BEYOND THE MEAN ICER: INCORPORATING VALUE-AT-RISK, EXPECTED SHORTFALL, AND EXCEEDANCE CURVES INTO PROBABILISTIC SENSITIVITY ANALYSIS FOR RISK-INFORMED HEALTH TECHNOLOGY ASSESSMENT
Author(s)
Eleftherios Zarkadoulas, FHAS CERA MBA1, Jurjen van der Schans, PhD1, Mark Connolly, BA, MSc, PhD1, Nikos Kotsopoulos, MSc, PhD2, Maarten Postma, PhD1.
1University of Groningen, Groningen, Netherlands, 2Health Economist, University of Athens, Athens, Greece.
1University of Groningen, Groningen, Netherlands, 2Health Economist, University of Athens, Athens, Greece.
OBJECTIVES: Standard probabilistic sensitivity analysis (PSA) in cost-effectiveness analysis (CEA) reports mean incremental cost-effectiveness ratios, mean net monetary benefit (NMB), and cost-effectiveness acceptability curves (CEACs). These metrics characterise central tendency and probability of cost-effectiveness but do not quantify the severity of extreme adverse outcomes. In large-scale vaccination programmes—where parameter uncertainty is skewed and fiscal exposure is substantial—mean values may mask material tail risk. This paper proposes extending PSA with Value-at-Risk (VaR) and Expected Shortfall (ES) from actuarial science, alongside outcomes reduction exceedance curves.
METHODS: A conceptual framework integrating tail-risk measures into PSA output distributions was developed. VaR at confidence level α identifies the boundary of adverse NMB tail scenarios; ES estimates the conditional mean beyond that threshold. Both metrics are computed directly from Monte Carlo outputs without model modification. For comparative evaluations, parametric distributions are fitted to confidence intervals via moment-matching. Exceedance curves from simulated outcomes distributions provide continuous probability profiles of incremental public health impact.
RESULTS: Two interventions with comparable mean NMB and similar CEACs may differ substantially in ES, reflecting different fiscal tail exposure invisible to standard reporting. Exceedance curves reveal that equivalent expected outcomes reductions can imply very different probabilities of surpassing meaningful thresholds. These tools are analogous to coherent risk measures in Solvency II and Basel III, where distinguishing probability from severity of loss is foundational.
CONCLUSIONS: Integrating VaR and ES into PSA provides an actuarially consistent characterisation of economic tail risk, complementing mean NMB and CEAC reporting. For vaccination programmes with substantial fiscal exposure, these metrics support procurement planning and risk-sharing. Exceedance curves extend the framework to public health impact, enabling probabilistic communication of benefit thresholds under uncertainty.
METHODS: A conceptual framework integrating tail-risk measures into PSA output distributions was developed. VaR at confidence level α identifies the boundary of adverse NMB tail scenarios; ES estimates the conditional mean beyond that threshold. Both metrics are computed directly from Monte Carlo outputs without model modification. For comparative evaluations, parametric distributions are fitted to confidence intervals via moment-matching. Exceedance curves from simulated outcomes distributions provide continuous probability profiles of incremental public health impact.
RESULTS: Two interventions with comparable mean NMB and similar CEACs may differ substantially in ES, reflecting different fiscal tail exposure invisible to standard reporting. Exceedance curves reveal that equivalent expected outcomes reductions can imply very different probabilities of surpassing meaningful thresholds. These tools are analogous to coherent risk measures in Solvency II and Basel III, where distinguishing probability from severity of loss is foundational.
CONCLUSIONS: Integrating VaR and ES into PSA provides an actuarially consistent characterisation of economic tail risk, complementing mean NMB and CEAC reporting. For vaccination programmes with substantial fiscal exposure, these metrics support procurement planning and risk-sharing. Exceedance curves extend the framework to public health impact, enabling probabilistic communication of benefit thresholds under uncertainty.
Conference/Value in Health Info
2026-11, ISPOR Europe 2026, Vienna, Austria
Value in Health, Volume 29, Issue 12S
Code
EE748
Topic
Economic Evaluation, Health Technology Assessment, Methodological & Statistical Research
Topic Subcategory
Novel & Social Elements of Value
Disease
Vaccines