Recurrent event models: an application to offenders found not criminally responsible on account of mental disorder and their interactions with the health care and criminal justice systems

Prior to committing an offence for which they are ultimately found not criminally responsible (NCR), offenders may have contact with the health care and criminal justice systems. Understanding the frequency of these contacts can potentially help to prevent such offences by informing strategies for intervention. In particular, escalation in contact frequency could foreshadow the committing of an index offence. Inspired by real data, in this project, we investigate models that describe such escalation. In particular, we consider two classes of models: time-to-event models that are framed in terms of numbers of contacts in an interval, and time-between-events models that are framed in terms of times between two successive contacts. Both classes of models can incorporate predictor variables and between-subject heterogeneity (via random effects). The properties of the maximum likelihood estimators of the escalation rate and the performance of the Kolmogorov-Smirnov test of goodness-of-fit are assessed using simulations under various scenarios.