Recurrent Events Analysis

An extension of the Cox proportional hazards model that treats recurrent events as independent within a subject, using a robust sandwich variance estimator to correct for the correlation. The model assumes that the baseline hazard is common across all events and that the subject remains at risk for subsequent events immediately after a prior event. This is the most commonly applied model for recurrent events due to its simplicity and efficiency, but it relies on the assumption that events are unordered and exchangeable.

A stratified Cox model that analyzes ordered events by stratifying on the event rank. Two variations exist:

• PWP Total Time (PWP-TT): The time scale resets to zero after each event, measuring time from study entry.
• PWP Gap Time (PWP-GT): The clock resets after each event, measuring the time since the last occurrence. This model assumes that a subject cannot be at risk for the k-th event until the (k-1)-th event has occurred, making it ideal for ordered, sequential processes like tumor recurrences.

A marginal model that simultaneously models the time to each ordered event from the study origin, treating each event type as a separate stratum. Unlike the PWP model, a subject is considered at risk for all events from the start of observation, regardless of whether prior events have occurred. This approach is useful when the scientific interest lies in the population-averaged effect of covariates on each specific event, rather than conditioning on the event history.

A non-parametric estimator that plots the population-averaged cumulative number of events over time, analogous to the Nelson-Aalen estimator for recurrent events. The MCF does not require proportional hazards assumptions and provides a direct, interpretable visualization of the event burden in a treatment group. It handles varying follow-up times and is robust to the underlying correlation structure, making it a standard first-line descriptive tool before fitting regression models.

Extends the Andersen-Gill framework by incorporating a subject-specific random effect (frailty) to explicitly model the unobserved heterogeneity that induces within-subject correlation. Common distributions for the frailty term include Gamma and log-normal. This approach allows the estimation of the degree of dependence between events and can distinguish between a subject's underlying susceptibility and the effect of covariates. It is particularly useful when event occurrences are strongly clustered within individuals.

A critical distinction in recurrent event analysis:

• Conditional Models (PWP-GT): Condition on the subject's event history. The risk set for event k only includes subjects who have experienced event k-1. This answers: 'What is the effect of treatment on the time between recurrences?'
• Marginal Models (WLW): Do not condition on prior events. All subjects are in the risk set for all events from time zero. This answers: 'What is the treatment effect on the time to the k-th event in the population?' The choice depends on whether the scientific question targets a within-subject trajectory or a population-level comparison.