Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 32 / 6 / a / Solution

Use one row per consecutive at-risk episode, retaining a patient identifier for dependence and an episode number for event order. In calendar time, the intervals are $(\text{start},\text{stop}]$; status is one if the row ends in a headache and zero if it ends in censoring. Patient 001 contributes

The fifth episode is censored, not a fifth observed headache. All rows retain $z=0$. This start-stop recurrent-event data layout corresponds to the counting-process intensity in survival analysiswhere $Y_i(t)$ indicates that the patient is currently observed and eligible for a headache. Fit the regression coefficient by Cox partial likelihood using the resulting risk sets, and estimate the baseline cumulative hazard nonparametrically, for example by the Breslow estimator. Patient rows are portions of one history, not new independent patients.