Interval-censored survival data with informative examination times: parametric models and approximate inference

We develop parametric methods for analysing interval-censored data when examination and survival times are not independent. The hazard function is modelled by introducing individual frailties related to the frequency of examinations. Model parameters may be obtained by direct maximization of the marginal log-likelihood. We develop a simpler approximate method in which the frailties are estimated by empirical Bayes. The two approaches are equivalent asymptotically as the number of examinations on each individual increases. Simulations suggest that the approximate method is adequate for estimating regression parameters even when the number of examinations on each individual is small. The methods are used to estimate age and period effects on HIV incidence in a cohort of repeat attenders at genito-urinary clinics in London, U.K.