Nonparametric estimation for cumulative duration of adverse events

Analysis of adverse events (AE) for drug safety assessment presents challenges to statisticians in observational studies as well as in clinical trials since AEs are typically recurrent with varying duration and severity. Routine analyses often concentrate on the number of patients who had at least one occurrence of a specific AE or a group of AEs, or the time to occurrence of the first event. We argue that other information in AE data particularly cumulative duration of events is also important, particularly for benefit-risk assessment. We propose a nonparametric method to estimate the mean cumulative duration (MCD) based on the nonparametric cumulative mean function estimate, together with a robust estimate for the variance of the estimate, as in Lawless and Nadeau (1995). This approach can be easily used to analyze multiple, overlapped and severity weighted AE durations. This method can also be used for estimating the difference between two MCDs. Estimation in the presence of censoring due to informative dropouts and/or a terminal event is also considered. The method can be implemented in standard softwares such as SAS. We illustrate the use of the method with a numerical example. Small sample properties of this approach are examined via simulation.