Recurrent events are often analyzed in social sciences and medical studies, for example recurring infections, depressions or cancer recurrences.
Which factors are associated with a higher or lower risk of recurrence?
records the cumulative number of events generated by the process; specifically,
The intensity function describes the instantaneous probability of an event occurring at time
When a heterogeneous group of individuals or processes is considered, the assumption of a common event intensity is no longer plausible.
Greater generality can be achieved by incorporating fixed or time-varying covariates in the intensity function.
As a counterpart of the Kaplan–Meier curve, which is used to describe the time to a terminal event, recurrent event data can be described using the mean cumulative function, which is the average number of cumulative events experienced by an individual in the study at each point in time since the start of follow-up.
The logarithm of the expected number of recurrences is modeled by a linear combination of explanatory variables.
The marginal means/rates model considers all recurrent events of the same subject as a single counting process and does not require time-varying covariates to reflect the past history of the process, which makes it a more flexible model.
[2] Instead, the full history of the counting process may influence the mean function of recurrent events.
In multi-state models, the recurrent event processes of individuals are described by different states.
[2] Extensions of the Cox proportional hazard models are popular models in social sciences and medical science to assess associations between variables and risk of recurrence, or to predict recurrent event outcomes.
Many extensions of survival models based on the Cox proportional hazards approach have been proposed to handle recurrent event data.
If the correlated nature of the data is ignored, the confidence intervals (CI) for the estimated rates could be artificially narrow, which may result in false positive results.
Robust variance estimators are based on a jackknife estimate, which anticipates correlation within subjects and provides robust standard errors.
In frailty models, a random effect is included in the recurrent event model which describes the individual excess risk that can not be explained by the included covariates.
The frailty term induces dependence among the recurrence times within subjects.