Signature
P = n / N
| Inputs | Definition | Unit |
|---|---|---|
n | Number of patients with one or more episodes of the event during follow-up, each patient counted once whatever the number of episodes | count of patients |
N | Number of patients at risk at the start of follow-up in the arm concerned, greater than zero | count of patients |
P | Proportion of patients with at least one episode of the adverse event, of the stated type and grade, during the follow-up period | probability from 0 to 1, over the stated period |
|---|
Function
Adverse event rate to model input function
Maps the adverse event counts in a trial safety table, with their denominators of patients or person-time, to the probability of an event in one model cycle, and maps those probabilities to the expected adverse event cost and QALY loss per patient. The general rate and probability conversions are on the Transition Probability page (HE-FN-TP-001); the records here apply them to adverse event data and add the cost and QALY weighting.
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Implementations
Excel
Adverse event proportion in one cell
Excel divides the named cell holding the number of patients with an event by the named cell holding the number at risk.
=PatientsWithEvent/PatientsAtRisk
Assumptions
Equal follow-up for every patient in the arm
All N patients are followed for the whole period. When arms are treated or followed for different lengths of time, for example because one drug is stopped early for toxicity or progression, the proportion understates the event frequency per unit of treatment time in the arm with less time at risk, and the person-time rate HE-FM-AER-002 is used instead.
Same adverse event definition in every arm
The event term, the severity cut-off (for example CTCAE grade 3 or higher) and the attribution rule are the same in every arm compared. All-cause counts in both arms keep the comparison randomised; counts judged related to the drug depend on investigator attribution.
Worked examples
Grade 3 or higher diarrhoea on the new drug over 24 weeks
In the article's illustrative trial, 36 of 200 patients on the new drug have grade 3 or higher diarrhoea within 24 weeks, a proportion of 0.18. The figure describes the whole 24 weeks, not each four-week cycle.
n = 36; N = 200; P = 0.18
Grade 3 or higher diarrhoea on the comparator over 24 weeks
In the same illustrative trial, 16 of 200 patients on the comparator have the event within 24 weeks, a proportion of 0.08.
n = 16; N = 200; P = 0.08
Common errors
Comparing crude adverse event proportions across unequal exposure
Illustrative figures: in two arms, 20 of 100 patients each have an event, a proportion of 0.20 in both. If the new drug arm accumulated 1,000 patient-weeks at risk because many patients stopped early, and the comparator 2,000, the rates are 0.02 and 0.01 per patient-week. Equal proportions hide a doubled event frequency per unit of treatment time.
Sources
Probability and rate definitions applied to adverse event counts
Gidwani R, Russell LB. Estimating transition probabilities from published evidence: a tutorial for decision modelers. PharmacoEconomics. 2020;38(11):1153-1164. Section on converting to the cycle length, which defines a probability as the number of events in a period divided by the number of people followed for that period, and a rate as events divided by total time at risk.
Canonical Identity
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