POTENTIAL BIAS ASSOCIATED WITH MODELING THE EFFECTIVENESS OF TREATMENT USING AN OVERALL HAZARD RATIO

   Purpose: Clinical trials often report treatment efficacy in terms of the reduction of all-cause mortality [i.e., overall hazard ratio (OHR)], and not the reduction in disease-specific mortality [i.e., disease-specific hazard ratio (DSHR)]. Using an OHR to reduce all-cause mortality beyond the time horizon of the clinical trial may introduce bias if the relative proportion of other-cause mortality increases with age. We aim to quantify this bias.

   Methods:  We simulated a hypothetical cohort of patients with a generic disease that increases the age-, sex-, and race-specific mortality rate (μ_ASR) by a constant additive disease-specific rate (μ_Dis). We assumed a DSHR of 0.75 (unreported) and an OHR of 0.80 (reported, derived from DSHR and assumptions of clinical trial population). We quantified the bias in terms of the difference in life expectancy (LE) gains with treatment between using an OHR approach to reduce all-cause mortality over a lifetime [(μ_ASR+ μ_Dis)xOHR] compared with using a DSHR approach to reduce disease-specific mortality [μ_ASR+(μ_Dis)xDSHR]. We varied the starting age of the cohort from 40 to 70 years old.

   Results : The OHR bias increases as DSHR decreases and with younger starting ages of the cohort. For a cohort of 60 year-old sick patients, the mortality rate under OHR approach crosses μ_ASR at the age of 90 (see figure) and LE gain is overestimated by 0.6 years (a 3.7% increase). We also used OHR as an estimate of DSHR [μ_ASR+(μ_Dis)xOHR] (as the latter is not often reported). This resulted in a slight shift in the mortality rate compared to the DSHR approach (see figure), yielding in an underestimation of the LE gain.

   Conclusions:  The use of an OHR approach to model treatment effectiveness beyond the time horizon of the trial overestimates the effectiveness of the treatment. Under an OHR approach it is possible that sick individuals at some point will face a lower mortality rate compared with healthy individuals. We recommend either to derive a DSHR from trials and use the DSHR approach, or to use the OHR as an estimate of DSHR in the model, which is a conservative assumption.