Potential Bias Associated with Modeling the Effectiveness of Healthcare Interventions in Reducing Mortality Using an Overall Hazard Ratio

  • Fernando Alarid-EscuderoEmail author
  • Karen M. Kuntz
Original Research Article



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.


Author Contributions

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.

Data availability statement

Data and statistical code are provided in the dsHR R package hosted in the GitHub repository The version of dsHR released in this article is available at

Supplementary material

40273_2019_859_MOESM1_ESM.pdf (169 kb)
Supplementary material 1 (PDF 168 kb)


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Drug Policy ProgramCenter for Research and Teaching in Economics (CIDE)-CONACyTAguascalientesMexico
  2. 2.Division of Health Policy and Management, School of Public HealthUniversity of MinnesotaMinneapolisUSA

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