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Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling.

Increasingly complex models are being used to evaluate the cost-effectiveness of medical interventions. We describe the multiple sources of uncertainty that are relevant to such models, and their relation to either probabilistic or deterministic sensitivity analysis. A Bayesian approach appears natural in this context. We explore how sensitivity analysis to patient heterogeneity and parameter uncertainty can be simultaneously investigated, and illustrate the necessary computation when expected costs and benefits can be calculated in closed form, such as in discrete-time discrete-state Markov models. Information about parameters can either be expressed as a prior distribution, or derived as a posterior distribution given a generalized synthesis of available data in which multiple sources of evidence can be differentially weighted according to their assumed quality. The resulting joint posterior distributions on costs and benefits can then provide inferences on incremental cost-effectiveness, best presented as posterior distributions over net-benefit and cost-effectiveness acceptability curves. These ideas are illustrated with a detailed running example concerning the cost-effectiveness of hip prostheses in different age-sex subgroups. All computations are carried out using freely available software for conducting Markov chain Monte Carlo analysis.

Adult↗

Uncertainty due to model choice in variant Creutzfeldt-Jakob disease projections.

For some statistical applications, uncertainty due to unverifiable assumptions can be much greater than that arising from the random variability that is quantified by conventional confidence intervals. The case of projecting possible maximum numbers of eventual deaths due to variant Creutzfeldt-Jakob disease in the United Kingdom provides an extreme example of this phenomenon. The need for parametric extrapolation of the incubation distribution, along with non-identifiability of the number of infected persons, makes assumptions very influential. Several publications in leading science journals gave upper bounds that were 100-fold to 20 000-fold lower than projections from other plausible models given here that fit the data about as well. The crucial assumption for projections is how the risk of death increases with time since infection, and exponential growth is an obvious choice for pessimistic models. Parametric extrapolation from the generalized lambda, generalized F, or lognormal distributions produced upper bounds much lower than exponential extrapolation (i.e. assuming a Gompertz distribution, which fit the data up to early 2002 quite well). Had the publications considered such possibilities, they would have reached much weaker conclusions and been less suitable for leading general science journals. The scientific publication process may have inherent disincentives for thorough assessment of uncertainty.

Adolescent↗

Tibia lead levels and methodological uncertainty in 12-year-old children.

In vivo bone lead measurements with 109Cd-based K-shell X-ray fluorescence (XRF) have been used to assess long-term lead exposure in adults. Tibia lead levels were measured in 210 children (106 boys, 104 girls) of 11-12(1/2) years of age in a lead smelter town and in a control (nonexposed) town. Tibia lead levels, methodological uncertainties, and models of some of the factors influencing them are presented. 109Cd-based K-shell XRF tibia lead methodological uncertainty in children is comparable to that in adults.

Child↗

Uncertainty in fitted estimates of apparent in vivo metabolic constants for chloroform.

It has become common practice to rely on fitted estimates of apparent in vivo metabolic constants (e.g., Vmax and KM) in the parameterization of PBPK models. Yet, quantitative estimates of precision in these fitted parameters are not routinely reported. Such information is needed to assess the reliability of model predictions. The purpose of this study was to assess the precision in estimates of Vmax and KM for chloroform, accounting for both the statistical uncertainties in parameter estimates from individual data sets and any additional uncertainty due to differences in the parameter estimates derived from various experiments. Joint confidence regions for Vmax and KM from each experiment, generated using maximum likelihood techniques, were used to evaluate these questions. Three previously published data sets were considered. Estimates of Vmax and KM obtained from these data sets differed more than could be explained as a consequence of a limited number of observations, measurement error, or stochastic error. Issues associated with the use of maximum likelihood techniques to estimate joint confidence regions, the estimation of metabolic constants from individual experiments within a gas uptake study versus the full data set, the degree of overlap in the joint confidence regions for metabolic constants obtained from separate data sets, and the implications for risk assessment are discussed.

Animals↗

The development and application of a multilevel decision analysis model for the remediation of contaminated groundwater under uncertainty.

A study was initiated which combined elements of stochastic hydrology, risk assessment, simulation modeling, cost analysis and decision making to define the optimum remediation choice(s) for a Superfund site in the southern United States. The effort focused upon the premise that groundwater remediation is inherently complex due to uncertainties in the geological matrix as well as in contaminant concentrations at points of compliance and/or exposure. The technical analyst should supply the decision maker with estimates of these uncertainties as well as the cost penalties required to reduce them to manageable levels. Monte Carlo transport modeling was employed to define the probability of contaminant excursions from the site, while geostatistical simulation identified a joint plume configuration and its attendant probability. Bayesian modeling was used to define the worth of additional data. These individual components were combined within a Decision Model to identify optimum remediation configurations for a given levels of risk tolerance which could be supplied by the decision maker or affected community. Sensitivity analyses were conducted to define ranges over which the decision would not be affected by variation in the respective decision parameter.

Decision Making↗

Uncertainty calculations for theoretical flight power curves.

The comparison of theoretical and experimental estimates of the mechanical power requirement for flight is currently impossible owing to the absence of complete experimental data based on mechanical power, as opposed to measurements of metabolic rates. Nevertheless, comparisons of measured and predicted characteristic speeds, and inferred power curves are frequently made, despite the total absence of uncertainty estimates of the theoretically predicted quantities. Here the method for correct calculation of uncertainty estimates in mechanical power models is outlined in detail, and analytical and numerical results are derived for realistic examples. The sensitivity of the calculated variations in power requirement varies greatly among the independent variables, and the practical and theoretical consequences of this variation are discussed. Pending the arrival of appropriate experimental measurements, it is now possible, in principle, to make quantitative comparisons with theoretical predictions.

Animals↗

Prefrontal, parietal, and temporal cortex networks underlie decision-making in the presence of uncertainty.

Decision-making in the presence of uncertainty, i.e., selecting a sequence of responses in an uncertain environment according to a self-generated plan of action, is a complex activity that involves both cognitive and noncognitive processes. Using functional magnetic resonance imaging, the neural substrates of decision-making in the presence of uncertainty are examined. Normal control subjects show a significant activation of a frontoparietal and limbic neural system during a two-choice prediction task relative to a two-choice response task. The most prevalent response strategy during the two-choice prediction task was "win-stay/lose-shift," where subjects will repeat the previous response if it successfully predicted the stimulus and switch to the alternative response otherwise. Increased frequency of responses that are consistent with this strategy is associated with activation in the superior temporal gyrus. In comparison, increased frequency of response inconsistent with win-stay/lose-shift is associated with parietal cortex activation. These results support the hypothesis that subjects use a frontoparietal neural system to establish a contingency based decision-making strategy even in the presence of random reinforcement.

Adult↗

Bonus and Penalty in Common Pool Resource Dilemmas under Uncertainty.

Common pool resource (CPR) dilemmas constitute a class of social dilemmas in which equilibrium behavior results in Pareto deficient outcomes that are not at all desirable by the group. We focus on a class of CPR dilemmas that, in addition to strategic uncertainty about the harvesting behavior of the other group members, include environmental uncertainty about the size of the CPR. In an attempt to decrease the rate of requests from the common pool, and thereby increase individual payoffs, we extend previous research-both theoretically and experimentally-in two different directions. In the bonus treatment, a reward is given to the agent(s) who requests the least, and in the penalty treatment, a charge is imposed on the agent(s) who requests the most. We show that under equilibrium play the bonus treatment decreases total group request, whereas the penalty treatment increases it. Our experimental results do not support this prediction. Rather, both treatments considerably decrease the rate of request and, therefore, increase the rate of provision. The penalty treatment is shown to be more effective in reducing individual requests and enhancing provision rates than the bonus treatment. Copyright 2001 Academic Press.

Journal Article↗

Human variability and noncancer risk assessment- An analysis of the default uncertainty factor

A 10-fold uncertainty factor is used for noncancer risk assessments to allow for possible interindividual differences between humans in the fate of the chemical in the body (kinetics) and target organ sensitivity (dynamics). Analysis of a database on the variability in each of these aspects is consistent with an even subdivision of the 10-fold factor into 10(0.5) (3.16) for kinetics and 10(0.5) (3.16) for dynamics. Analysis of the number of subjects in a normally and log-normally distributed population which would not be covered by factors of 3.16 supports this subdivision and also the use of a 10-fold factor to allow for both aspects. Analysis of kinetic data for subgroups of the population indicates that the standard default value of 3.16 for kinetics will not be adequate for all routes of elimination and all groups of the population. A scheme is proposed which would allow the selection of appropriate default uncertainty factors based on knowledge of the biological fate and effects of the chemical under review. Copyright 1998 Academic Press.

Journal Article↗

Uncertainty analysis methods for comparing predictive models and biomarkers: A case study of dietary methyl mercury exposure.

Biologically based markers (biomarkers) are currently used to provide information on exposure, health effects, and individual susceptibility to chemical and radiological wastes. However, the development and validation of biomarkers are expensive and time consuming. To determine whether biomarker development and use offer potential improvements to risk models based on predictive relationships or assumed values, we explore the use of uncertainty analysis applied to exposure models for dietary methyl mercury intake. We compare exposure estimates based on self-reported fish intake and measured fish mercury concentrations with biomarker-based exposure estimates (i.e., hair or blood mercury concentrations) using a published data set covering 1 month of exposure. Such a comparison of exposure model predictions allowed estimation of bias and random error associated with each exposure model. From these analyses, both bias and random error were found to be important components of uncertainty regarding biomarker-based exposure estimates, while the diary-based exposure estimate was susceptible to bias. Application of the proposed methods to a simple case study demonstrates their utility in estimating the contribution of population variability and measurement error in specific applications of biomarkers to environmental exposure and risk assessment. Such analyses can guide risk analysts and managers in the appropriate validation, use, and interpretation of exposure biomarker information.

Animals↗

An analysis of the need for an additional uncertainty factor for infants and children.

Uncertainty factors have been used for over 40 years to establish safe intakes of threshold toxicants. Tenfold factors are used to allow for species differences and for human variability, with extra factors for database inadequacies. The proposal to introduce an additional 10-fold factor for pesticides when exposure of infants and children is anticipated implies either age-related differences between species or differences within humans which exceed those present in adults. Alternatively, the extra factor could be related to deficiencies of current testing methods or concerns over irreversibility in developing organ systems. Available data do not provide a scientific rationale for the extra factor due to inadequacy of inter- and intraspecies uncertainty factors. Justification for the factor therefore must relate to the adequacy and sensitivity of current methods or concern about irreversible effects in the developing organism.

Animals↗

The use of mechanistic data and the handling of scientific uncertainty in carcinogen risk assessments. The trichloroethylene example.

The purpose of this paper is to explore how risk assessors actually use mechanistic data in carcinogen risk assessment and to discuss how the handling of scientific uncertainty may affect the outcome of the risk assessment. The analysis is performed by comparing 29 trichloroethylene risk assessment documents in general and 2 of these, namely the ECETOC (1994, Trichloroethylene: Assessment of Human Carcinogenic Hazard, Technical Report No. 60) and the OECD/EU (1996, Initial Assessment Report for the 4th SIAM (Screening Information Data Set Initial Assessment Meeting), May 1996: Trichloroethylene, sponsor country, United Kingdom [Draft]), in more detail. It is concluded that in this example the ECETOC required less evidence for considering a carcinogenic mechanism irrelevant to humans than did the OECD/EU risk assessors. There are examples of when two risk assessors have selected different primary data for their argumentation and also examples of how one and the same primary publication was interpreted differently. Biased data selection and evaluation of primary data that correlate to the risk assessor's overall conclusions have also been identified. The general comparison of all 29 TCE risk assessment documents indicates that the assessment of scientific uncertainty in the mechanistic data affects the overall conclusions.

Animals↗

Uncertainties in predicting the demographic impact of AIDS.

A model giving the demographic impact of AIDS is analysed to examine the sensitivity of the projections when various complicating features are included. The model deals with age and sexual partner change rate as continuous variables and uses a device to specify arbitrary correlations between the ages of the people who form sexual partnerships. The device ensures consistency, in that the amount of partner formation is the same regardless of whether the partnerships are counted from the point of view of males or females. Arbitrary correlation between partner change rate and fertility is also permitted. The results show the uncertainty in model predictions that population growth will reduce over the next 20 years to approximately zero in parts of East Africa severely affected by the AIDS epidemic. The main sources of uncertainty in the model predictions are assumptions concerning the correlation between ages in a partnership, the correlation between partner change rate and fertility, the incubation period of AIDS, and the variability of the female partner change rate.

Acquired Immunodeficiency Syndrome↗

Uncertainty in white matter fiber tractography.

In this work we address the uncertainty associated with fiber paths obtained in white matter fiber tractography. This uncertainty, which arises for example from noise and partial volume effects, is quantified using a Bayesian modeling framework. The theory for estimating the probability of a connection between two areas in the brain is presented, and a new model of the local water diffusion profile is introduced. We also provide a theorem that facilitates the estimation of the parameters in this diffusion model, making the presented method simple to implement.

Algorithms↗

Vernier acuity with noisy lines: estimation of relative position uncertainty.

Vernier acuity experiments were carried out to obtain estimates of the minimal number of spatial samples extracted, and of the equivalent noise figure characterizing inherent limitations of the visual system in relative position detection tasks. Results are interpreted by modelling the visual system as an ideal detector limited by external noise and internal position uncertainty resulting from structural limitations and neural noise. Accordingly, we estimate that less than ten samples per line are extracted by the observer and that the equivalent noise figure or position uncertainty is of the order of 20 arc s.

Humans↗

Uncertainty analysis of human EEG spectra: a multivariate information theoretical method for the analysis of brain activity.

Short time Fourier power spectra yield activity related data of the EEG. The mean power densities of frequency bands have proved a reliable descriptive parameter of that activity. Due to their distributional properties of these data their analysis by conventional statistics is restricted to nonparametric univariate or at most bivariate tests. In order to account for the many-relational characteristics of EEG data, uncertainty analysis was employed and specific data transformations were developed. This technique was applied to some of our experimental records. The results confirm prior knowledge of the functional diversity of brain areas and demonstrate the general applicability of uncertainty analysis to this problem. In addition, the spatio-temporal coordination of these activities suggests a systems interpretation: These neuronal processes follow the self-organizing principle.

Analysis of Variance↗

The relationship of uncertainty, control, commitment, and threat of recurrence to coping strategies used by women diagnosed with breast cancer.

The purpose of this descriptive correlational study was to investigate the relationship between commitments, uncertainty about the cancer situation, threat of recurrence, and control of the cancer situation and the set of coping strategies used by women to cope with their breast cancer diagnosis. Lazarus and Folkman's theory of psychological stress provided the framework. The sample consisted of 227 nonhospitalized women who had had a diagnosis of breast cancer. Two sets of canonical variate sets were significant at the .001 level with canonical correlations of .52 and .47. The first canonical set indicated that the use of escape-avoidance and accepting responsibility but not positive reappraisal strategies were characteristics of those women who had low commitment and low control together with high uncertainty and high threat of recurrence. The second set indicated that seeking social support, as well as the use of planful problem solving, escape-avoidance, positive reappraisal, and self-controlling strategies was adopted by women who had high threat of recurrence and high control.

Adaptation, Psychological↗

Robust and self-tuning blood flow control during extracorporeal circulation in the presence of system parameter uncertainties.

Three different discrete controllers were designed and tuned to be used in conjunction with a rotary blood pump during cardiopulmonary heart-lung support. The controllers were designed to operate in both steady and pulsatile modes. The system and methods were tested in a circulatory haemodynamic simulator. To guarantee stable control of the non-linear circulatory system in the presence of patient parameter uncertainties, a proportional plus integral (PI) and an H infinity controller were robustly tuned, using a non-linear time-varying model. (H infinity refers to the Hardy space, the set of bounded functions, analytic in the right half plane. The H infinity controller is the solution to the H infinity norm optimisation problem.) A self-tuning general predictive controller (GPC), together with an adaptive Kalman filter (KF) estimator, was compared with the two robustly tuned controllers. The closed-loop blood flow control circuit was set up in simulation routines first. The blood flow controllers were validated in a circulatory hydrodynamic simulator (MOCK) combined with a rotary blood pump. Parameters of the system simulator were changed continuously, and the controllers were tested over a wide range of different operating points. Disturbances in the form of discontinuous additive parameter uncertainties were applied. The closed-loop systems remained robustly stable. The robustly tuned H infinity controller showed the best control performance, in contrast to the GPC controller, which was near instability in regions of strongly varying non-linear system gain. Compared with the H infinity controller, the PI controller showed slightly worse behaviour, but the closed-loop response was acceptable, even in regions of strongly varying non-linear system gain and during pulsatile perfusion. The rotary blood pump could provide stationary and pulsatile perfusion under control conditions. Controlled variables were hereby mean blood flow, pulsatility index and heart rate. All three controllers were developed for an arterial mean flow of 0-6 l min(-1) and a heart rate of up to 70 beats per minute. Pulsatile closed-loop perfusion could provide up to 30 mmHg pressure variation in the simulated ascending aorta at a mean flow of 3 l min(-1).

Aorta↗