Often in clinical trial safety data analysis, people are confused with the basic concept of "number of events" vs "number of subjects with events". Obviously, the number of events counts the events (event level) while number of subjects counts the subjects (subject level).
Using adverse event (AE) summary as an example,the difference between “the number of AEs” and “the number of subjects with AEs” sometimes may not be very obvious for some people. For the number of AEs, since the same subject can have more than one adverse events, we can not really calculate the percentage since the numerator and denominator could be any number. It is a mistake if you divide the number of events with the number of subjects under a treatment arm. You could have an unreasonably large percentage (sometimes larger than 100%).
For the number of subjects with AEs, we always count by subject. If a subject has more than one AEs, it will be counted one once. Therefore, the numerator (the number of subjects with AEs) is always smaller than the denominator (number of subjects exposed). We can calculate the percentage and the percentage should always be less than 100%. We can this percentage as 'incidence of AEs'. The following table (extracted from a document in FDA's website) is an example of AE presentation (counted by subjects).
The statistical summary tables for adverse events are often constructed to present the both total # of AEs and # of subjects with AEs (or precisely the number of subjects with at least one AEs). However, in the table, there will be no percentage calculated for total # of AEs. If the readers are not clear about the concept of "# of AEs" vs "# of subjects with AEs), they could question the correctness of the summary table. Very often, they might count the # of subjects with AEs and compare with the # of AEs and find discrepancies (sure there will be discrepancies). The reason? some subjects must have more than one AEs.
In some situations, we can indeed calculate the rate, proportion for # of Events (number of adverse events). For example, for total number of AEs, we could calculate how many of these events are mild, moderate, severe. You could see this information presented in package insert for some approved drugs on the market. We could also calculate the incidence rate of AEs by using the total number of AEs as numerator and total number of infusions, total number of dose distributed, or total number of person years as denominator. In these situations, we should always understand what the numerator is and what the denominator is. For a good presentation of the statistical summary table, the numerator and denominator used for calculation should be specified in the footnote. A few years ago, I saw a commercial presentation comparing a company's product safety with other competitive products. When they calculate the AE frequency for their product, they use (total number of AEs) / (the total number of doses). When they calculate the AE frequency for other competitive products, they use (total number of AEs) / (total number of subjects). Since each subject receives more than one doses, their calculation of the AE frequency for their product is markedly lower. However, this trick is wrong and unethical.