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.

Bayesian experimental design for models with intractable likelihoods

In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables.

A methodological approach to reporting corrected small field relative outputs

Purpose The goal of this work was to set out a methodology for measuring and reporting small field relative output and to assess the application of published correction factors across a population of linear accelerators. Methods and materials Measurements were made at 6 MV on five Varian iX accelerators using two PTW T60017 unshielded diodes. Relative output readings and profile measurements were made for nominal square field sizes of side 0.5 to 1.0 cm. The actual in-plane (A) and cross-plane (B) field widths were taken to be the FWHM at the 50% isodose level. An effective field size, defined as FSeff=A·B, was calculated and is presented as a field size metric. FSeffFSeff was used to linearly interpolate between published Monte Carlo (MC) calculated kQclin,Qmsrfclin,fmsr values to correct for the diode over-response in small fields. Results The relative output data reported as a function of the nominal field size were different across the accelerator population by up to nearly 10%. However, using the effective field size for reporting showed that the actual output ratios were consistent across the accelerator population to within the experimental uncertainty of ±1.0%. Correcting the measured relative output using kQclin,Qmsrfclin,fmsr at both the nominal and effective field sizes produce output factors that were not identical but differ by much less than the reported experimental and/or MC statistical uncertainties. Conclusions In general, the proposed methodology removes much of the ambiguity in reporting and interpreting small field dosimetric quantities and facilitates a clear dosimetric comparison across a population of linacs

Approximate Bayesian computation using auxiliary model based estimates

We present a novel approach for developing summary statistics for use in approximate Bayesian computation (ABC) algorithms using indirect infer- ence. We embed this approach within a sequential Monte Carlo algorithm that is completely adaptive. This methodological development was motivated by an application involving data on macroparasite population evolution modelled with a trivariate Markov process. The main objective of the analysis is to compare inferences on the Markov process when considering two di®erent indirect mod- els. The two indirect models are based on a Beta-Binomial model and a three component mixture of Binomials, with the former providing a better ¯t to the observed data.

Bioeconomic modelling and risk assessment of tiger prawn (Penaeus esculentus) stock enhancement in Exmouth Gulf, Australia

A bioeconomic model was developed to evaluate the potential performance of brown tiger prawn stock enhancement in Exmouth Gulf, Australia. This paper presents the framework for the bioeconomic model and risk assessment for all components of a stock enhancement operation, i.e. hatchery, grow-out, releasing, population dynamics, fishery, and monitoring, for a commercial scale enhancement of about 100 metric tonnes, a 25% increase in average annual catch in Exmouth Gulf. The model incorporates uncertainty in estimates of parameters by using a distribution for the parameter over a certain range, based on experiments, published data, or similar studies. Monte Carlo simulation was then used to quantify the effects of these uncertainties on the model-output and on the economic potential of a particular production target. The model incorporates density-dependent effects in the nursery grounds of brown tiger prawns. The results predict that a release of 21 million 1 g prawns would produce an estimated enhanced prawn catch of about 100 t. This scale of enhancement has a 66.5% chance of making a profit. The largest contributor to the overall uncertainty of the enhanced prawn catch was the post-release mortality, followed by the density-dependent mortality caused by released prawns. These two mortality rates are most difficult to estimate in practice and are much under-researched in stock enhancement.

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

Estimating the burden of disease attributable to physical inactivity in South Africa in 2000

Objectives. To quantify the burden of disease attributable to physical inactivity in persons 15 years or older, by age group and sex, in South Africa for 2000. Design. The global comparative risk assessment (CRA) methodology of the World Health Organization was followed to estimate the disease burden attributable to physical inactivity. Levels of physical activity for South Africa were obtained from the World Health Survey 2003. A theoretical minimum risk exposure of zero, associated outcomes, relative risks, and revised burden of disease estimates were used to calculate population-attributable fractions and the burden attributed to physical inactivity. Monte Carlo simulation-modelling techniques were used for the uncertainty analysis. Setting. South Africa. Subjects. Adults ≥ 15 years. Outcome measures. Deaths and disability-adjusted life years (DALYs) from ischaemic heart disease, ischaemic stroke, breast cancer, colon cancer, and type 2 diabetes mellitus. Results. Overall in adults ≥ 15 years in 2000, 30% of ischaemic heart disease, 27% of colon cancer, 22% of ischaemic stroke, 20% of type 2 diabetes, and 17% of breast cancer were attributable to physical inactivity. Physical inactivity was estimated to have caused 17 037 (95% uncertainty interval 11 394 - 20 407), or 3.3% (95% uncertainty interval 2.2 - 3.9%) of all deaths in 2000, and 176 252 (95% uncertainty interval 133 733 - 203 628) DALYs, or 1.1% (95% uncertainty interval 0.8 - 1.3%) of all DALYs in 2000. Conclusions. Compared with other regions and the global average, South African adults have a particularly high prevalence of physical inactivity. In terms of attributable deaths, physical inactivity ranked 9th compared with other risk factors, and 12th in terms of DALYs. There is a clear need to assess why South Africans are particularly inactive, and to ensure that physical activity/inactivity is addressed as a national health priority.

Estimating the burden of disease attributable to four selected environmental risk factors in South Africa

INTRODUCTION: The first South African National Burden of Disease study quantified the underlying causes of premature mortality and morbidity experienced in South Africa in the year 2000. This was followed by a Comparative Risk Assessment to estimate the contributions of 17 selected risk factors to burden of disease in South Africa. This paper describes the health impact of exposure to four selected environmental risk factors: unsafe water, sanitation and hygiene; indoor air pollution from household use of solid fuels; urban outdoor air pollution and lead exposure. METHODS: The study followed World Health Organization comparative risk assessment methodology. Population-attributable fractions were calculated and applied to revised burden of disease estimates (deaths and disability adjusted life years, [DALYs]) from the South African Burden of Disease study to obtain the attributable burden for each selected risk factor. The burden attributable to the joint effect of the four environmental risk factors was also estimated taking into account competing risks and common pathways. Monte Carlo simulation-modeling techniques were used to quantify sampling, uncertainty. RESULTS: Almost 24 000 deaths were attributable to the joint effect of these four environmental risk factors, accounting for 4.6% (95% uncertainty interval 3.8-5.3%) of all deaths in South Africa in 2000. Overall the burden due to these environmental risks was equivalent to 3.7% (95% uncertainty interval 3.4-4.0%) of the total disease burden for South Africa, with unsafe water sanitation and hygiene the main contributor to joint burden. The joint attributable burden was especially high in children under 5 years of age, accounting for 10.8% of total deaths in this age group and 9.7% of burden of disease. CONCLUSION: This study highlights the public health impact of exposure to environmental risks and the significant burden of preventable disease attributable to exposure to these four major environmental risk factors in South Africa. Evidence-based policies and programs must be developed and implemented to address these risk factors at individual, household, and community levels.

Estimating the burden of disease attributable to high cholesterol in South Africa in 2000

Objectives To estimate the burden of disease attributable to high cholesterol in adults aged 30 years and older in South Africa in 2000. Design World Health Organization comparative risk assessment (CRA) methodology was followed. Small community studies were used to derive the prevalence by population group. Population-attributable fractions were calculated and applied to revised burden of disease estimates for the relevant disease categories for each population group. The total attributable burden for South Africa in 2000 was obtained by adding the burden attributed to high cholesterol for the four population groups. Monte Carlo simulation-modelling techniques were used for uncertainty analysis. Setting South Africa. Subjects Black African, coloured, white and Indian adults aged 30 years and older. Outcome measures Mortality and disability-adjusted life years (DALYs) from ischaemic heart disease (IHD) and ischaemic stroke. Results Overall, about 59% of IHD and 29% of ischaemic stroke burden in adult males and females (30+ years) were attributable to high cholesterol (≥ 3.8 mmol/l), with marked variation by population group. High cholesterol was estimated to have caused 24 144 deaths (95% uncertainty interval 22 404 - 25 286) or 4.6% (95% uncertainty interval 4.3 - 4.9%) of all deaths in South Africa in 2000. Since most cholesterol-related cardiovascular disease events occurred in middle or old age, the loss of life years comprised a smaller proportion of the total: 222 923 DALYs (95% uncertainty interval 206 712 - 233 460) or 1.4% of all DALYs (95% uncertainty interval 1.3 - 1.4%) in South Africa in 2000. Conclusions High cholesterol is an important cardiovascular risk factor in all population groups in South Africa.

Estimating the burden of disease attributable to high blood pressure in South Africa in 2000

Objectives To estimate the burden of disease attributable to high blood pressure (BP) in adults aged 30 years and older in South Africa in 2000. Design World Health Organization comparative risk assessment (CRA) methodology was followed. Mean systolic BP (SBP) estimates by age and sex were obtained from the 1998 South African Demographic and Health Survey adult data. Population-attributable fractions were calculated and applied to revised burden of disease estimates for the relevant disease categories for South Africa in 2000. Monte Carlo simulation modelling techniques were used for uncertainty analysis. Setting South Africa Subjects Adults aged 30 years and older. Outcome measures Mortality and disability-adjusted life years (DALYs) from ischaemic heart disease (IHD), stroke, hypertensive disease and other cardiovascular disease (CVD). Results High BP was estimated to have caused 46 888 deaths (95% uncertainty interval 44 878 - 48 566) or 9% (95% uncertainty interval 8.6 - 9.3%) of all deaths in South Africa in 2000, and 390 860 DALYs (95% uncertainty interval 377 955 - 402 256) or 2.4% of all DALYs (95% uncertainty interval 2.3 - 2.5%) in South Africa in 2000. Overall, 50% of stroke, 42% of IHD, 72% of hypertensive disease and 22% of other CVD burden in adult males and females (30+ years) were attributable to high BP (systolic BP ≥ 115 mmHg). Conclusions High BP contributes to a considerable burden of CVD in South Africa and results indicate that there is considerable potential for health gain from implementing BP-lowering interventions that are known to be highly costeffective.

Estimating the burden of disease attributable to lead exposure in South Africa in 2000

Objectives To estimate the burden of disease attributable to lead exposure in South Africa in 2000. Design World Health Organization comparative risk assessment (CRA) methodology was followed. Recent community studies were used to derive mean blood lead concentrations in adults and children in urban and rural areas. Population-attributable fractions were calculated and applied to revised burden of disease estimates for the relevant disease categories for South Africa in the year 2000. Monte Carlo simulation-modelling techniques were used for the uncertainty analysis. Setting South Africa. Subjects Children under 5 and adults 30 years and older. Outcome measures Cardiovascular mortality and disability-adjusted life years (DALYs) in adults 30 years and older and mild mental disability DALYs in children under 5 years. Results Lead exposure was estimated to cause 1 428 deaths (95% uncertainty interval 1 086-1 772) or 0.27% (95% uncertainty interval: 0.21 - 0.34%) of all deaths in South Africa in 2000. Burden of disease attributed to lead exposure was dominated by mild mental disability in young children, accounting for 75% of the total 58 939 (95% uncertainty interval 55 413 - 62 500) attributable DALYs. Cardiovascular disease in adults accounted for the remainder of the burden. Conclusions Even with the phasing out of leaded petrol, exposure to lead from its ongoing addition to paint, paraoccupational exposure and its use in backyard 'cottage industries' will continue to be an important public health hazard in South Africa for decades. Young children, especially those from disadvantaged communities, remain particularly vulnerable to lead exposure and poisoning.

Directional persistence and the optimality of run-and-tumble chemotaxis

E. coli does chemotaxis by performing a biased random walk composed of alternating periods of swimming (runs) and reorientations (tumbles). Tumbles are typically modelled as complete directional randomisations but it is known that in wild type E. coli, successive run directions are actually weakly correlated, with a mean directional difference of ∼63°. We recently presented a model of the evolution of chemotactic swimming strategies in bacteria which is able to quantitatively reproduce the emergence of this correlation. The agreement between model and experiments suggests that directional persistence may serve some function, a hypothesis supported by the results of an earlier model. Here we investigate the effect of persistence on chemotactic efficiency, using a spatial Monte Carlo model of bacterial swimming in a gradient, combined with simulations of natural selection based on chemotactic efficiency. A direct search of the parameter space reveals two attractant gradient regimes, (a) a low-gradient regime, in which efficiency is unaffected by directional persistence and (b) a high-gradient regime, in which persistence can improve chemotactic efficiency. The value of the persistence parameter that maximises this effect corresponds very closely with the value observed experimentally. This result is matched by independent simulations of the evolution of directional memory in a population of model bacteria, which also predict the emergence of persistence in high-gradient conditions. The relationship between optimality and persistence in different environments may reflect a universal property of random-walk foraging algorithms, which must strike a compromise between two competing aims: exploration and exploitation. We also present a new graphical way to generally illustrate the evolution of a particular trait in a population, in terms of variations in an evolvable parameter.

Estimating the burden of disease attributable to childhood and maternal undernutrition in South Africa in 2000

OBJECTIVES To estimate the disease burden attributable to being underweight as an indicator of undernutrition in children under 5 years of age and in pregnant women for the year 2000. DESIGN World Health Organization comparative risk assessment (CRA) methodology was followed. The 1999 National Food Consumption Survey prevalence of underweight classified in three low weight-for-age categories was compared with standard growth charts to estimate population-attributable fractions for mortality and morbidity outcomes, based on increased risk for each category and applied to revised burden of disease estimates for South Africa in 2000. Maternal underweight, leading to an increased risk of intra-uterine growth retardation and further risk of low birth weight (LBW), was also assessed using the approach adopted by the global assessment. Monte Carlo simulation-modeling techniques were used for the uncertainty analysis. SETTING South Africa. SUBJECTS Children under 5 years of age and pregnant women. OUTCOME MEASURES Mortality and disability-adjusted life years (DALYs) from protein- energy malnutrition and a fraction of those from diarrhoeal disease, pneumonia, malaria, other non- HIV/AIDS infectious and parasitic conditions in children aged 0 - 4 years, and LBW. RESULTS Among children under 5 years, 11.8% were underweight. In the same age group, 11,808 deaths (95% uncertainty interval 11,100 - 12,642) or 12.3% (95% uncertainty interval 11.5 - 13.1%) were attributable to being underweight. Protein-energy malnutrition contributed 44.7% and diarrhoeal disease 29.6% of the total attributable burden. Childhood and maternal underweight accounted for 2.7% (95% uncertainty interval 2.6 - 2.9%) of all DALYs in South Africa in 2000 and 10.8% (95% uncertainty interval 10.2 - 11.5%) of DALYs in children under 5. CONCLUSIONS The study shows that reduction of the occurrence of underweight would have a substantial impact on child mortality, and also highlights the need to monitor this important indicator of child health.

Estimating the burden of disease attributable to diabetes in South Africa in 2000

OBJECTIVES To estimate the burden of disease attributable to diabetes by sex and age group in South Africa in 2000. DESIGN The framework adopted for the most recent World Health Organization comparative risk assessment (CRA) methodology was followed. Small community studies used to derive the prevalence of diabetes by population group were weighted proportionately for a national estimate. Population-attributable fractions were calculated and applied to revised burden of disease estimates. Monte Carlo simulation-modelling techniques were used for uncertainty analysis. SETTING South Africa. SUBJECTS Adults 30 years and older. OUTCOME MEASURES Mortality and disability-adjusted life years (DALYs) for ischaemic heart disease (IHD), stroke, hypertensive disease and renal failure. RESULTS Of South Africans aged >or= 30 years, 5.5% had diabetes which increased with age. Overall, about 14% of IHD, 10% of stroke, 12% of hypertensive disease and 12% of renal disease burden in adult males and females (30+ years) were attributable to diabetes. Diabetes was estimated to have caused 22,412 (95% uncertainty interval 20,755 - 24,872) or 4.3% (95% uncertainty interval 4.0 - 4.8%) of all deaths in South Africa in 2000. Since most of these occurred in middle or old age, the loss of healthy life years comprises a smaller proportion of the total 258,028 DALYs (95% uncertainty interval 236,856 - 290,849) in South Africa in 2000, accounting for 1.6% (95% uncertainty interval 1.5 - 1.8%) of the total burden. CONCLUSIONS Diabetes is an important direct and indirect cause of burden in South Africa. Primary prevention of the disease through multi-level interventions and improved management at primary health care level are needed.

Stochastic growth models for analyzing crustacean data

The contemporary methodology for growth models of organisms is based on continuous trajectories and thus it hinders us from modelling stepwise growth in crustacean populations. Growth models for fish are normally assumed to follow a continuous function, but a different type of model is needed for crustacean growth. Crustaceans must moult in order for them to grow. The growth of crustaceans is a discontinuous process due to the periodical shedding of the exoskeleton in moulting. The stepwise growth of crustaceans through the moulting process makes the growth estimation more complex. Stochastic approaches can be used to model discontinuous growth or what are commonly known as "jumps" (Figure 1). However, in stochastic growth model we need to ensure that the stochastic growth model results in only positive jumps. In view of this, we will introduce a subordinator that is a special case of a Levy process. A subordinator is a non-decreasing Levy process, that will assist in modelling crustacean growth for better understanding of the individual variability and stochasticity in moulting periods and increments. We develop the estimation methods for parameter estimation and illustrate them with the help of a dataset from laboratory experiments. The motivational dataset is from the ornate rock lobster, Panulirus ornatus, which can be found between Australia and Papua New Guinea. Due to the presence of sex effects on the growth (Munday et al., 2004), we estimate the growth parameters separately for each sex. Since all hard parts are shed too often, the exact age determination of a lobster can be challenging. However, the growth parameters for the aforementioned moult processes from tank data being able to estimate through: (i) inter-moult periods, and (ii) moult increment. We will attempt to derive a joint density, which is made up of two functions: one for moult increments and the other for time intervals between moults. We claim these functions are conditionally independent given pre-moult length and the inter-moult periods. The variables moult increments and inter-moult periods are said to be independent because of the Markov property or conditional probability. Hence, the parameters in each function can be estimated separately. Subsequently, we integrate both of the functions through a Monte Carlo method. We can therefore obtain a population mean for crustacean growth (e. g. red curve in Figure 1). [GRAPHICS]