Markov Model in Economic Evaluation for diabetes
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Markov Model, diabetes

Author: Xuanqian Xie

I would like to illustrate the Markov Model in Economic Evaluation using an example of intensive blood-glucose control with metformin versus usual care for overweight type 2 diabetes, based on my Master thesis and the corresponding publication in a peer-reviewed journal.

 

Markov models are often employed to represent stochastic processes, that is, random processes that evolve over time. In a health care context, Markov models are particularly suited to modelling chronic disease, of which diabetes mellitus is a good example. Basically, a health economic evaluation using Markov modelling distinguishes states, transition probabilities for movement between the states over a discrete time period (the ‘Markov’ cycle). By attaching estimates of resource use and health outcome consequence to the states and transitions in the model, and then running the model over a large number of cycles, it is possible to estimate the long-term costs and outcomes associated with a disease and a particular healthcare intervention. To express the results in a cost-utility analysis also information on the utility values of each of the states needs to be available. These ingredients of the model are subsequently introduced, based on a general strategy to use the scientific literature to populate the model and, where this is impossible or inappropriate, supplement these data with data collected from clinical experts. In this study eight clinical experts have been interviewed in Beijing. Finally, a strategy is described for handling uncertainty in the analysis.

 

The structure of the model is shown in fig 1. (The outline of the Markov model structure.)

Fig 1: The outline of the Markov model structure

 

Legend of fig 1

Node type:

A square node represents a decision, such as either intensive control or usual care.

A round node with an “M” depict Markov nodes (two arms).

A round node represents a chance node, which is the patents’ probability to die or suffer complications.

The triangle nodes are terminal nodes, which are path endpoints.

 

States and probabilities

States of diabetes patients are distinguished on the basis of the long-term complications of the disease. This study takes the UKPDS 34 as a starting point, distinguishing 10 non-fatal disease states, of which 7 are long-term and 3 are temporary (see below). Patients in the ‘well’-state are defined as not suffering from any long-term complications. From this state, patients can enter into seven different long-term disease states. For example, once patients suffer a long-term complication such as Non-fatal myocardial infarction, they enter into the state named ‘Complication A: Non-fatal MI’. The health status of patients in any of the complication states is lower than that of the ‘Well’ state. If patients suffer two or more long-term complications, or suffer one complication twice or more, it was assumed that patients enter the “severe complications” state. Each combination of two or more diseases is included in the definition of this state. It was assumed that the “severe complications” state is floor state in our study, and that is the worst health state for anyone living. It was also assumed that patients’ health states are only temporarily affected by treatment related to three eye diseases. These treatments are retinal photocoagulation, cataract extraction and treatment of vitreous haemorrhage. The approach implies that patients who receive these treatments do not transfer to other states after they receive one of these, but of course the cost of each of these treatment s are included in the model. Finally, when patients die from any cause, they enter the ‘Death’ state, which is an absorbing state.

 

Given the clinical characteristics of the disease and e.g. the availability of cost data of diabetes patients from statistical reports on an annual basis, a one-year cycle length was applied in this study. After every cycle (year) patients can move from one state into the other, or remain in the same state.

 

Based on the cohort and exclusion criteria of the UKPDS, we assume that newly diagnosed diabetes patents do not have any long-term complications, which translates to the probability of being in the “well” state as 1 at time 0. Therefore, the possibility that patients are in any other state at the start of the study is zero.

 

In order to simplify this study, it is assumed that transition probabilities are constant over time (the Markovian assumption), but we are ware of the fact that some transition probabilities to arrive in particular states are linked with the length of time that patients suffer from diabetes. This applies to e.g. renal failure. In the literature many data are presented as rates, whereas in a Markov model one needs probabilities. The formula of converting rates into probabilities is provided in equation 1.

(1)  P=1-e-rt (P= Annual transition probabilities, r = event rate per year in UKPDS 34, t = 1 year)

 

The length of follow-up of patients in clinical trials is different from that in Markov models. Basically, once patients reach the clinical endpoints, normally they are seldom followed up beyond that point in clinical trials. However, Markov models are quite different in this respect because patients can transit to states in each cycle, until they die. And any patients must be in a single defined state in a certain cycle. So, in principle, a lifetime perspective is possible using modelling. For the purpose of our study though we have chosen to develop a model with a length of follow-up corresponding to the length of follow-up as applied in the UKPDS study, where the median follow-up of patients was 10.7 years, which corresponds to 11 cycles of one year in the model. The main intention of the study is to generalize the UKPDS findings to another setting, which we feel justifies this time-horizon. However, we are aware that age-related death/diseases rates increase with patient age, and that 11 years of follow up represents only about half of the average life-expectancy of patients diagnosed with type 2 diabetes, so our findings can not easily be extrapolated to a life-time perspective.

 

The intensive blood-glucose strategy was not applied widely in Chinese clinical practices. Only 11.5% diabetes’ HbA1c level meets the target (6.5 %) of Chinese clinical guideline in a recent survey [9, 16]. Definitions of usual care policy and intensive treatment policy are based on UKPDS 34 [6].  Usual care policy: Maintaining FPG below 15mmol/L (6.1 to 15.0 m mol/L) and avoiding symptoms of hyperglycaemia. Patients could use oral agents and insulin to control FPG. Intensive treatment policy with metformin: Obtaining near-normal FPG (ie, <6.0 m mol/L) with metformin. Other oral agents and types of insulin will be added with the aim of maintaining FPG below 6.0 mmol/L.

 

Reference: Xie X, Vondeling H. Cost-utility analysis of intensive blood glucose control with metformin versus usual care in overweight type 2 diabetes mellitus patients in Beijing, P.R. China. Value Health 2008; 11 Suppl 1:S23-S32 Link: http://www.ncbi.nlm.nih.gov/pubmed/18387063 (This paper was based on my Master thesis.)