FDA Adverse Event Reporting System (FAERS) analysis
The FAERS application of the nferX platform supports viewing adverse event profiles of all marketed products through multiple lenses - Count, Proportional Reporting Ratio (PRR), and an nferX Adverse Event (AE) Score. AEScore=ln(count)∗1/(1+e−(prr−1.5)). Count is the raw number of reports between a drug and an adverse event. The proportional reporting ratio (PRR) is a simple way to get a measure of how common an adverse event for a particular drug is compared to how common the event is in the overall database. A PRR >1 for a drug-event combination indicates that a greater proportion of the reports for the drug are for the event than the proportion of events in the rest of the database, while a PRR of 2 for a drug event combination indicates that the proportion of reports for the drug-event combination is twice the proportion of the event in the overall database. The PRR is computed as follows:PRR=(m/n)/((M−m)/(N−n))
m = number of reports with drug and event
n = number of reports with drug
M = number of reports with event in database
N = number of reports in database
Count of an event with a query drug is a good first measure of association. But it has the problem that generally common events will often show up at the top, where we are often more interested in events that are differentially associated with the query drug over other drugs. An issue with PRR is that it is noisy when the total number of event reports is small. If there are three reports of some oddly specific event and one occurs with the query drug, that event will likely have a very high PRR, but it may not be the event we would be most interested in for a drug (in FAERS such rare events are often not even proper adverse events) - we want events that occur often, and also are differentially associated with a drug - a balance between count and PRR.
The AE score tries to strike this balance in an all-in-one measure. It up-weights events that occur often for the query drug (this is the ln(count) term), and that are differentially associated with the query drug (this is the sigmoid term).
The sigmoid(PRR-1.5) term ranges smoothly from 0 to 1. It's equal to 0.5 at PRR = 1.5. When PRR = 6, sigmoid(PRR-1.5)=0.99; so PRR values >= 6 are all treated roughly equivalently by the AE score. Thus, extremely high PRRs due to small counts will not swing the AE score much beyond PRR = 6, and the ln(count) term will down-weight those small-count cases, so that they do not show up at the top of the AE score list.
A nice property of AE score is that, for a given query drug, the AE scores of the events with that drug turn out to roughly follow an exponential distribution, particularly at the tails. We can then fit exponential distributions to the scores, and analyze them. A benefit of the exponential fit is that we can make more robust claims about how significant a certain score is for a query drug, even if the empirical data is sparse/noisy at the tails for a particular drug.