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Joined 2026-09-21 Message
Incoming links: Within-patient recurrent-event dependence
Past exam of the mathematics course of the University of Cambridge 2013 iii Paper 32 6 Solution 2026-10-07
The episodes from one patient share treatment, biological susceptibility and prior history, so they are not independent observations. Treating every row as an unrelated subject can substantially understate uncertainty. Two approaches address this within-patient recurrent-event dependence:
- A patient-clustered sandwich covariance matrix retains a suitable working Cox mean/intensity model but groups score contributions by patient. If is the patient's score contribution and the observed information, its form is . Independent patients, rather than independent rows, determine the sampling units. This corrects uncertainty for within-patient dependence when the working estimating equation is appropriate; it does not repair an incorrect mean model.
- A shared frailty model introduces a common latent positive multiplier for all of patient 's episode hazards, often with a specified gamma or lognormal distribution. Given frailty and the relevant history, the event mechanism is modeled through that patient's intensity. Estimate treatment and frailty parameters by integrating or profiling the latent effect. This models persistent heterogeneity directly, but relies on the frailty assumptions and generally gives a conditional treatment-effect interpretation.
Start-stop recurrent-event data layout 2026-10-07
Represent each person's successive eligible episodes by separate left-open, right-closed intervals, retaining a common patient identifier and event-order information. A recurrence ends an interval and can be followed by another one; administrative censoring ends the final interval without an event. The row's entry time determines risk set membership. Multiple rows remain one patient history, with possible within-patient recurrent-event dependence.