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

Area of Science:

• Health economics
• Mathematical modeling
• Biostatistics

Background:

• Markov models are crucial for cost-effectiveness analysis in healthcare.
• Probabilistic analysis is generally preferred over deterministic analysis for Markov models.

Purpose of the Study:

• To compare the performance of probabilistic and deterministic analyses in estimating expected rewards within Markov models.
• To mathematically justify the differences in Markov rewards between probabilistic and deterministic analyses.

Main Methods:

• Application of Jensen's inequality to compare expected Markov rewards.
• Conducting simulation studies to assess bias and accuracy of both analytical approaches.

Main Results:

• Probabilistic analysis demonstrated higher Markov rewards (life-years, quality-adjusted life-years) compared to deterministic analysis.
• Simulations indicated that probabilistic analyses yielded greater life-years, bias, and mean square error.
• Weaker evidence (smaller sample sizes) and longer time horizons amplified bias, leading to overestimated rewards in both methods.

Conclusions:

• Probabilistic analysis may lead to increased bias, particularly when underlying evidence is weak.
• Researchers using Markov models should be cognizant of potential overestimation of rewards with probabilistic analysis under conditions of limited evidence.