title: Identifying best-fitting inputs in health-economic model calibration: a Pareto frontier approach.
abstract: To identify best-fitting input sets using model calibration, individual calibration target fits are often combined into a single goodness-of-fit (GOF) measure using a set of weights. Decisions in the calibration process, such as which weights to use, influence which sets of model inputs are identified as best-fitting, potentially leading to different health economic conclusions. We present an alternative approach to identifying best-fitting input sets based on the concept of Pareto-optimality. A set of model inputs is on the Pareto frontier if no other input set simultaneously fits all calibration targets as well or better.
  
  
  
  We demonstrate the Pareto frontier approach in the calibration of 2 models: a simple, illustrative Markov model and a previously published cost-effectiveness model of transcatheter aortic valve replacement (TAVR). For each model, we compare the input sets on the Pareto frontier to an equal number of best-fitting input sets according to 2 possible weighted-sum GOF scoring systems, and we compare the health economic conclusions arising from these different definitions of best-fitting.
  
  
  
  For the simple model, outcomes evaluated over the best-fitting input sets according to the 2 weighted-sum GOF schemes were virtually nonoverlapping on the cost-effectiveness plane and resulted in very different incremental cost-effectiveness ratios ($79,300 [95% CI 72,500-87,600] v. $139,700 [95% CI 79,900-182,800] per quality-adjusted life-year [QALY] gained). Input sets on the Pareto frontier spanned both regions ($79,000 [95% CI 64,900-156,200] per QALY gained). The TAVR model yielded similar results.
  
  
  
  Choices in generating a summary GOF score may result in different health economic conclusions. The Pareto frontier approach eliminates the need to make these choices by using an intuitive and transparent notion of optimality as the basis for identifying best-fitting input sets.
authors.affiliation: University of Minnesota School of Public Health, Division of Health Policy and Management, Minneapolis, MN (EAE)
authors.forename: Eva A
authors.initials: EA
authors.lastname: Enns
authors.affiliation: Ivey Business School, University of Western Ontario, London, ON, Canada (LEC)
authors.forename: Lauren E
authors.initials: LE
authors.lastname: Cipriano
authors.affiliation: Stanford University Medical School, Stanford, CA (CTS)
authors.forename: Cyrena T
authors.initials: CT
authors.lastname: Simons
authors.affiliation: Institute for Technology Assessment, Massachusetts General Hospital, Boston, MA (CYK)|Harvard Medical School, Boston, MA (CYK)
authors.forename: Chung Yin
authors.initials: CY
authors.lastname: Kong
mesh_terms: D001024:Aortic Valve Stenosis / Q000191:economics / Q000503:physiopathology / Q000601:surgery; D003362:Cost-Benefit Analysis / Q000379:methods*; D003661:Decision Support Techniques; D004470:Economics, Medical; D006801:Humans; D008390:Markov Chains; D017059:Models, Econometric; D019057:Quality-Adjusted Life Years; D012720:Severity of Illness Index; D065467:Transcatheter Aortic Valve Replacement / Q000191:economics
keywords: Pareto frontier; calibration; calibration uncertainty; health-economic model; model uncertainty; parameter estimation; parameter uncertainty