Purpose: Markov models as used in health care economic evaluation normally involve cycle times that are large enough that the issue of timing errors is potentially relevant. It has become standard practice to use half-cycle correction as a means of addressing this issue. This paper questions this practice.
Method: Logical argument and simulation modeling of examples.
Result: The case is made for treating costs and accumulated quality-adjusted life years (QALYs) differently in calculations from Markov models. It is shown that half-cycle correction is often conceptually unjustified in the calculation of cost differences between two treatment options. For QALYs, the following theorem applies: THEOREM: Suppose that a Markov model is used to compare two decision options and (a) the initial probability distribution among Markov states is the same for both options; (b) the quality of life scores for each Markov state are the same for both options; (c) the discount factor applied to each quality of life score is calculated only in terms of the modeled time at which that quality of life score is calculated. Then half-cycle correction will give exactly the same result for the estimated lifetime difference in quality adjusted life years as methods which count the whole of a cycle according to the probability distribution either at the beginning or at the end of the cycle. PROOF: The only difference between the methods is the time by which the initial quality of life difference is multiplied. Since the initial quality of life difference is zero, by conditions (a) and (b), the difference between the methods is also zero. In cases where it is appropriate to make an assumption that costs or QALYs are accumulated continuously in time, it is shown that a method based on Simpson's rule allows increased cycle lengths and hence considerable reduction in overall computational effort with no loss of accuracy.
Conclusion: Half-cycle correction should not be regarded as a standard tool in the analysis of Markov models.
Candidate for the Lee B. Lusted Student Prize Competition