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Expert Rev Pharmacoecon Outcomes Res. 2019 May 22:1-7. doi: 10.1080/14737167.2019.1615886. [Epub ahead of print]

Comparison of the expected rewards between probabilistic and deterministic analyses in a Markov model.

Author information

a Evidence Development and Standards , Health Quality Ontario , Toronto , Canada.
b Carrefour de l'innovation et de l'évaluation en santé , Centre de recherche du Centre hospitalier de l'Universite de Montreal , Montreal , Canada.
c Department of Mathematics and Statistics , University of Regina , Regina , Canada.


Objectives: In Markov models that evaluate the cost-effectiveness of health-care technologies, it is generally recommended to use probabilistic analysis instead of deterministic analysis. We sought to compare the performance of probabilistic and deterministic analysis in estimating the expected rewards in a Markov model. Methods: We applied Jensen's inequality to compare the expected Markov rewards between probabilistic and deterministic analysis and conducted a simulation study to compare the bias and accuracy between the two approaches. Results: We provided mathematical justification why probabilistic analysis is associated with greater Markov rewards (life-years and quality-adjusted life-years) compared with deterministic analysis. In our simulations, probabilistic analyses tended to generate greater life-years, bias, and mean square error for the estimated rewards compared with deterministic analyses. When the expected values of transition probabilities were the same, weaker evidence derived from smaller sample sizes resulted in larger Markov rewards compared with stronger evidence derived from larger sample sizes. When longer time horizons were applied in cases of weak evidence, there was a substantial increase in bias where the rewards in both probabilistic and deterministic analysis were overestimated. Conclusion: Authors should be aware that probabilistic analysis may lead to increased bias when the evidence is weak.


Jensen’s inequality; Markov model; Probabilistic analysis; bias; simulation

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