Risk Ratios versus Hazard Ratios in Comparative Effectiveness Research: An Illustration Using Clinical Trial Data

Background: Limitations of using hazard ratios (HRs) rather than risk ratios (RRs) to quantify exposure-outcome associations in longitudinal analyses have been previously described, but little work has demonstrated these concepts in real data. Given the widespread use of HRs instead of RRs, additional insights are valuable.

Objectives: To compare HRs and RRs calculated at various points in follow-up from randomized clinical trials.

Methods: This study used data from two trials obtained from Project Data Sphere investigating panitumumab-FOLFOX4 versus FOLFOX4 as first and second-line therapy for metastatic colorectal cancer. We used trial data for those individuals with wild-type (WT) KRAS mutation status, a known modifier of the benefit of this therapy. We estimated the treatment effect as a RR, using the Kaplan-Meier (KM) estimator to calculate cumulative incidence (risks) for each treatment, and HR, using a Cox model under the assumption of proportional hazards, per trial protocol. Effect measure estimates were calculated at the end of follow-up and at various times from randomization.

Results: The 206-week risk of disease progression or death was ≥96%, irrespective of treatment arm. The median time to event was 248 (IQR: 127, 453) and 208 (IQR: 109, 384) days among the treated and comparator, respectively. The KM cumulative incidence curves diverged at the beginning of follow-up but came together at later points of follow-up. The RR and HR estimates differed at the end of follow-up: HR=0.81 (95% CI: 0.72, 0.91) and RR=0.99 (95% CI: 0.97, 1.01). The RRs monotonically increased over follow-up: RR=0.65, 0.87, 0.92, 0.94, 0.96, 1.00 at 90, 270, 450, 630, 810, and 990 days, respectively. The HR did not, instead plateauing around the final estimate: 0.65, 0.77, 0.78, 0.79, 0.79, 0.81, respectively.

Conclusions: The estimated HR and RR for WT KRAS at the end of follow-up appear contradictory for panitumumab efficacy. However, they convey two distinct findings, both key to understanding the treatment benefit. (1) The treated group had a longer median time to event compared to the untreated: reflected in the final HR, where the model assumed proportional hazards. (2) The two treatment groups experienced similar risk of the outcome by the end of follow-up: captured by the final RR. The KM cumulative incidence curve is non-parametric. Thus, it captures this treatment benefit while providing estimates of risk (and thus RRs) at each time point. By contrast, the HR, under the proportional hazards assumption, incorporates prior hazards into the final estimate, obscuring the risk at various timepoints. These results plainly illustrate why (1) HR estimates should be presented with RR and cumulative risk estimates and (2) choice of follow-up is important in comparative effectiveness studies.