{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T10:57:01Z","timestamp":1756810621062,"version":"3.40.5"},"reference-count":14,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T00:00:00Z","timestamp":1618963200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Health Economics"],"published-print":{"date-parts":[[2021,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Operationalizing cost\u2010effectiveness analysis (CEA) requires that decisionmakers select maximum willingness to pay thresholds (<jats:italic>K<\/jats:italic>). We generalize previous methods used to estimate K using highly flexible hyperbolic absolute risk aversion (HARA) utility functions that encompass a wide range of risk behavior. For HARA utility, we calculate formulas for relative risk aversion (<jats:italic>r<\/jats:italic>*) and relative prudence (<jats:italic>\u03c0<\/jats:italic><jats:sup>\u2217<\/jats:sup>), using literature\u2010based estimates to calibrate our HARA model. We then assess optimal WTP thresholds (<jats:italic>K<\/jats:italic>) in absolute value and relative to income (K\/M). Across the most\u2010plausible range of risk preference parameters (<jats:italic>r<\/jats:italic>* and <jats:italic>\u03c0<\/jats:italic><jats:sup>\u2217<\/jats:sup>), optimal <jats:italic>K<\/jats:italic>\/<jats:italic>M<\/jats:italic> ratios sit (approximately) in the range of 1 to 3, although we cannot readily rule out larger <jats:italic>K<\/jats:italic>\/<jats:italic>M<\/jats:italic> values. The optimal <jats:italic>K<\/jats:italic> always increases with income, while <jats:italic>K<\/jats:italic>\/<jats:italic>M<\/jats:italic> falls with income if utility has increasing relative risk aversion. Results of this more\u2010general model of economic utility are broadly consistent with previous work using more\u2010restrictive Weibull functions. More precision in measuring the key parameters\u2014particularly relative prudence (<jats:italic>\u03c0<\/jats:italic><jats:sup>\u2217<\/jats:sup>) will narrow down the range of <jats:italic>K<\/jats:italic>\/<jats:italic>M<\/jats:italic> estimates. The highly general HARA structure illuminates why and how optimal CEA thresholds change with income. An appendix illuminates how relative risk aversion and relative prudence relate to each other.<\/jats:p>","DOI":"10.1002\/hec.4268","type":"journal-article","created":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T09:05:58Z","timestamp":1619082358000},"page":"1697-1702","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Estimating optimal willingness to pay thresholds for cost\u2010effectiveness analysis: A generalized method"],"prefix":"10.1002","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4533-0682","authenticated-orcid":false,"given":"Charles E","family":"Phelps","sequence":"first","affiliation":[{"name":"University of Rochester  Rochester New York USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chris","family":"Cinatl","sequence":"additional","affiliation":[{"name":"CNO Financial Group  Chicago Illinois USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,4,21]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1257\/aer.96.5.1821"},{"volume-title":"Consumption uncertainty and precautionary saving","year":"2016","author":"Christelis D.","key":"e_1_2_9_3_1"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.3310\/hta19140"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6296(96)00506-1"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jval.2017.12.009"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.2307\/2938334"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11166-005-5102-x"},{"volume-title":"Cost\u2010effectiveness in health and medicine","year":"2017","author":"Neumann P. J.","key":"e_1_2_9_9_1"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1093\/restud\/rdt032"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jval.2019.03.003"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jval.2019.05.008"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00056139"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/hec.3085"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.7326\/M20-1392"}],"container-title":["Health Economics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/hec.4268","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/hec.4268","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/hec.4268","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,27]],"date-time":"2023-08-27T07:56:12Z","timestamp":1693122972000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/hec.4268"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,21]]},"references-count":14,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2021,7]]}},"alternative-id":["10.1002\/hec.4268"],"URL":"https:\/\/doi.org\/10.1002\/hec.4268","archive":["Portico"],"relation":{},"ISSN":["1057-9230","1099-1050"],"issn-type":[{"type":"print","value":"1057-9230"},{"type":"electronic","value":"1099-1050"}],"subject":[],"published":{"date-parts":[[2021,4,21]]},"assertion":[{"value":"2020-04-10","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-03-20","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-04-21","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}