The half-cycle correction revisited: redemption of a kludge

Decision-analytic software commonly used to implement discrete Markov models requires transitions to occur between simulated health states either at the beginning or at the end of each cycle. The result is an over- or underestimation, respectively, of quality-adjusted life expectancy and cost, compared with the results that would be obtained if transitions were modeled to occur randomly throughout each cycle. The standard half-cycle correction (HCC) is used to remedy the bias. However, the standard approach to the HCC is problematic: It does not account for discounting or for the shape of intermediate state membership functions. Application of the standard approach to the HCC also has no numerical effect on the resulting incremental cost-effectiveness ratio or change in net health benefit under certain circumstances. Alternatives to the standard HCC, in order of ease of use, include no correction, the life-table approach, the cycle-tree method, and a correction based on Simpson's rule. For less complex decision models in which the computational burden is not large, reducing the cycle length to a month or less and using no correction should result in small estimation biases. With more complex models, where cycle lengths larger than 1 month may be necessary to make computation feasible, we recommend the cycle tree approach. The latter is relatively easy to apply and has an intuitive appeal: Hypothetical subjects who transition from one state to another, on average halfway through a cycle, should receive half of the value associated with the state from which they come and half the value of the state to which they are going.