gms | German Medical Science

Background: Time to event (TTE) analyses are recommended for the safety analysis because AEs can occur at any time and follow-up duration often differs between treatment groups. Additionally, competing risks precluding their occurrence should be considered when performing and reporting analyses [1], [2]. Different statistical approaches coexist and finding the right one for the right purpose is not always straightforward. This study intends to help defining the appropriate approach when estimating treatment effects in the context of the benefit assessment of new medications. The interpretation of the results involves the concept of estimands, which reflects what exactly is estimated given the population, endpoint, post-randomisation events and statistical approach.

Methods: A simulation study with 600 patients equally allocated to two treatment arms was conducted. Median survival was set to 10 months in control and 20 months in verum (HR=0.5). Patients still at risk were administratively censored after 30 months. Median time to first AE was allowed to vary between 1 and 20 months in both arms independently. All possible safety scenarios were hence covered: from superiority to inferiority of verum, as well as small to large effects. Simulated trials were analysed for safety in a competing risk setting where death was defined as the competing event. Both estimates were computed: cause specific hazard ratio (HR) with a Cox model and subdistribution-based HR (sHR) with the Fine&Gray model [3].

Results: The differences between both settings mostly depend on the time of occurrence of both events. HR remains very close to the simulated hazard. When median TTE is much lower for the event of interest, the competing event has no crucial effect and both settings deliver equivalent estimates. However, when median TTE is of the same order of magnitude for both events or when the competing event occurs earlier, sHR>HR because patients remain in the risk set after the occurrence of the competing event, even if the event of interest is precluded. When HR<1, sHR can either show a reduced superiority, equality or even inferiority, depending on the time to first competing event.

Conclusion: The question of the benefit assessment is better answered with HR that points the treatment with the lowest instantaneous risk. sHR assesses the probability of an event over the entire follow-up time by combining the hazards of both events within a single cumulative incidence function. It is a less relevant approach in the context of the benefit assessment since the treatment effect on survival and safety cannot be differentiated. It is especially inappropriate when the events considered are not of the same order of severity: even if prolongated survival exposes to higher probability of AEs, longer living might still be desirable. Decision making in the context of benefit assessment should result from considering individual hazards for all relevant dimensions and conclude about acceptable trade-offs. “While on treatment/alive” estimands assessed with HR unbiasedly describe the profile of a medication. sHRs are more appropriate for pharmaeconomic questions.

The authors declare that they have no competing interests.

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