Melanoma cell colony expansion parameters revealed by approximate Bayesian computation

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ.

An efficient DSE using conditional multivariate complex Gaussian distribution

This paper presents an efficient noniterative method for distribution state estimation using conditional multivariate complex Gaussian distribution (CMCGD). In the proposed method, the mean and standard deviation (SD) of the state variables is obtained in one step considering load uncertainties, measurement errors, and load correlations. In this method, first the bus voltages, branch currents, and injection currents are represented by MCGD using direct load flow and a linear transformation. Then, the mean and SD of bus voltages, or other states, are calculated using CMCGD and estimation of variance method. The mean and SD of pseudo measurements, as well as spatial correlations between pseudo measurements, are modeled based on the historical data for different levels of load duration curve. The proposed method can handle load uncertainties without using time-consuming approaches such as Monte Carlo. Simulation results of two case studies, six-bus, and a realistic 747-bus distribution network show the effectiveness of the proposed method in terms of speed, accuracy, and quality against the conventional approach.

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.

Estimating the burden of disease attributable to iron deficiency anaemia in South Africa in 2000

OBJECTIVES To estimate the extent of iron deficiency anaemia (IDA) among children aged 0 - 4 years and pregnant women aged 15 - 49 years, and the burden of disease attributed to IDA in South Africa in 2000. DESIGN The comparative risk assessment (CRA) methodology of the World Health Organization (WHO) was followed using local prevalence and burden estimates. IDA prevalence came from re-analysis of the South African Vitamin A Consultative Group study in the case of the children, and from a pooled estimate from several studies in the case of the pregnant women (haemoglobin level < 11 g/dl and ferritin level < 12 microg/l). Monte Carlo simulation-modelling was used for the uncertainty analysis. SETTING South Africa. SUBJECTS Children under 5 years and pregnant women 15 - 49 years. OUTCOME MEASURES Direct sequelae of IDA, maternal and perinatal deaths and disability-adjusted life years (DALYs) from mild mental disability related to IDA. Results. It is estimated that 5.1% of children and 9 - 12% of pregnant women had IDA and that about 7.3% of perinatal deaths and 4.9% of maternal deaths were attributed to IDA in 2000. Overall, about 174,976 (95% uncertainty interval 150,344 - 203,961) healthy years of life lost (YLLs), or between 0.9% and 1.3% of all DALYs in South Africa in 2000, were attributable to IDA. CONCLUSIONS This first study in South Africa to quantify the burden from IDA suggests that it is a less serious public health problem in South Africa than in many other developing countries. Nevertheless, this burden is preventable, and the study highlights the need to disseminate the food-based dietary guidelines formulated by the National Department of Health to people who need them and to monitor the impact of the food fortification programme.

Fast unscented transformation-based transient stability margin estimation incorporating uncertainty of wind generation

Intermittent generation from wind farms leads to fluctuating power system operating conditions pushing the stability margin to its limits. The traditional way of determining the worst case generation dispatch for a system with several semi-scheduled wind generators yields a conservative solution. This paper proposes a fast estimation of the transient stability margin (TSM) incorporating the uncertainty of wind generation. First, the Kalman filter (KF) is used to provide linear estimation of system angle and then unscented transformation (UT) is used to estimate the distribution of the TSM. The proposed method is compared with the traditional Monte Carlo (MC) method and the effectiveness of the proposed approach is verified using Single Machine Infinite Bus (SMIB) and IEEE 14 generator Australian dynamic system. This method will aid grid operators to perform fast online calculations to estimate TSM distribution of a power system with high levels of intermittent wind generation.

Bayesian computational methods for spatial analysis of images

This thesis introduces a new way of using prior information in a spatial model and develops scalable algorithms for fitting this model to large imaging datasets. These methods are employed for image-guided radiation therapy and satellite based classification of land use and water quality. This study has utilized a pre-computation step to achieve a hundredfold improvement in the elapsed runtime for model fitting. This makes it much more feasible to apply these models to real-world problems, and enables full Bayesian inference for images with a million or more pixels.

Low voltage EPMA: Experiments on a new frontier in microanalysis—analytical spatial resolution

Field emission (FE) electron gun sources provide new capabilities for high lateral resolution EPMA. The determination of analytical lateral resolution is not as straightforward as that for electron microscopy imaging. Results from two sets of experiments to determine the actual lateral resolution for accurate EPMA are presented for Kα X-ray lines of Si and Al and Lα of Fe at 5 and 7 keV in a silicate glass. These results are compared to theoretical predictions and Monte Carlo simulations of analytical lateral resolution. The experiments suggest little is gained in lateral resolution by dropping from 7 to 5 keV in EPMA of this silicate glass.

Anatomical modelling of the pregnant radiotherapy patient

This study aimed to take existing anatomical models of pregnant women, currently used for radiation pro-tection and nuclear medicine dose calculations, and adapt them for use in the calculation of fetal dose from external beam radiotherapy (EBRT). The models investigated were ‘KATJA’, which was provided as an MCNPX geometry file, and ‘RPI-P6’, which was provided in a simple, voxelized bina-ry format. In-house code was developed, to convert both mod-els into an `egsphant’ format, suitable for use with DOSXYZnrc. The geometries and densities of the resulting phantoms were evaluated and found to accurately represent the source data. As an example of the use of the phantoms, the delivery of a cranial EBRT treatment was simulated using the BEAMnrc and DOSXYZnrc Monte Carlo codes and the likely out-of-field doses to the fetus in each model was calculated. The results of these calculations showed good agreement (with-in one standard deviation) between the doses calculated in KATJA and PRI-P6, despite substantial anatomical differ-ences between the two models. For a 36 Gy prescription dose to a 233.2 cm3 target in the right brain, the mean doses calcu-lated in a region of interest covering the entire uterus were 1.0 +/- 0.6 mSv for KATJA and 1.3 +/- 0.9 mSv for RPI-P6. This work is expected to lead to more comprehensive studies of EBRT treatment plan design and its effects on fetal dose in the future.

An evaluation of the effectiveness of Value-at-Risk (VaR) models for Australian banks under Basel III

This study compares Value-at-Risk (VaR) measures for Australian banks over a period that includes the Global Financial Crisis (GFC) to determine whether the methodology and parameter selection are important for capital adequacy holdings that will ultimately support a bank in a crisis period. VaR methodology promoted under Basel II was largely criticised during the GFC for its failure to capture downside risk. However, results from this study indicate that 1-year parametric and historical models produce better measures of VaR than models with longer time frames. VaR estimates produced using Monte Carlo simulations show a high percentage of violations but with lower average magnitude of a violation when they occur. VaR estimates produced by the ARMA GARCH model also show a relatively high percentage of violations, however, the average magnitude of a violation is quite low. Our findings support the design of the revised Basel II VaR methodology which has also been adopted under Basel III.

Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design

The total entropy utility function is considered for the dual purpose of Bayesian design for model discrimination and parameter estimation. A sequential design setting is proposed where it is shown how to efficiently estimate the total entropy utility for a wide variety of data types. Utility estimation relies on forming particle approximations to a number of intractable integrals which is afforded by the use of the sequential Monte Carlo algorithm for Bayesian inference. A number of motivating examples are considered for demonstrating the performance of total entropy in comparison to utilities for model discrimination and parameter estimation. The results suggest that the total entropy utility selects designs which are efficient under both experimental goals with little compromise in achieving either goal. As such, the total entropy utility is advocated as a general utility for Bayesian design in the presence of model uncertainty.

Bayesian parametric bootstrap for models with intractable likelihoods

In this paper it is demonstrated how the Bayesian parametric bootstrap can be adapted to models with intractable likelihoods. The approach is most appealing when the semi-automatic approximate Bayesian computation (ABC) summary statistics are selected. After a pilot run of ABC, the likelihood-free parametric bootstrap approach requires very few model simulations to produce an approximate posterior, which can be a useful approximation in its own right. An alternative is to use this approximation as a proposal distribution in ABC algorithms to make them more efficient. In this paper, the parametric bootstrap approximation is used to form the initial importance distribution for the sequential Monte Carlo and the ABC importance and rejection sampling algorithms. The new approach is illustrated through a simulation study of the univariate g-and- k quantile distribution, and is used to infer parameter values of a stochastic model describing expanding melanoma cell colonies.

Scalable Bayesian Computation for intractable likelihoods in image analysis

The inverse temperature hyperparameter of the hidden Potts model governs the strength of spatial cohesion and therefore has a substantial influence over the resulting model fit. The difficulty arises from the dependence of an intractable normalising constant on the value of the inverse temperature, thus there is no closed form solution for sampling from the distribution directly. We review three computational approaches for addressing this issue, namely pseudolikelihood, path sampling, and the approximate exchange algorithm. We compare the accuracy and scalability of these methods using a simulation study.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. 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. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend 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 cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Angular dependence of the response of the nanoDot OSLD system for measurements at depth in clinical megavoltage beams

Purpose The purpose of this investigation was to assess the angular dependence of a commercial optically stimulated luminescence dosimeter (OSLD) dosimetry system in MV x-ray beams at depths beyondd max and to find ways to mitigate this dependence for measurements in phantoms. Methods Two special holders were designed which allow a dosimeter to be rotated around the center of its sensitive volume. The dosimeter's sensitive volume is a disk, 5 mm in diameter and 0.2 mm thick. The first holder rotates the disk in the traditional way. It positions the disk perpendicular to the beam (gantry pointing to the floor) in the initial position (0°). When the holder is rotated the angle of the disk towards the beam increases until the disk is parallel with the beam (“edge on,” 90°). This is referred to as Setup 1. The second holder offers a new, alternative measurement position. It positions the disk parallel to the beam for all angles while rotating around its center (Setup 2). Measurements with five to ten dosimeters per point were carried out for 6 MV at 3 and 10 cm depth. Monte Carlo simulations using GEANT4 were performed to simulate the response of the active detector material for several angles. Detector and housing were simulated in detail based on microCT data and communications with the manufacturer. Various material compositions and an all-water geometry were considered. Results For the traditional Setup 1 the response of the OSLD dropped on average by 1.4% ± 0.7% (measurement) and 2.1% ± 0.3% (Monte Carlo simulation) for the 90° orientation compared to 0°. Monte Carlo simulations also showed a strong dependence of the effect on the composition of the sensitive layer. Assuming the layer to completely consist of the active material (Al2O3) results in a 7% drop in response for 90° compared to 0°. Assuming the layer to be completely water, results in a flat response within the simulation uncertainty of about 1%. For the new Setup 2, measurements and Monte Carlo simulations found the angular dependence of the dosimeter to be below 1% and within the measurement uncertainty. Conclusions The dosimeter system exhibits a small angular dependence of approximately 2% which needs to be considered for measurements involving other than normal incident beams angles. This applies in particular to clinicalin vivo measurements where the orientation of the dosimeter is dictated by clinical circumstances and cannot be optimized as otherwise suggested here. When measuring in a phantom, the proposed new setup should be considered. It changes the orientation of the dosimeter so that a coplanar beam arrangement always hits the disk shaped detector material from the thin side and thereby reduces the angular dependence of the response to within the measurement uncertainty of about 1%. This improvement makes the dosimeter more attractive for clinical measurements with multiple coplanar beams in phantoms, as the overall measurement uncertainty is reduced. Similarly, phantom based postal audits can transition from the traditional TLD to the more accurate and convenient OSLD.