Bayesian mixtures for modelling complex medical data : a case study in Parkinson’s disease

Mixture models are a flexible tool for unsupervised clustering that have found popularity in a vast array of research areas. In studies of medicine, the use of mixtures holds the potential to greatly enhance our understanding of patient responses through the identification of clinically meaningful clusters that, given the complexity of many data sources, may otherwise by intangible. Furthermore, when developed in the Bayesian framework, mixture models provide a natural means for capturing and propagating uncertainty in different aspects of a clustering solution, arguably resulting in richer analyses of the population under study. This thesis aims to investigate the use of Bayesian mixture models in analysing varied and detailed sources of patient information collected in the study of complex disease. The first aim of this thesis is to showcase the flexibility of mixture models in modelling markedly different types of data. In particular, we examine three common variants on the mixture model, namely, finite mixtures, Dirichlet Process mixtures and hidden Markov models. Beyond the development and application of these models to different sources of data, this thesis also focuses on modelling different aspects relating to uncertainty in clustering. Examples of clustering uncertainty considered are uncertainty in a patient’s true cluster membership and accounting for uncertainty in the true number of clusters present. Finally, this thesis aims to address and propose solutions to the task of comparing clustering solutions, whether this be comparing patients or observations assigned to different subgroups or comparing clustering solutions over multiple datasets. To address these aims, we consider a case study in Parkinson’s disease (PD), a complex and commonly diagnosed neurodegenerative disorder. In particular, two commonly collected sources of patient information are considered. The first source of data are on symptoms associated with PD, recorded using the Unified Parkinson’s Disease Rating Scale (UPDRS) and constitutes the first half of this thesis. The second half of this thesis is dedicated to the analysis of microelectrode recordings collected during Deep Brain Stimulation (DBS), a popular palliative treatment for advanced PD. Analysis of this second source of data centers on the problems of unsupervised detection and sorting of action potentials or "spikes" in recordings of multiple cell activity, providing valuable information on real time neural activity in the brain.

Comparison of three-dimensional profiles over time

In this paper, we describe an analysis for data collected on a three-dimensional spatial lattice with treatments applied at the horizontal lattice points. Spatial correlation is accounted for using a conditional autoregressive model. Observations are defined as neighbours only if they are at the same depth. This allows the corresponding variance components to vary by depth. We use the Markov chain Monte Carlo method with block updating, together with Krylov subspace methods, for efficient estimation of the model. The method is applicable to both regular and irregular horizontal lattices and hence to data collected at any set of horizontal sites for a set of depths or heights, for example, water column or soil profile data. The model for the three-dimensional data is applied to agricultural trial data for five separate days taken roughly six months apart in order to determine possible relationships over time. The purpose of the trial is to determine a form of cropping that leads to less moist soils in the root zone and beyond.We estimate moisture for each date, depth and treatment accounting for spatial correlation and determine relationships of these and other parameters over time.

The association between objectively measured neighborhood features and walking in middle-aged adults

Purpose: To explore the role of the neighborhood environment in supporting walking Design: Cross sectional study of 10,286 residents of 200 neighborhoods. Participants were selected using a stratified two-stage cluster design. Data were collected by mail survey (68.5% response rate). Setting: The Brisbane City Local Government Area, Australia, 2007. Subjects: Brisbane residents aged 40 to 65 years. Measures Environmental: street connectivity, residential density, hilliness, tree coverage, bikeways, and street lights within a one kilometer circular buffer from each resident’s home; and network distance to nearest river or coast, public transport, shop, and park. Walking: minutes in the previous week categorized as < 30 minutes, ≥ 30 < 90 minutes, ≥ 90 < 150 minutes, ≥ 150 < 300 minutes, and ≥ 300 minutes. Analysis: The association between each neighborhood characteristic and walking was examined using multilevel multinomial logistic regression and the model parameters were estimated using Markov chain Monte Carlo simulation. Results: After adjustment for individual factors, the likelihood of walking for more than 300 minutes (relative to <30 minutes) was highest in areas with the most connectivity (OR=1.93, 99% CI 1.32-2.80), the greatest residential density (OR=1.47, 99% CI 1.02-2.12), the least tree coverage (OR=1.69, 99% CI 1.13-2.51), the most bikeways (OR=1.60, 99% CI 1.16-2.21), and the most street lights (OR=1.50, 99% CI 1.07-2.11). The likelihood of walking for more than 300 minutes was also higher among those who lived closest to a river or the coast (OR=2.06, 99% CI 1.41-3.02). Conclusion: The likelihood of meeting (and exceeding) physical activity recommendations on the basis of walking was higher in neighborhoods with greater street connectivity and residential density, more street lights and bikeways, closer proximity to waterways, and less tree coverage. Interventions targeting these neighborhood characteristics may lead to improved environmental quality as well as lower rates of overweight and obesity and associated chromic disease.

Optimal sitting and sizing of distributed generators considering plug-in electric vehicles

Some uncertainties such as the stochastic input/output power of a plug-in electric vehicle due to its stochastic charging and discharging schedule, that of a wind unit and that of a photovoltaic generation source, volatile fuel prices and future uncertain load growth, all together could lead to some risks in determining the optimal siting and sizing of distributed generators (DGs) in distributed systems. Given this background, under the chance constrained programming (CCP) framework, a new method is presented to handle these uncertainties in the optimal sitting and sizing problem of DGs. First, a mathematical model of CCP is developed with the minimization of DGs investment cost, operational cost and maintenance cost as well as the network loss cost as the objective, security limitations as constraints, the sitting and sizing of DGs as optimization variables. Then, a Monte Carolo simulation embedded genetic algorithm approach is developed to solve the developed CCP model. Finally, the IEEE 37-node test feeder is employed to verify the feasibility and effectiveness of the developed model and method. This work is supported by an Australian Commonwealth Scientific and Industrial Research Organisation (CSIRO) Project on Intelligent Grids Under the Energy Transformed Flagship, and Project from Jiangxi Power Company.

Change Point Estimation in Monitoring Survival Time

Precise identification of the time when a change in a hospital outcome has occurred enables clinical experts to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for survival time of a clinical procedure in the presence of patient mix in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change in the mean survival time of patients who underwent cardiac surgery. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. Markov Chain Monte Carlo is used to obtain posterior distributions of the change point parameters including location and magnitude of changes and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time CUSUM control charts for different magnitude scenarios. The proposed estimator shows a better performance where a longer follow-up period, censoring time, is applied. In comparison with the alternative built-in CUSUM estimator, more accurate and precise estimates are obtained by the Bayesian estimator. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Using approximate Bayesian computation to estimate transmission rates of nosocomial pathogens

In this paper, we apply a simulation based approach for estimating transmission rates of nosocomial pathogens. In particular, the objective is to infer the transmission rate between colonised health-care practitioners and uncolonised patients (and vice versa) solely from routinely collected incidence data. The method, using approximate Bayesian computation, is substantially less computer intensive and easier to implement than likelihood-based approaches we refer to here. We find through replacing the likelihood with a comparison of an efficient summary statistic between observed and simulated data that little is lost in the precision of estimated transmission rates. Furthermore, we investigate the impact of incorporating uncertainty in previously fixed parameters on the precision of the estimated transmission rates.

Detecting common dynamics in transitory components

This paper considers VECMs for variables exhibiting cointegration and common features in the transitory components. While the presence of cointegration between the permanent components of series reduces the rank of the long-run multiplier matrix, a common feature among the transitory components leads to a rank reduction in the matrix summarizing short-run dynamics. The common feature also implies that there exists linear combinations of the first-differenced variables in a cointegrated VAR that are white noise and traditional tests focus on testing for this characteristic. An alternative, however, is to test the rank of the short-run dynamics matrix directly. Consequently, we use the literature on testing the rank of a matrix to produce some alternative test statistics. We also show that these are identical to one of the traditional tests. The performance of the different methods is illustrated in a Monte Carlo analysis which is then used to re-examine an existing empirical study. Finally, this approach is applied to provide a check for the presence of common dynamics in DSGE models.

Tracheobronchial and alveolar dose of submicrometer particles for different population age groups in Italy

Exposure to ultrafine particles (diameter less than 100 nm) is an important topic in epidemiological and toxicological studies. This study used the average particle number size distribution data obtained from our measurement survey in major micro-environments, together with the people activity pattern data obtained from the Italian Human Activity Pattern Survey to estimate the tracheobronchial and alveolar dose of submicrometer particles for different population age groups in Italy. We developed a numerical methodology based on Monte Carlo method, in order to estimate the best combination from a probabilistic point of view. More than 106 different cases were analyzed according to a purpose built sub-routine and our results showed that the daily alveolar particle number and surface area deposited for all of the age groups considered was equal to 1.5 x 1011 particles and 2.5 x 1015 m2, respectively, varying slightly for males and females living in Northern or Southern Italy. In terms of tracheobronchial deposition, the corresponding values for daily particle number and surface area for all age groups was equal to 6.5 x 1010 particles and 9.9 x 1014 m2, respectively. Overall, the highest contributions were found to come from indoor cooking (female), working time (male) and transportation (i.e. traffic derived particles) (children).

Robust facial feature extraction and matching

Automated feature extraction and correspondence determination is an extremely important problem in the face recognition community as it often forms the foundation of the normalisation and database construction phases of many recognition and verification systems. This paper presents a completely automatic feature extraction system based upon a modified volume descriptor. These features form a stable descriptor for faces and are utilised in a reversible jump Markov chain Monte Carlo correspondence algorithm to automatically determine correspondences which exist between faces. The developed system is invariant to changes in pose and occlusion and results indicate that it is also robust to minor face deformations which may be present with variations in expression.

Novel methods and the maximum likelihood estimation technique for estimating traffic critical gap

Most unsignalised intersection capacity calculation procedures are based on gap acceptance models. Accuracy of critical gap estimation affects accuracy of capacity and delay estimation. Several methods have been published to estimate drivers’ sample mean critical gap, the Maximum Likelihood Estimation (MLE) technique regarded as the most accurate. This study assesses three novel methods; Average Central Gap (ACG) method, Strength Weighted Central Gap method (SWCG), and Mode Central Gap method (MCG), against MLE for their fidelity in rendering true sample mean critical gaps. A Monte Carlo event based simulation model was used to draw the maximum rejected gap and accepted gap for each of a sample of 300 drivers across 32 simulation runs. Simulation mean critical gap is varied between 3s and 8s, while offered gap rate is varied between 0.05veh/s and 0.55veh/s. This study affirms that MLE provides a close to perfect fit to simulation mean critical gaps across a broad range of conditions. The MCG method also provides an almost perfect fit and has superior computational simplicity and efficiency to the MLE. The SWCG method performs robustly under high flows; however, poorly under low to moderate flows. Further research is recommended using field traffic data, under a variety of minor stream and major stream flow conditions for a variety of minor stream movement types, to compare critical gap estimates using MLE against MCG. Should the MCG method prove as robust as MLE, serious consideration should be given to its adoption to estimate critical gap parameters in guidelines.

A CAD interface for GEANT4

Often CAD models already exist for parts of a geometry being simulated using GEANT4. Direct import of these CAD models into GEANT4 however,may not be possible and complex components may be diffcult to define via other means. Solutions that allow for users to work around the limited support in the GEANT4 toolkit for loading predefined CAD geometries have been presented by others, however these solutions require intermediate file format conversion using commercial software. Here within we describe a technique that allows for CAD models to be directly loaded as geometry without the need for commercial software and intermediate file format conversion. Robustness of the interface was tested using a set of CAD models of various complexity; for the models used in testing, no import errors were reported and all geometry was found to be navigable by GEANT4. Funding source: Cancer Australia (Department of Health and Ageing) Research Grant 614217