Signature
r = d / PT
| Inputs | Definition | Unit |
|---|---|---|
d | Number of adverse events counted: every episode when each episode is costed, or first episodes only when patients leave the at-risk pool after an event | count of events |
PT | Time at risk summed over all patients in the arm, greater than zero | person-time, for example patient-weeks |
r | Number of adverse events per unit of person-time at risk | events per patient-week or per patient-year |
|---|
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 rate per person-time in one cell
Excel divides the named cell holding the event count by the named cell holding the person-time at risk.
=EventCount/PersonTime
Assumptions
Constant adverse event rate over follow-up
The rate is an average over the follow-up period. If events concentrate in the first weeks of treatment, a single rate understates the early risk and overstates the later risk.
Event count and person-time defined together
For first events, each patient's time at risk stops at the first episode; for all episodes, it runs to the end of follow-up or treatment. Dividing all episodes by time to first event, or first events by total time, misstates the rate.
Worked examples
Adverse event rate on a drug stopped early
Illustrative figures: 20 first episodes during 1,000 patient-weeks at risk give a rate of 0.02 per patient-week.
d = 20; PT = 1000; r = 0.02
Adverse event rate on a comparator with longer exposure
Illustrative figures: the same 20 first episodes during 2,000 patient-weeks at risk give 0.01 per patient-week, half the rate of the arm stopped early although the proportions with an event are equal.
d = 20; PT = 2000; r = 0.01
Common errors
Treating adverse events per patient as a proportion
Illustrative figures: if 36 of 200 patients have 60 episodes between them, 60 divided by 200 gives 0.30 episodes per patient over the period, not the proportion with an event, which is 0.18. Entering 0.30 into a conversion that expects a proportion overstates the probability of a first episode.
Sources
Rate as events over time at risk for adverse event data
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 rate as the number of events divided by the total time at risk.
Canonical Identity
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