Updating Markov models to integrate cross-sectional and longitudinal studies.

Clinical trials are typically conducted over a population within a defined time period in order to illuminate certain characteristics of a health issue or disease process. Cross-sectional studies provide a snapshot of these disease processes over a large number of people but do not allow us to model the temporal nature of disease, which is essential for modelling detailed prognostic predictions. Longitudinal studies, on the other hand, are used to explore how these processes develop over time in a number of people but can be expensive and time-consuming, and many studies only cover a relatively small window within the disease process. This paper explores the application of intelligent data analysis techniques for building reliable models of disease progression from both cross-sectional and longitudinal studies. The aim is to learn disease 'trajectories' from cross-sectional data by building realistic trajectories from healthy patients to those with advanced disease. We focus on exploring whether we can 'calibrate' models learnt from these trajectories with real longitudinal data using Baum-Welch re-estimation so that the dynamic parameters reflect the true underlying processes more closely. We use Kullback-Leibler distance and Wilcoxon rank metrics to assess how calibration improves the models to better reflect the underlying dynamics.