Estimating the new event-free survival

BackgroundIn acute myeloid leukemia studies, event-free survival (EFS) is defined as time until treatment failure, relapse, or death, whichever occurs first. Since 2020 and 2022, respectively, the US Food and Drug Administration and the European LeukemiaNet recommend analysing treatment failures as day-1 events. This data modification can lead to a potentially large drop in the estimated EFS at day 1. If censoring occurs, the Kaplan-Meier estimator obtained from the recoded data underestimates this drop. Our aim is to obtain an unbiased estimate for EFS as basis for further inference. MethodsWe define "event on day 1" as one event type and " event after day 1" as a competing event in the original data and use the Aalen-Johansen estimator of the cumulative incidence curve to estimate event-specific transition probabilities, which are combined in one EFS estimate. To analyse effects on day 1 treatment failure and other post-day-1 EFS events separately, a formal link to cure models is established by equating treatment failures with the "cured" proportion in cure model terminology. Additionally, a variance estimator, confidence intervals, confidence bands, and simultaneous testing procedures are derived. ResultsOur new estimation method differs from the Kaplan-Meier estimator in settings in which some treatment failures are censored, as in the interim analysis of the AMLSG 09-09 study. If almost no treatment failures are censored, the two estimation methods do not differ. The cure model and simultaneous testing are able to estimate effects on day 1 treatment failure and other post-day-1 EFS events separately and function independently of whether data is modified. ConclusionsThe Kaplan-Meier estimator evaluated on the recoded data underestimates the drop at day 1 if treatment failures are censored. With sufficient follow-up, this bias disappears, and results coincide with our novel approach.