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PubMed1998

Topics in dose-response modeling.

Great uncertainty exists in conducting dose-response assessment for microbial pathogens. The data to support quantitative modeling of dose-response relationships are meager. Our philosophy in developing methodology to conduct microbial risk assessments has been to rely on data analysis and formal inferencing from the available data in constructing dose-response and exposure models. The probability of illness is a complex function of factors associated with the disease triangle: the host, the pathogen, and the environment including the food vehicle and indigenous microbial competitors. The epidemiological triangle and interactions between the components of the triangle are used to illustrate key issues in dose-response modeling that impact the estimation of risk and attendant uncertainty. Distinguishing between uncertainty (what is unknown) and variability (heterogeneity) is crucial in risk assessment. Uncertainty includes components that are associated with (i) parameter estimation for a given assumed model, and (ii) the unknown "true" model form among many plausible alternatives such as the exponential, Beta-Poisson, probit, logistic, and Gompertz. Uncertainty may be grossly understated if plausible alternative models are not tested in the analysis. Examples are presented of the impact of variability and uncertainty on species, strain, or serotype of microbial pathogens; variability in human response to administered doses of pathogens; and effects of threshold and nonthreshold models. Some discussion of the usefulness and limitations of epidemiological data is presented. Criteria for development of surrogate dose-response models are proposed for pathogens for which human data are lacking. Alternative dose-response models which consider biological plausibility are presented for predicting the probability of illness.

Adult↗
PubMed2004

A three-dimensional theoretical model incorporating spatial detection uncertainty in continuous detector PET.

In this paper, we will describe a theoretical model of the spatial uncertainty for a line of response, due to the imperfect localization of events on the detector heads of a positron emission tomography (PET) camera. The forward acquisition problem is modelled by a Gaussian distribution of the position of interaction on a detector head, centred at the measured position. The a posteriori probability that an event originates from a certain point in the field of view (FOV) is calculated by integrating all the possible lines of response (LORs) through this point, weighted with the Gaussian detection likelihood at the LOR's end points. We have calculated these a posteriori probabilities both for perpendicular and oblique coincidences. For the oblique coincidence case it was necessary to incorporate the effect of the crystal thickness in the calculations. We found in the perpendicular incidence case as well as in the oblique incidence case that the probability density function cannot be analytically expressed in a closed form, and it was thus calculated by means of numerical integration. A Gaussian was fit to the transversal profiles of this function for a given distance to the detectors. From these fits, we can conclude that the profiles can be accurately approximated by a Gaussian, both for perpendicular and oblique coincidences. The FWHM reaches a maximum at the detector heads, and decreases towards the centre of the FOV, as was expected. Afterwards we extended this two-dimensional model to three dimensions, thus incorporating the spatial uncertainty in both transversal directions. This theoretical model was then evaluated and a very good agreement was found with theoretical calculations and with geometric Monte Carlo simulations. Possible improvements for the above-described incorporation of crystal thickness are discussed. Therefore a detailed Monte Carlo study has been performed in order to investigate the interaction probability of photons of different energies along their path in several detector materials dedicated to PET. Finally two approaches for the incorporation of this theoretical model in reconstruction algorithms are outlined.

Algorithms↗
PubMed1997

Air pollution and mortality: the implications of uncertainties in regression modeling and exposure measurement.

In a previous paper, we showed that the mean effects on daily mortality associated with air pollution are essentially the same for gases and particulate matter (PM) and are invariant with respect to particle size and composition, based on 27 statistical studies that had been published at that time. Since then, a new analysis reported stronger mortality associations for the fine fractions of PM obtained from dichotomous samplers, relative to the coarse fractions. In this paper, we show that differential measurement errors known to be present in dichotomous sampler data preclude reliable determination of such statistical relationships by particle size. Further, it is necessary to consider gaseous pollutants simultaneously with particles to provide robust estimates of the responsibilities for the implied daily mortality gradients. Finally, certain regression model specifications may be sensitive to differences in frequency distribution characteristics according to particle size.

Air Pollution↗
PubMed1993

Uncertainties in pharmacokinetic modeling for perchloroethylene: II. Comparison of model predictions with data for a variety of different parameters.

In this paper we compare expectations derived from 10 different human physiologically based pharmacokinetic models for perchloroethylene with data on absorption via inhalation, and concentrations in alveolar air and venous blood. Our most interesting finding is that essentially all of the models show a time pattern of departures of predictions of air and blood levels relative to experimental data that might be corrected by more sophisticated model structures incorporating either (a) heterogeneity of the fat compartment (with respect to either perfusion or partition coefficients or both) or (b) intertissue diffusion of perchloroethylene between the fat and muscle/VRG groups. Similar types of corrections have recently been proposed to reduce analogous anomalies in the fits of pharmacokinetic models to the data for several volatile anesthetics. A second finding is that models incorporating resting values for alveolar ventilation in the region of 5.4 L/min seemed to be most compatible with the most reliable set of perchloroethylene uptake data.

Biological Transport, Active↗
PubMed2005

Deriving the expected utility of a predictive model when the utilities are uncertain.

Predictive models are often constructed from clinical databases with the goal of eventually helping make better clinical decisions. Evaluating models using decision theory is therefore natural. When constructing a model using statistical and machine learning methods, however, we are often uncertain about precisely how the model will be used. Thus, decision-independent measures of classification performance, such as the area under an ROC curve, are popular. As a complementary method of evaluation, we investigate techniques for deriving the expected utility of a model under uncertainty about the model's utilities. We demonstrate an example of the application of this approach to the evaluation of two models that diagnose coronary artery disease.

Artificial Intelligence↗
PubMed2001

A quantitative risk assessment for fumonisins B1 and B2 in US corn.

Quantitative risk analysis permits modifying risk estimates with changes in variables such as exposure. This analysis for exposure to the mycotoxin fumonism describes the magnitude of adverse effects, variability in the population and uncertainty of models as a range of possible outcomes. The most sensitive adverse response in rats, nephrotoxic lesions, was used for the dose-response analysis. Dietary intake of corn products was estimated from a 3-day consumption survey. Levels of corn in each product were estimated by standard methods. Fumonisin levels in corn products were estimated from Food and Drug Administration (FDA) surveillance data and distributions of fumonisin consumption were modelled for each eater in the survey population. Uncertainty for predictions made from each model and uncertainty resulting from model selection were described. Results of the dose-response and exposure analyses were assimilated in a two-dimensional Monte-Carlo simulation. Distributions representing variability and uncertainty were iteratively selected to form an array of estimates of the risk. On the basis of this analysis, current dietary levels of fumonisin would not result in renal lesions even at upper levels of exposure. To avoid toxicity at much higher doses, limiting corn intake would be more effective than would limiting the level of fumonisin in corn.

Animals↗
PubMed2001

Predicting long-range transport: a systematic evaluation of two multimedia transport models.

The United Nations Environment Program has recently developed criteria to identify and restrict chemicals with a potential for persistence and long-range transport (persistent organic pollutants or POPs). There are many stakeholders involved, and the issues are not only scientific but also include social, economic, and political factors. This work focuses on one aspect of the POPs debate, the criteria for determining the potential for long-range transport (LRT). Our goal is to determine if current models are reliable enough to support decisions that classify a chemical based on the LRT potential. We examine the robustness of two multimedia fate models for determining the relative ranking and absolute spatial range of various chemicals in the environment. We also consider the effect of parameter uncertainties and the model uncertainty associated with the selection of an algorithm for gas-particle partitioning on the model results. Given the same chemical properties, both models give virtually the same ranking. However, when chemical parameter uncertainties and model uncertainties such as particle partitioning are considered, the spatial range distributions obtained for the individual chemicals overlap, preventing a distinct rank order. The absolute values obtained for the predicted spatial range or travel distance differ significantly between the two models for the uncertainties evaluated. We find that to evaluate a chemical when large and unresolved uncertainties exist, it is more informative to use two or more models and include multiple types of uncertainty. Model differences and uncertainties must be explicitly confronted to determine how the limitations of scientific knowledge impact predictions in the decision-making process.

Decision Making↗
PubMed2005

Assessing uncertainty in simulation-based maritime risk assessment.

Recent work in the assessment of risk in maritime transportation systems has used simulation-based probabilistic risk assessment techniques. In the Prince William Sound and Washington State Ferries risk assessments, the studies' recommendations were backed up by estimates of their impact made using such techniques and all recommendations were implemented. However, the level of uncertainty about these estimates was not available, leaving the decisionmakers unsure whether the evidence was sufficient to assess specific risks and benefits. The first step toward assessing the impact of uncertainty in maritime risk assessments is to model the uncertainty in the simulation models used. In this article, a study of the impact of proposed ferry service expansions in San Francisco Bay is used as a case study to demonstrate the use of Bayesian simulation techniques to propagate uncertainty throughout the analysis. The conclusions drawn in the original study are shown, in this case, to be robust to the inherent uncertainties. The main intellectual merit of this work is the development of Bayesian simulation technique to model uncertainty in the assessment of maritime risk. However, Bayesian simulations have been implemented only as theoretical demonstrations. Their use in a large, complex system may be considered state of the art in the field of computational sciences.

Journal Article↗
PubMed2005

Incorporation of uncertainty in health economic modelling studies.

In a recent leading article in PharmacoEconomics, Nuijten described some methods for incorporating uncertainty into health economic models and for utilising the information on uncertainty regarding the cost effectiveness of a therapy in resource allocation decision-making. His proposals are found to suffer from serious flaws in statistical and health economic reasoning.Nuijten's suggestions for incorporating uncertainty: (a) wrongly interpret the p-value as the probability that the null hypothesis is true; (b) represent this probability wrongly by truncating the input distribution; and (c) in the specific example of an antiparkinsonian drug uses a completely inappropriate p-value of 0.05 when the null hypothesis would, in reality, be emphatically disproved by the data.His suggestions regarding minimum important differences in cost effectiveness: (a) introduce areas of indifference that suggest inappropriate reliance on cost minimisation while failing to recognise that decisions should be based on expected costs versus benefits; and (b) offer no guidance on how the probabilities associated with these areas could be used in decision-making. Furthermore, Nuijten's model for Parkinson's disease is over-simplified to the point of providing a bad example of modelling practice, which may mislead the readers of PharmacoEconomics. The rationale for this paper is to ensure that readers do not apply inappropriate analyses as a result of following the proposals contained in Nuijten's paper. In addition to a detailed critique of Nuijten's proposals, we provide brief summaries of the currently accepted best practice in cost-effectiveness decision-making under uncertainty.

Antiparkinson Agents↗
PubMed2007

On the translation of uncertainty from toxicokinetic to toxicodynamic models--the TCDD example.

When estimating human health risks from exposure to TCDD using toxicokinetic and toxicodynamic models, it is important to understand how model choice and assumptions necessary for modeling add to the uncertainty of risk estimates. Several toxicokinetic models have been proposed for the risk assessment of dioxins, in particular the elimination kinetics in humans has been a matter of constant debate. For a long time, a simple linear elimination kinetics has been common choice. Thus, it was used for the statistical analysis of the largest occupationally exposed cohort, the German Boehringer cohort. We challenge this assumption by considering, amongst others, a nonlinear modified Michaelis-Menten-type elimination kinetics, the so-called Carrier kinetics. Using the area under the lipid TCDD concentration time curve as dose metrics, we model the time to cancer-related death using the Cox proportional hazards model as toxicodynamic model. This risk assessment set-up was simulated in order to quantify uncertainty of both the dose (TCDD body burden) and the risk estimates, depending on the use of the kinetic model, variations of carcinogenic effect of TCDD and variations of latency period (lag time). If past exposure is estimated assuming a linear elimination kinetics although a Carrier kinetics actually holds, then high exposures in reality will be underestimated through statistical analysis and low exposures will be overestimated, respectively. This bias will carry over on the estimated individual concentration-time curves and the therefrom derived TCDD dose metric values. Using biased dose values when estimating a dose-response relationship will finally lead to biased risk estimates. The extent of bias and the decrease of precision are quantified in selected scenarios through this simulation approach. Our findings are in concordance with recent results in the field of dioxin risk assessment. They also reinforce the general demand for the scheduled uncertainty assessments in risk analyses.

Adult↗
PubMed2002

Rigorous uncertainty assessment in contaminant transport inverse modelling: a case study of fluoride diffusion through clay liners.

Inverse methods used in assessing landfill liner design have not yet taken advantage of current developments in inverse procedures. Here, a method for inverting contaminant transport models is presented including a general error model and procedures for differentially weighted multiple response regression. General error models are employed in cases where the residuals are heteroscedastic and correlated, and lead to valid inference on model parameter and predictive uncertainty. The Shuffled Complex Evolution algorithm is used to optimise model parameters. Model parameter uncertainty is assessed by exploring the posterior probability distribution with the Metropolis algorithm, a Markov chain Monte Carlo sampling method. The inverse method is applied to simultaneously determine the sorption and diffusion parameters from laboratory diffusion cell experiments. In these experiments, fluoride migration through kaolin clays was measured by sampling the source and collector cells over time. To uniquely determine the transport model parameters, it was necessary to simultaneously fit the observed data from two independent diffusion cell experiments with different initial concentrations. The jointly fitted transport model parameters compared well with those fitted to independent batch experiments.

Aluminum Silicates↗
PubMed2006

Modelling Southern Ocean ecosystems: krill, the food-web, and the impacts of harvesting.

The ecosystem approach to fisheries recognises the interdependence between harvested species and other ecosystem components. It aims to account for the propagation of the effects of harvesting through the food-web. The formulation and evaluation of ecosystem-based management strategies requires reliable models of ecosystem dynamics to predict these effects. The krill-based system in the Southern Ocean was the focus of some of the earliest models exploring such effects. It is also a suitable example for the development of models to support the ecosystem approach to fisheries because it has a relatively simple food-web structure and progress has been made in developing models of the key species and interactions, some of which has been motivated by the need to develop ecosystem-based management. Antarctic krill, Euphausia superba, is the main target species for the fishery and the main prey of many top predators. It is therefore critical to capture the processes affecting the dynamics and distribution of krill in ecosystem dynamics models. These processes include environmental influences on recruitment and the spatially variable influence of advection. Models must also capture the interactions between krill and its consumers, which are mediated by the spatial structure of the environment. Various models have explored predator-prey population dynamics with simplistic representations of these interactions, while others have focused on specific details of the interactions. There is now a pressing need to develop plausible and practical models of ecosystem dynamics that link processes occurring at these different scales. Many studies have highlighted uncertainties in our understanding of the system, which indicates future priorities in terms of both data collection and developing methods to evaluate the effects of these uncertainties on model predictions. We propose a modelling approach that focuses on harvested species and their monitored consumers and that evaluates model uncertainty by using alternative structures and functional forms in a Monte Carlo framework.

Animals↗