Weighted Hazard Ratio Estimation for Delayed and Diminishing Treatment Effect

However, when the true hazard ratio is large the proposed model overestimates the treatment effect and the treatment profile over time. In the delayed treatment scenario, the estimated treatment effect profile over time is typically close to the true profile. For both scenarios, we have demonstrated analytically that the hazard ratio functions are approximately equal under small treatment effects.

When the assumed rate of how quickly the treatment effect profile is diminishing or delaying differs in the analysis from that in the true data generating mechanism, the estimated hazard ratio profile from the WHR approach is biased. Since in practice the true HR time profile may differ from that assumed in the WHR analysis, it may be preferable to use alternative approaches for effect estimation.