Scottish and Northumbrian statisticians' meeting: 20 May 2005, University of Newcastle upon Tyne

We consider two topics in which data accrues over time and the aim is to use individual-specific history in modelling the present and predicting or affecting the future.

The first topic is the analysis of recurrent event data. The complete history of events to time t needs properly to be taken into account when modelling the intensity if the martingale properties needed for inference are to hold. Aalen, Borgan and colleagues have shown recently how dynamic covariates can be used to allow for time-varying heterogeneity between individuals. We build on these ideas for data complicated by both intermittent missing periods and terminal dropout. An application to diarrhoea prevalence and incidence is given.

Dynamic methods can also be used to provide adaptive treatment allocation for patients with chronic conditions, under which treatment choice reacts to individual patients' developing longitudinal profiles. As the second topic, we describe, extend and apply Murphy's regret-based method for optimal dynamic treatment modelling for observational data. Regret parameterisation and estimation methods are discussed, and an application in anti-coagulation is described.