Modelling and monitoring of medical time series
In this thesis we examine several extensions to the dynamic linear model framework, outlined by Harrison and Stevens (1976), in order to adapt these models for use in the on-line analysis of medical time series that arise from routine clinical settings. The situation with which we are most concerned is that where we are monitoring individual patients and wish to detect abrupt changes in the patient's condition as soon as possible. A detailed background to the study and application of dynamic linear models is given, and other techniques for time series monitoring are also discussed when appropriate. We present a selection of specific models that we feel may prove to be of practical use in the modelling and monitoring of medical time series, and we illustrate how these models may be utilized in order to distinguish between a variety of alternative changepoint-types. The sensitivity of these models to the specification of prior information is examined in detail. The medical background to the time series examined requires the development of models and techniques enabling us to analyze generally unequally-spaced time series. We test the performance of the resulting models and techniques using simulated data. We then attempt to build a framework for bivariate time series modelling, allowing, once more, for the possibility of unequally spaced data. In particular, we suggest mechanisms whereby causality and feedback may be introduced into such models. Finally, we report on several applications of this methodology to actual medical time series arising in various contexts including kidney and bone-marrow transplantation and foetal heart monitoring.