Recurrent events
What question does this help answer?
Whether an exposure or treatment changes how often events happen over follow-up, not only how soon the first one arrives.
Why not time to the first event
Analysing only the first event discards every later one. A treatment that mainly prevents second and third admissions is almost invisible to it, and the study pays for follow-up it then ignores. Analyses of repeat heart-failure hospitalizations have shown larger and more precise treatment effects than the time-to-first-event analysis of the same trial.
The main approaches
- Andersen-Gill: a Cox model in which each patient contributes one interval per event. It estimates one hazard ratio shared across events and needs a robust (sandwich) variance clustered on the patient, because events within a patient are not independent.
- Marginal rate models (Lin, Wei, Yang and Ying): the Andersen-Gill form fitted with a robust variance and read, under a proportional-rates assumption, as a ratio of mean event rates over time, pictured as the mean cumulative number of events per patient. A Poisson or negative binomial rate ratio comes from a different model; report which measure was estimated rather than treating them as interchangeable.
- Prentice-Williams-Peterson: stratifies by event number, so the second event is compared only among patients who had a first. Later strata are small and selected.
- Negative binomial regression on each patient's event count, with follow-up time as an offset: a rate ratio that allows patients to differ in their underlying rate, at the cost of ignoring when events happened.
- Frailty models: a patient-level random effect that represents how event-prone each patient is.
Death and other terminal events
A patient who dies can have no further admissions. If death is simply censored, a treatment that increases mortality can appear to reduce admissions. Report death alongside the recurrent outcome, analyse a composite of recurrent events and death, or model the two jointly, and say which.
Sizing
No form in Mallard's sizing catalog fits. A recurrent-event study is sized from the expected event rate, the follow-up time and how much patients vary in their rate; the Poisson forms ignore that variation and give too small a study.
Why Mallard may recommend it
Mallard may name a recurrent-event analysis when the outcome can happen more than once and patients are followed over time, and it will question a plan that analyses only the first event without saying why.
What to watch out for
Treating each event as a fresh, independent observation gives standard errors that are too small: one patient's events are correlated, so an Andersen-Gill model needs a robust variance clustered on the patient, or a frailty term. And death stops further events. A treatment that shortens survival can look as if it prevents admissions, so the terminal event is analysed alongside the recurrent one, never quietly censored.
Clinical example
Question: Does a transitional-care programme reduce heart-failure readmissions over a year? Analysis: All readmissions per patient, as a negative binomial rate ratio with follow-up time as the offset or an Andersen-Gill model with patient-clustered standard errors, with cardiovascular death reported alongside rather than censored.
- Modelling recurrent events: a tutorial for analysis in epidemiology (opens in a new tab) · Int J Epidemiol · doi 10.1093/ije/dyu222
- Analysing recurrent hospitalizations in heart failure: a review of statistical methodology, with application to CHARM-Preserved (opens in a new tab) · Eur J Heart Fail · doi 10.1002/ejhf.29