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The Half-Cycle Correction Explained: Two Alternative Pedagogical Approaches

Division of Nephrology, Sunny-brook & Women's College Health Sciences Centre, Toronto, Canada, Departments of Medicine and Health Policy Management and Evaluation, Faculty of Medicine, University of Toronto, Toronto, Canada

Michelle Bott

Department of Professional Practice, Guelph General Hospital, Guelph, Ontario

Murray Krahn

Division of General Internal Medicine, University Health Network, Toronto, Canada, Departments of Medicine and Health Policy Management and Evaluation, Faculty of Medicine, University of Toronto, Toronto, Canada

Students of Markov decision models are often taught to add a half-cycle's worth of incremental utility to the cumulative total for each health state. The reason for this ``half-cycle correction'' is often illustrated by a graph of the proportion of the hypothetical Markov cohort remaining in a given state. The ideal graph is shown as a smooth, declining, curve that represents the transition of patients randomly throughout each cycle. On the same graph, the effect of the accounting of state membership at the end of each cycle in discrete, computer-based approximations of the ideal Markov process is shown. Students are able to clearly see that the cumulative incremental utility in the discrete case underestimates the desired quantity. Likewise, they find the concept of shifting the ideal curve to the right by one-half cycle to reduce the latter discrepancy to be intuitive. However, students often find the approximate equivalence of shifting the ideal state membership curve and adding a half-cycle's worth of incremental utility to the total for the state at the beginning of a discrete Markov process to be a difficult cognitive leap. This article describes 2 pedagogical devices, algebraic and intuitive/visual approaches, that may assist the instructor of Markov theory to convey the latter concept. Elements of adult learning theory are discussed, which may help the instructor to choose which approach to employ. Implementation of the half-cycle correction in commonly used decision-analytic software is also discussed.

Key Words: Markov chains • models • educational • statistical.

This version was published on September 1, 2008

Medical Decision Making, Vol. 28, No. 5, 706-712 (2008)
DOI: 10.1177/0272989X08315241


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