Evaluation of Markov Models with Discontinuities

Area of Science:

• Health economics
• Mathematical modeling
• Pharmacoeconomics

Background:

• Markov models are susceptible to time discretization errors.
• Existing methods like half-cycle correction and life-table methods aim to reduce these errors.
• Numerical integration techniques have been proposed but may not account for discontinuities.

Purpose of the Study:

• To develop and evaluate a method for assessing Markov models with cost discontinuities.
• To address limitations of existing numerical integration techniques when discontinuities are present.

Main Methods:

• A novel method was derived using the trapezoidal rule, averaging cost values at points of discontinuity.
• A published Markov model with a 1-year cycle length and a cost discontinuity was adapted.
• The proposed method was compared against other corrections using a daily cycle length model as the gold standard.

Main Results:

• The life-table method outperformed models assuming transitions at cycle start/end.
• Numerical integration without discontinuity handling introduced significant errors.
• The averaged cost model demonstrated minimal errors, particularly with the trapezoidal and Simpson's 1/3 rules.

Conclusions:

• The trapezoidal rule applied to an averaged model is recommended for Markov models with discontinuities.
• This approach provides mathematical justification and demonstrated superior accuracy compared to Simpson's 3/8 rule in empirical tests.