Potential bias associated with modeling the effectiveness of healthcare interventions in reducing mortality using an overall hazard ratio

In this paper, we quantified the bias associated with using oHR as an intervention’s effectiveness beyond the time horizon of the clinical trial and derived an expression of dsHR as a function of the estimated oHR and the characteristics of the trial’s study population.

Abstract

Background

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.

Methods

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.

Results

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%.

Conclusions

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.

Download paper here and the accompanying R package can be downloaded here.