Potential Bias Associated with Modeling the Effectiveness of Healthcare Interventions in Reducing Mortality Using an Overall Hazard Ratio
Clinical trials often report intervention efficacy in terms of the reduction in all-cause mortality between the treatment and control arms (i.e., an overall hazard ratio [oHR]) instead of the reduction in disease-specific mortality (i.e., a disease-specific hazard ratio [dsHR]). Using oHR to reduce all-cause mortality beyond the time horizon of the trial may introduce bias if the relative proportion of other-cause mortality increases with age. We sought to quantify this oHR extrapolation bias and propose a new approach to overcome this bias.
We simulated a hypothetical cohort of patients with a generic disease that increased background mortality by a constant additive disease-specific rate. We quantified the bias in terms of the percentage change in life expectancy gains with the intervention under an oHR compared with a dsHR approach as a function of the cohort start age, the disease-specific mortality rate, dsHR, and the duration of the intervention’s effect. We then quantified the bias in a cost-effectiveness analysis (CEA) of implantable cardioverter-defibrillators based on efficacy estimates from a clinical trial.
For a cohort of 50-year-old patients with a disease-specific mortality of 0.05, a dsHR of 0.5, a calculated oHR of 0.55, and a lifetime duration of effect, the bias was 28%. We varied these key parameters over wide ranges and the resulting bias ranged between 3 and 140%. In the CEA, the use of oHR as the intervention’s effectiveness overestimated quality-adjusted life expectancy by 9% and costs by 3%, biasing the incremental cost-effectiveness ratio by − 6%.
The use of an oHR approach to model the intervention’s effectiveness beyond the time horizon of the trial overestimates its benefits. In CEAs, this bias could decrease the cost of a QALY, overestimating interventions’ cost effectiveness.
FA-E and KMK: study design and analysis. All authors participated in the interpretation of the data, drafting of the manuscript, critical revision of the manuscript, and approval of the final manuscript.
Compliance with Ethical Standards
Dr Alarid-Escudero was supported by a grant from Fulbright-García Robles and the National Council of Science and Technology of Mexico (CONACYT) as part of Dr Alarid-Escudero’s doctoral program. Drs Kuntz and Alarid-Escudero were supported by a grant from the National Cancer Institute (U01-CA-199335) as part of the Cancer Intervention and Surveillance Modeling Network (CISNET). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The funding agencies had no role in the design of the study, interpretation of results, or writing of the manuscript. The funding agreement ensured the authors’ independence in designing the study, interpreting the data, writing, and publishing the report.
Conflict of interest
FA-E reports no conflicts of interest. KMK reports no conflicts of interest.
- 1.Kuntz KM, Russell LB, Owens DK, Sanders GD, Trikalinos TA, Salomon JA. Decision models in cost-effectiveness analysis. In: Neumann PJ, Sanders GD, Russell LB, Siegel JE, Ganiats TG, editors. Cost-effectiveness Heal Med. Second. New York: Oxford University Press; 2017. p. 105–36.CrossRefGoogle Scholar
- 6.Gold MR, Siegel JE, Russell LB, Weinstein MC. Cost-effectiveness in health and medicine. New York: Oxford University Press; 1996.Google Scholar
- 8.National Institute for Health and Care Excellence. Guide to the methods of technology appraisal 2013 [Internet]. London, UK; 2013. p. 1–93. Available from: http://www.nice.org.uk/article/pmg9/resources/non-guidance-guide-to-the-methods-of-technology-appraisal-2013-pdf.
- 10.Cox DR. Models and life-tables regression. J R Stat Soc. 1972;34:187–220.Google Scholar
- 14.Neumann PJ, Sanders GD, Russell LB, Siegel JE, Ganiats TG, editors. Cost-effectiveness in health and medicine. Second. New York: Oxford University Press, Incorporated; 2017.Google Scholar
- 15.Briggs A, Sculpher M, Claxton K. Decision modelling for health economic evaluation. New York: Oxford University Press; 2006.Google Scholar
- 16.Canadian Agency for Drugs and Technologies in Health (CADTH). Guidelines for the Economic Evaluation of Health Technologies. 3rd ed. 2006.Google Scholar
- 19.Drummond MF, Sculpher MJ, Torrance GW, O’Brien BJ, Stoddart GL. Methods for the economic evaluation of health care programmes. 3rd ed. New York: Oxford University Press; 2005.Google Scholar
- 23.Williams C, Lewsey JD, Briggs AH, Mackay DF. Estimation of survival probabilities for use in cost-effectiveness analysis: a comparison of a multi-state modelling survival analysis approach with partitioned survival and Markov decision-analytic modelling. Med Decis Mak. 2017;37:427–39.CrossRefGoogle Scholar
- 24.Kuntz KM, Weinstein MC. Modelling in economic evaluation. In: Drummond MF, McGuire A, editors. Econ eval heal care merging theory with pract. 2nd ed. New York: Oxford University Press; 2001. p. 141–71.Google Scholar
- 25.Arias E. United States Life Tables, 2009. Nat Vital Stat Rep. 2014;62(7):1–63.Google Scholar
- 34.Technology Evaluation Center. Special report: cost-effectiveness of implantable cardioverter-defibrillators in a MADIT-II population. Assess Progr. 2004;19:1–2.Google Scholar
- 39.Sanders GD, Owens DK, Hlatky MA. Potential cost-effectiveness of wearable cardioverter-defibrillator early post myocardial infarction. Innov Card Rhythm Manag. 2015;6:1929–40.Google Scholar
- 40.Theuns DAMJ, Smith T, Hunink MGM, Bardy GH, Jordaens L. Effectiveness of prophylactic implantation of cardioverter-defibrillators without cardiac resynchronization therapy in patients with ischaemic or non-ischaemic heart disease: a systematic review and meta-analysis. Europace. 2010;12:1564–70.CrossRefGoogle Scholar