  Safety analyses in terms of adverse events (AEs) are an important aspect of
benefit-risk assessments of therapies. Compared to efficacy analyses AE
analyses are often rather simplistic. The probability of an AE of a specific
type is typically estimated by the incidence proportion, sometimes the
incidence density or the Kaplan-Meier estimator are proposed. But these
analyses either do not account for censoring, rely on a too restrictive
parametric model, or ignore competing events. With the non-parametric
Aalen-Johansen estimator as the gold-standard, these potential sources of bias
are investigated in a data example from oncology and in simulations, both in
the one-sample and in the two-sample case. As the estimators may have large
variances at the end of follow-up, the estimators are not only compared at the
maximal event time but also at two quantiles of the observed times. To date,
consequences for safety comparisons have hardly been investigated in the
literature. The impact of using different estimators for group comparisons is
unclear, as, for example, the ratio of two both underestimating or
overestimating estimators may or may not be comparable to the ratio of the
gold-standard estimator. Therefore, the ratio of the AE probabilities is also
calculated based on different approaches. By simulations investigating constant
and non-constant hazards, different censoring mechanisms and event frequencies,
we show that ignoring competing events is more of a problem than falsely
assuming constant hazards by use of the incidence density and that the choice
of the AE probability estimator is crucial for group comparisons.
