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Background The SAVVY project aims to improve the analyses of adverse events (AEs), whether prespecified or emerging, in clinical trials through the use of survival techniques appropriately dealing with varying follow-up times and competing events (CEs). Although statistical methodologies have advanced, in AE analyses, often the incidence proportion, the incidence density, or a non-parametric Kaplan-Meier estimator are used, which ignore either censoring or CEs. In an empirical study including randomized clinical trials from several sponsor organizations, these potential sources of bias are investigated. The main purpose is to compare the estimators that are typically used to quantify AE risk within trial arms to the non-parametric Aalen-Johansen estimator as the gold-standard for estimating cumulative AE probabilities. A follow-up paper will consider consequences when comparing safety between treatment groups. Methods Estimators are compared with descriptive statistics, graphical displays, and a more formal assessment using a random effects meta-analysis. The influence of different factors on the size of deviations from the gold-standard is investigated in a meta-regression. Comparisons are conducted at the maximum follow-up time and at earlier evaluation times. CEs definition does not only include death before AE but also end of follow-up for AEs due to events related to the disease course or safety of the treatment. Results Ten sponsor organizations provided 17 clinical trials including 186 types of investigated AEs. The one minus Kaplan-Meier estimator was on average about 1.2-fold larger than the Aalen-Johansen estimator and the probability transform of the incidence density ignoring CEs was even 2-fold larger. The average bias using the incidence proportion was less than 5%. Assuming constant hazards using incidence densities was hardly an issue provided that CEs were accounted for. The meta-regression showed that the bias depended mainly on the amount of censoring and on the amount of CEs. Conclusions The choice of the estimator of the cumulative AE probability and the definition of CEs are crucial. We recommend using the Aalen-Johansen estimator with an appropriate definition of CEs whenever the risk for AEs is to be quantified and to change the guidelines accordingly.