Background: Competing risk analyses aim to correctly estimate the time to the occurrence of an event of interest (EI) in the presence of a competing event (CE) - i.e., an event that may prevent from observing the EI. Competing risk analyses have been extensively described in the literature and are often present in epidemiological studies. Still, in 2016, Walraven et al estimated that half of Kaplan–Meier (KM) risk estimates published in prominent medical journals were prone to competing risk bias.
Objectives: To assess the bias amplitude depending on the percentage of EI and of CE.
Methods: The times of occurrence were simulated for 5,000 patients using three parametric distributions (exponential, Weibull, gamma) for CE, exponential distribution for EI and uniform law for the censoring time. The times to events ranged from 0 to 365 days. Several scenarios were studied with a percentage of CE varying between 1% and 80%. The cumulative incidence function (CIF) was estimated using the Aalen-Johansen (AJ) model and the biased estimate of 1-KM. The bias of 1-KM was estimated at days 100, 200 and 300 in all scenarios. The restricted mean survival time at day 300 was estimated for AJ and 1-KM models. The mean and the standard deviation (SD) of the bias were calculated after 100 simulations for each distribution.
Results: For the Weibull distribution, the bias of 1-KM at day 300 was estimated at 0.06 (± 0.004 SD), 0.10 (± 0.005 SD) and 0.20 (± 0.007 SD) for 7%, 11% and 23% of CE and 54%, 52% and 46% of EI, respectively. The difference of the restricted mean survival time at day 300 was estimated at 3.8 (± 1.0 days SD), 9.1 (± 1.0 days SD), 26.0 (± 1.2 days SD) for 7%, 11% and 23% of CE and 54%, 52% and 46% of EI, respectively. Similar biases were observed for other distributions. For the exponential distribution, the bias of 1-KM at day 300 was estimated at 0.11 (± 0.005 SD) for 51% of EI and 13% of CE. The difference of the restricted mean survival time at day 300 was estimated at 13.8 (± 1.4 days SD) for 51% of EI and 13% of CE.
Conclusions: With frequent EI (50%) and smaller proportion of CE observed, a non-negligible bias is measured. The expected bias depends on a large variety of factors not all covered in this analysis. However, this illustration highlights the importance of considering competing risk analyses when a competing event is present. Especially when there is more than 10% of CE, which causes an error of more than 0.1 in the predicted cumulative incidence value with 1-KM estimator.
