HALF-CYCLE CORRECTION AND SIMPSON'S METHOD TESTED IN REAL HEALTH ECONOMIC MODELS – DOES IT MATTER WHICH METHOD WE USE?

Purpose:    To test the practical impact of replacing half-cycle correction with Simpson’s method in Markov models of cost-effectiveness.

Method:    Markov models are frequently used in cost-effectiveness modeling, particularly when modeling chronic diseases.  In Markov models, time is handled as a series of discrete cycles, where events of interest are counted either at the beginning or end of each cycle. In real life, these events can occur at any time within each cycle, hence, this is best represented as a continuous probability function. This means we are actually interested in the integral of a continuous function even though events are counted either at the start or end of the cycles. Uncorrected, Markov models systematically overestimate (events at cycle start) or underestimate (events at cycle end) event frequency. The most common adjustment in health economic modeling is half-cycle correction; shifting cycle estimates by half a period. While this method reduces model bias, it has been criticized both at the SMDM meeting in 2009, and in an MDM paper for being a poor approximation to the integration problem. Opponents to half-cycle correction suggest using Simpson’s method, an old mathematical approximation to estimating the integral of a continuous line represented by discrete points.    We have used three recently developed health economic models to test whether replacing half-cycle correction with Simpson’s method makes a practical difference. All models are Markov models with several events and health states modeling cost-utility in a lifetime perspective. We ran the three models for a number of different scenarios and interventions.

Result:    Results varied from -17.2% to 0.19% in terms of incremental costs for Simpson’s method compared to half-cycle correction. In terms of differences in quality-adjusted life-years, results varied between -0.75% and 0.67%.   Differences in net health benefit varied between -0.06% and 0.21%, while differences in incremental net health benefit varied between -1.56% and 12.7%. INHB did not change from positive to negative or vice versa in any comparisons.

Conclusion:    In our analyses, cost differences varied substantially between half-cycle correction and Simpson’s method. In terms of quality-adjusted life-years, differences were small in our models. Conclusions did not change in any of our analyses, however changes in incremental net health benefit was not negligible, suggesting that conclusions could be altered under specific circumstances.