Use of Copulas for Correlated Sampling of Cost and Utility Parameters During Probabilistic Sensitivity Analysis for Cost-Effectiveness Analyses


Lim S1, LoPresti M2, Murofushi T3
1INTAGE Healthcare Inc., Kawasaki-shi, 14, Japan, 2INTAGE Healthcare Inc., Chiyoda-ku, Tokyo, Japan, 3INTAGE Healthcare Inc., Chiyoda-ku, 13, Japan

OBJECTIVES: For probabilistic sensitivity analysis (PSA) in cost-effectiveness models (CEM), cost and utility parameters are typically assigned separate probability distributions and sampled independently. However, nonlinear correlation could exist between cost and utility, which may also follow different functional forms of probability distributions. Thus, joint sampling of cost and utility parameters to account for potential nonlinear correlation may yield more realistic outcomes. This research explored the potential impact on PSA of joint sampling through copulas.

METHODS: A Markov model of orthopedic surgery in R by Naylor et al. (2023) was utilized as the framework. Joint sampling via the Clayton copula was conducted for reoperation costs through Gamma distribution and reoperation utility through Beta distribution. Different Kendall tau correlations (-0.5 to 0.5) were assumed among cohorts to specify copulas. Ten thousand simulations of incremental costs, quality-adjusted life years (QALY), incremental cost-effective ratios (ICER) per cohort, as well as estimates of Kendall tau correlation between incremental costs and QALYs were computed.

RESULTS: Means, medians, interquartile ranges of incremental costs, QALYs, ICERs were similar among cohorts, and Kruskal-Wallis tests were not statistically significant. However, there was a slight monotonic trend for estimated values of tau between incremental cost and utility, with non-overlapping 95% CI among some cohorts with large tau differences.

CONCLUSIONS: For the current study, correlated sampling of key cost and utility parameters via copulas had relatively little impact on simulated values of incremental costs, QALYs, and ICERs but resulted in a small yet consistent trend in Kendall tau correlations of incremental costs and QALYs. Further research is needed to determine when correlated sampling of cost and utility parameters via copulas may bring additional benefits.

Conference/Value in Health Info

2023-11, ISPOR Europe 2023, Copenhagen, Denmark

Value in Health, Volume 26, Issue 11, S2 (December 2023)




Economic Evaluation, Health Technology Assessment, Methodological & Statistical Research, Study Approaches

Topic Subcategory

Cost-comparison, Effectiveness, Utility, Benefit Analysis, Decision & Deliberative Processes, Decision Modeling & Simulation


Musculoskeletal Disorders (Arthritis, Bone Disorders, Osteoporosis, Other Musculoskeletal), Surgery

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