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

ABSTRACT

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.

KEYWORDS:

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

Acknowledgments

We would like to thank Tim P. Morris, MRC Clinical Trials Unit at University College London, UK, for his valuable comments.

Declaration of interest

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties. The opinions expressed in this publication do not necessarily represent the opinions of Health Quality Ontario. No endorsement is intended or should be inferred.

Reviewer Disclosures

Peer reviewers on this manuscript have no relevant financial or other relationships to disclose.

Author contribution statement

Xuanqian Xie conceived the study idea and simulated the data. Xuanqian Xie and Man Wah Yeung designed the study and drafted the manuscript. Zhuoyu Wang, Myra Wang, Olga Gajic-Veljanoski, Vivian Ng, and Andrei Volodin provided important intellectual content, critically revised the manuscript, and interpreted the results. All authors approved this version and agree to be accountable for all aspects of the work.

Additional information

Funding

This paper was not funded.