbA1C ≥ 6.5%) have been defined. Additionally, transition intensities, transition probabilities, mean sojourn time in each state and also expected state specific survival time have been assessed. All the statistical analysis has been performed using the msm package in R software. Results: The mean age of patients at diagnosis was 26.12 years (SD=7.60), ranging from 10 to 49 years. The estimates of transition intensities reveal that a patient in state 1 is 16.4 (0.82/0.05) times more likely to move to state 2 than to move to diabetic state. Similarly, a patient in pre-diabetic is 7.5 (2.34/0.31) times more likely to move to diabetic state as compared to normal state. Additionally, once a patient is in a diabetic state there is 79% chances of remaining in a diabetic state as compared to 4% and 17% of moving to normal or pre-diabetic state, this implies that a patient who once in the diabetic state is difficult to move to a normal or pre-diabetic state. Conclusion: The estimated total length of time spent in each state is forecasted to be four months in normal state, five months in pre-diabetic state and 39 months in diabetic state. Hence, it has been concluded that, once the patient enters the diabetic state (HbA1c>6.4), the chances of getting back to normal or pre-diabetic state are very small.

Keywords

• Glycated hemoglobin
• Multistate Markov model
• Type 2 diabetes
• Type 1 diabetes mellitus