Correcting for selection using frailty models

Chronic diseases are roughly speaking lifelong transitions between the states: relapse and recovery. The long-term pattern of recurrent times-to-relapse can be investigated with routine register data on hospital admissions. The relapses become readmissions to hospital, and the time spent in hospital are gaps between subsequent times-at-risk. However, problems of selection and dependent censoring arise because the calendar period of observation is limited and the study population likely to be heterogeneous. We will theoretically verify that an assumption of conditional independence of all times-at-risk and gaps, given the latent individual frailty level, allows for consistent inference in the shared frailty model. Using simulation studies, we also investigate cases where gaps (and/or staggered entry) are informative for the individual frailty. We found that the use of the shared frailty model can be extended to situations, where gaps are dependent on the frailty, but short compared to the distribution of the times-to-relapse. Our motivating example deals with the course of schizophrenia. We analysed routine register data on readmissions in almost 9000 persons with the disorder. Marginal survival curves of time-to-first-readmission, time-to-second-readmission, etc. were estimated in the shared frailty model. Based on the schizophrenia literature, the conclusion of our analysis was rather surprising: one of a stable course of disorder.