The hazards of using hazard ratios from proportional hazard models in indirect treatment comparisons

Indirect treatment comparison (ITC) is widely used to estimate the comparative effectiveness of treatments when head-to-head trials are unavailable. For the typical scenario of anchored ITC where one trial compares drug A to drug C (AC trial) and another compares drug B to drug C (BC trial), the comparative effectiveness of drugs A versus B is calculated by subtracting (or dividing) the relative treatment effect of A versus C in the AC trial by that of B versus C in the BC trial, assuming the covariate distributions in both trials are balanced. This operation is valid only if the chosen effect measure is transitive, that is, in a three-arm randomized trial of drugs A, B, and C, the direct treatment effect of A versus B equals the indirect treatment effect of A versus B through their comparisons to C. For survival outcomes, many ITCs use the hazard ratio (HR) as the effect measure. In this article, we demonstrate that HR is generally not transitive and should be used with caution. As more reliable alternatives, we recommend effect measures with better transitivity properties: the restricted mean survival time (RMST) difference, the landmark survival probability difference (or ratio) at a prespecified time point, and the average hazard with survival weights (AH-SW) difference.