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Accurate half-cycle correction (HCC) in discrete-time state-transition models (DTSTMs) is crucial for reliable cost-effectiveness analysis. Simpson

Keywords:
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Area of Science:

  • Health economics and outcomes research
  • Mathematical modeling in healthcare
  • Numerical analysis and simulation

Background:

  • Discrete-time state-transition models (DTSTMs) are widely used in health economics.
  • Half-cycle correction (HCC) is recommended for DTSTMs but lacks theoretical consensus.
  • Uncertainty exists regarding the optimal method for HCC implementation.

Purpose of the Study:

  • To establish theoretical foundations for half-cycle correction (HCC).
  • To compare the performance of various numerical integration methods for HCC in DTSTMs.
  • To evaluate the impact of different correction methods on cost-effectiveness outcomes.

Main Methods:

  • Defined seven numerical integration methods (Riemann sums, trapezoids, life-table, Simpson's rules).
  • Applied methods to a 3-state Markov chain model for cost-effectiveness analysis.
  • Compared discrete-time model outcomes against a continuous-time gold standard.

Main Results:

  • Standard HCC is equivalent to trapezoidal and life-table methods.
  • All methods introduced approximation errors compared to the continuous-time standard.
  • Simpson's 1/3rd rule demonstrated the fastest convergence to the gold standard, especially with shorter cycle lengths.

Conclusions:

  • Cumulative outcomes in DTSTMs are susceptible to errors that accurate methods can mitigate.
  • Misconceptions regarding HCC error cancellation were clarified.
  • Recommendations and algorithms for practical HCC implementation using methods like Simpson's rules are provided.