gms | German Medical Science

Background: In Germany, the benefit assessment by G-BA is meant to show and grant the magnitude of added benefit of a new medication over the standard of care. For binary outcomes, responder analyses are performed that rely either on the hazard ratio (HR) obtained from a Cox proportional hazards (PH) regression or on the risk ratio (RR). But how do we decide which estimate is the right one? Should RR be preferred when the difference in time to event (TTE) is not on focus? The issue can be formalized with an example: the rate of relapse. As it can first remain silent, its clinical diagnosis can be delayed. Could HR highlight a difference solely due to, or widely emphasized by, different times to diagnosis? Shall we rather rely on RR? A simulation study was conducted.

Methods: 1300 patients were equally allocated to two arms. Administrative censoring was set to vary from 2 to 27 months and median TTE between1 and 50 months in both arms independently. All possible scenarios were covered: length of observation period, median TTE, magnitude of effects. Survival times were generated using the exponential distribution. Non-proportional hazard rates we obtained by combining two exponential distributions in one arm. HR and RR were estimated for each simulated trial.

Results: If observation times differ between the groups, the occurrence of the event of interest is precluded by shorter termination in one group. RR that does not consider censoring in inappropriate. Fake significant results are expected. If observation times do not differ, two scenarios are possible. If median TTE is the same in both arms, then RR=HR at any time. But if it differs, then the number of events can only be equal if (i) every patient has had an event, or (ii) the proportional hazard assumption (PH) is not met. In the first case, RR would not be significant, but HR would due to time only. In the second case, neither is recommended. If PH holds, median TTE differs between the groups and not everyone had an event by the end of the study, then the number of events cannot be equal, at any time after the study started. HR>RR because the effect of time adds up to that of responders.

Conclusion: RR should only be preferred to HR, when every patient had an event and no censoring occurred: an uncommon situation in clinical trials. In all other cases, we recommend relying on TTE-analysis. Different observation times between the groups (shorter survival, earlier discontinuation) and uneven censoring rates require TTE-analysis. Ignoring censoring would lead to artificial significance. Beside if a delay might exist between event and diagnostic, the offset is expected to be randomly distributed in both groups and to cancel out. If observation times do not differ between the groups, both estimates deliver equivalent results.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.