## Sunday, September 19, 2010

### Number of Events vs. Number of Subjects with Events

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.

Redman said...

How would you suggest to deal with an AE which changes in severity?

For example, a headache which went from Mild to Moderate and then to Severe, would usually be recorded as 3 separate records in the database. When we summarize the number of events per treatment, will there be 3 events or 1 event?

For number of subjects, it would be clear that this subject will contribute a count of 1 to the frequency table.

thanks!

Web blog from Dr. Deng said...

There is no regulatory guidance to suggest whether or not an AE with severity change should be reported as different AEs. There is a Q&A at Firstclinical.com (https://firstclinical.com/fda-gcp/?show=2010/FW%20AE%20reporting%20question%20-%20changes%20in%20severity) that seems to suggest that an AE with severity change should still be reported/recorded as the same AE (with maximum severity). However, I don't think there is any consensus.

One thing is for sure that if a medical history or a baseline condition has severity change, it should be recorded as a new AE.

Whether or not an AE with severity change is considered as a single AE or multiple AEs does not have impact on the calculation of the incidence of AEs since the summary is on subject level and the same AE reported multiple times will only be counted once.

It will have impact on any analyses that is based on the # of AEs, for example, AE density, AE adjusted for duration of exposure,...

Redman said...

Thanks for your explanation. This issue has come up a few times for me now, but I can see most companies would go with the simpler method of summarizing this example as 3 AEs. However, this could severely inflate the # of AEs, especially when an AE is decreasing in severity. If we have an AE which improved from Severe to Moderate and again to Mild, it's hard to justify this improvement as 3 AEs (i.e. 2 more events than if this AE did not improved at all).

In all, I feel that summary at the subject level is probably the most logical and clinically meaningful way to summarize these AEs.

Also, if we attempt to count this example as 1 AE, the programming work will need to focus on the start and end time of each AELLT, and this would be incredibly programming intensive.