Hazard Ratios and Alternative Effect Measures: An Applied Illustration

Abstract

Purpose: Although the limitations of hazard ratios (HRs) for quantifying treatment effects in right-censored data have been widely discussed, HRs are still preferentially reported over other, more interpretable effect measures. This may stem from the fact that there are few applied examples that directly contrast the HR and its interpretation with alternative effect measures.

Methods: We analyzed data from two randomized clinical trials comparing panitumumab plus standard-of-care chemotherapy (SOCC) with SOCC alone as first- and second-line treatment for metastatic colorectal cancer. We report the effect of treatment with panitumumab on progression-free survival (PFS) using a Cox proportional hazards model to estimate the HR and the Kaplan-Meier estimator of cumulative incidence (risk). Further analyses included examining the cumulative incidence curves; kernel-smoothed, non-parametric hazards curves; fitting the Cox model with a continuous time variable; and estimating restricted mean survival as well as median survival.

Results: The HR was 0.82 (95% confidence interval [CI]: 0.71, 0.93), while the risk ratio (or relative risk [i.e., ratio of the cumulative incidence among the treated versus comparator]) was 0.99 (95% CI: 0.96, 1.02). These two measures suggest apparently different conclusions: either a treatment benefit or no effect. Through subsequent analyses, we demonstrated that, while the cumulative incidence of the outcome was similar by the end of follow-up regardless of treatment, the panitumumab treated group experienced longer PFS than those randomized to SOCC. Substantial nonproportional hazards were evident with panitumumab treatment reducing the hazard of progression/mortality during the first ~1.75 years but associated with an increased hazard of progress/mortality thereafter.

Discussion: This example underscores the difficulties in interpreting HRs, particularly in the setting of qualitative violations of proportional hazards, and the value of quantifying treatment effects via multiple effect measures.