State Space Models in Medical Time Series

This thesis concerns the set-up and application of a state space model to medical time series. Considering medical count time series (such as number of asthma patients or a number of sudden infant death syndrome recorded over time), we discuss and propose non-linear and non-Gaussian state space models, in particular dynamic generalized linear models (DGLMs). Sequential Monte Carlo methods, also known as particle filters are employed for tracking a posterior state distribution. We assess the proposed methodology by way of an extensive simulation experiment. In the first simulation study, we found that the results from the Liu and West particle filter algorithm have shown better performance over the Storvik particle filter algorithm in terms of precision of the estimation of hyper-parameters and accuracy of forecasting. Beside, the obtained results from the Liu and West particle filter algorithm are quite similar from the ones that were obtained by the MCMC. In addition, in the second simulation study, we found the Liu and West particle filter algorithm with the Poisson model still does better than the other proposed models, even if it is incorrectly specified. The Smith (1985) method for model diagnostics is used. The results obtained from simulation studies showed that this methodology was successful. Finally, we developed a Bayesian monitoring model for evaluating the performance of the fitted model in a sequential way by using the Bayes factors and nonparametric binomial control chart with proposed runs rules. The novelty of this approach is to exploit the results obtained from the PSR or INTPSR for the model diagnostics to calculate the values of the Bayes factors. We found that the proposed control procedure provided an effective way of detecting out-of-control signals of the process.