The Costs of Future Polio Risk Management Policies

Decisionmakers need information about the anticipated future costs of maintaining polio eradication as a function of the policy options under consideration. Given the large portfolio of options, we reviewed and synthesized the existing cost data relevant to current policies to provide context for future policies. We model the expected future costs of different strategies for continued vaccination, surveillance, and other costs that require significant potential resource commitments. We estimate the costs of different potential policy portfolios for low-, middle-, and high-income countries to demonstrate the variability in these costs. We estimate that a global transition from routine immunization with oral poliovirus vaccine (OPV) to inactivated poliovirus vaccine (IPV) would increase the costs of managing polio globally, although routine IPV use remains less costly than routine OPV use with supplemental immunization activities. The costs of surveillance and a stockpile, while small compared to routine vaccination costs, represent important expenditures to ensure adequate response to potential outbreaks. The uncertainty and sensitivity analyses highlight important uncertainty in the aggregated costs and demonstrates that the discount rate and uncertainty in price and administration cost of IPV drives the expected incremental cost of routine IPV vs. OPV immunization.     

Decision Making for Risk Management: A Comparison of Graphical Methods for Presenting Quantitative Uncertainty

Previous research has shown that people err when making decisions aided by probability information. Surprisingly, there has been little exploration into the accuracy of decisions made based on many commonly used probabilistic display methods. Two experiments examined the ability of a comprehensive set of such methods to effectively communicate critical information to a decision maker and influence confidence in decision making. The second experiment investigated the performance of these methods under time pressure, a situational factor known to exacerbate judgmental errors. Ten commonly used graphical display methods were randomly assigned to participants. Across eight scenarios in which a probabilistic outcome was described, participants were asked questions regarding graph interpretation (e.g., mean) and made behavioral choices (i.e., act; do not act) based on the provided information indicated that decision‐maker accuracy differed by graphical method; error bars and boxplots led to greatest mean estimation and behavioral choice accuracy whereas complementary cumulative probability distribution functions were associated with the highest probability estimation accuracy. Under time pressure, participant performance decreased when making behavioral choices.     

Evaluation of Proactive and Reactive Strategies for Polio Eradication Activities in Pakistan and Afghanistan

Only Pakistan and Afghanistan reported any polio cases caused by serotype 1 wild polioviruses (WPV1s) in 2017. With the dwindling cases in both countries and pressure to finish eradication with the least possible resources, a danger exists of inappropriate prioritization of efforts between the two countries and insufficient investment in the two countries to finish the job. We used an existing differential‐equation‐based poliovirus transmission and oral poliovirus (OPV) evolution model to simulate a proactive strategy to stop transmission, and different hypothetical reactive strategies that adapt the quality of supplemental immunization activities (SIAs) in response to observed polio cases in Pakistan and Afghanistan. To account for the delay in perception and adaptation, we related the coverage of the SIAs in high‐risk, undervaccinated subpopulations to the perceived (i.e., smoothed) polio incidence. Continuation of the current frequency and quality of SIAs remains insufficient to eradicate WPV1 in Pakistan and Afghanistan. Proactive strategies that significantly improve and sustain SIA quality lead to WPV1 eradication and the prevention of circulating vaccine‐derived poliovirus (cVDPV) outbreaks. Reactive vaccination efforts that adapt moderately quickly and independently to changes in polio incidence in each country may succeed in WPV1 interruption after several cycles of outbreaks, or may interrupt WPV1 transmission in one country but subsequently import WPV1 from the other country or enable the emergence of cVDPV outbreaks. Reactive vaccination efforts that adapt independently and either more rapidly or more slowly to changes in polio incidence in each country may similarly fail to interrupt WPV1 transmission and result in oscillations of the incidence. Reactive strategies that divert resources to the country of highest priority may lead to alternating large outbreaks. Achieving WPV1 eradication and subsequent successful OPV cessation in Pakistan and Afghanistan requires proactive and sustained efforts to improve vaccination intensity in under‐vaccinated subpopulations while maintaining high population immunity elsewhere.     

Sensitivity Analysis of a Two‐Dimensional Quantitative Microbiological Risk Assessment: Keeping Variability and Uncertainty Separated

The aim of quantitative microbiological risk assessment is to estimate the risk of illness caused by the presence of a pathogen in a food type, and to study the impact of interventions. Because of inherent variability and uncertainty, risk assessments are generally conducted stochastically, and if possible it is advised to characterize variability separately from uncertainty. Sensitivity analysis allows to indicate to which of the input variables the outcome of a quantitative microbiological risk assessment is most sensitive. Although a number of methods exist to apply sensitivity analysis to a risk assessment with probabilistic input variables (such as contamination, storage temperature, storage duration, etc.), it is challenging to perform sensitivity analysis in the case where a risk assessment includes a separate characterization of variability and uncertainty of input variables. A procedure is proposed that focuses on the relation between risk estimates obtained by Monte Carlo simulation and the location of pseudo‐randomly sampled input variables within the uncertainty and variability distributions. Within this procedure, two methods are used—that is, an ANOVA‐like model and Sobol sensitivity indices—to obtain and compare the impact of variability and of uncertainty of all input variables, and of model uncertainty and scenario uncertainty. As a case study, this methodology is applied to a risk assessment to estimate the risk of contracting listeriosis due to consumption of deli meats.     

Variability and Uncertainty Meet Risk Management and Risk Communication

In the past decade, the use of probabilistic risk analysis techniques to quantitatively address variability and uncertainty in risks increased in popularity as recommended by the 1994 National Research Council that wrote Science and Judgment in Risk Assessment. Under the 1996 Food Quality Protection Act, for example, the U.S. EPA supported the development of tools that produce distributions of risk demonstrating the variability and/or uncertainty in the results. This paradigm shift away from the use of point estimates creates new challenges for risk managers, who now struggle with decisions about how to use distributions in decision making. The challenges for risk communication, however, have only been minimally explored. This presentation uses the case studies of variability in the risks of dying on the ground from a crashing airplane and from the deployment of motor vehicle airbags to demonstrate how better characterization of variability and uncertainty in the risk assessment lead to better risk communication. Analogies to food safety and environmental risks are also discussed. This presentation demonstrates that probabilistic risk assessment has an impact on both risk management and risk communication, and highlights remaining research issues associated with using improved sensitivity and uncertainty analyses in risk assessment.     

Sensitivity Analysis Using Risk Measures

In a quantitative model with uncertain inputs, the uncertainty of the output can be summarized by a risk measure. We propose a sensitivity analysis method based on derivatives of the output risk measure, in the direction of model inputs. This produces a global sensitivity measure, explicitly linking sensitivity and uncertainty analyses. We focus on the case of distortion risk measures, defined as weighted averages of output percentiles, and prove a representation of the sensitivity measure that can be evaluated on a Monte Carlo sample, as a weighted average of gradients over the input space. When the analytical model is unknown or hard to work with, nonparametric techniques are used for gradient estimation. This process is demonstrated through the example of a nonlinear insurance loss model. Furthermore, the proposed framework is extended in order to measure sensitivity to constant model parameters, uncertain statistical parameters, and random factors driving dependence between model inputs.     

Decision Analysis and Risk Management Decision Making: Issues and Methods

This paper provides an overview of decision analysis and its use in risk management decision making. The paper discusses the distinctive characteristics of decision analysis and compares these characteristics with those of its principal alternative—cost–benefit analysis. The paper also discusses each of the steps in a decision analysis and the strengths and limitations of the method.     

Evaluating Critical Uncertainty Thresholds in a Spatial Model of Forest Pest Invasion Risk

Pest risk maps can provide useful decision support in invasive species management, but most do not adequately consider the uncertainty associated with predicted risk values. This study explores how increased uncertainty in a risk model's numeric assumptions might affect the resultant risk map. We used a spatial stochastic model, integrating components for entry, establishment, and spread, to estimate the risks of invasion and their variation across a two-dimensional landscape for Sirex noctilio , a nonnative woodwasp recently detected in the United States and Canada. Here, we present a sensitivity analysis of the mapped risk estimates to variation in key model parameters. The tested parameter values were sampled from symmetric uniform distributions defined by a series of nested bounds (±5%, … , ±40%) around the parameters' initial values. The results suggest that the maximum annual spread distance, which governs long-distance dispersal, was by far the most sensitive parameter. At ±15% or larger variability bound increments for this parameter, there were noteworthy shifts in map risk values, but no other parameter had a major effect, even at wider bounds of variation. The methodology presented here is generic and can be used to assess the impact of uncertainties on the stability of pest risk maps as well as to identify geographic areas for which management decisions can be made confidently, regardless of uncertainty.     

Development and Consideration of Global Policies for Managing the Future Risks of Poliovirus Outbreaks: Insights and Lessons Learned Through Modeling

The success of the Global Polio Eradication Initiative promises to bring large benefits, including sustained improvements in quality of life (i.e., cases of paralytic disease and deaths avoided) and costs saved from cessation of vaccination. Obtaining and maintaining these benefits requires that policymakers manage the transition from the current massive use of oral poliovirus vaccine (OPV) to a world without OPV and free of the risks of potential future reintroductions of live polioviruses. This article describes the analytical journey that began in 2001 with a retrospective case study on polio risk management and led to development of dynamic integrated risk, economic, and decision analysis tools to inform global policies for managing the risks of polio. This analytical journey has provided several key insights and lessons learned that will be useful to future analysts involved in similar complex decision-making processes.     

Retrospective Cost-Effectiveness Analyses for Polio Vaccination in the United States

The history of polio vaccination in the United States spans 50 years and includes different phases of the disease, multiple vaccines, and a sustained significant commitment of resources. We estimated cost-effectiveness ratios and assessed the net benefits of polio vaccination applicable at various points in time from the societal perspective and we discounted these back to appropriate points in time. We reconstructed vaccine price data from available sources and used these to retrospectively estimate the total costs of the U.S. historical polio vaccination strategies (all costs reported in year 2002 dollars). We estimate that the United States invested approximately US dollars 35 billion (1955 net present value, discount rate of 3%) in polio vaccines between 1955 and 2005 and will invest approximately US dollars 1.4 billion (1955 net present value, or US dollars 6.3 billion in 2006 net present value) between 2006 and 2015 assuming a policy of continued use of inactivated poliovirus vaccine (IPV) for routine vaccination. The historical and future investments translate into over 1.7 billion vaccinations that prevent approximately 1.1 million cases of paralytic polio and over 160,000 deaths (1955 net present values of approximately 480,000 cases and 73,000 deaths). Due to treatment cost savings, the investment implies net benefits of approximately US dollars 180 billion (1955 net present value), even without incorporating the intangible costs of suffering and death and of averted fear. Retrospectively, the U.S. investment in polio vaccination represents a highly valuable, cost-saving public health program. Observed changes in the cost-effectiveness ratio estimates over time suggest the need for living economic models for interventions that appropriately change with time. This article also demonstrates that estimates of cost-effectiveness ratios at any single time point may fail to adequately consider the context of the investment made to date and the importance of population and other dynamics, and shows the importance of dynamic modeling.     

Decision Making for Group Risk Reduction: Dealing with Epistemic Uncertainty

Group risk is usually represented by FN curves showing the frequency of different accident sizes for a given activity. Many governments regulate group risk through FN criterion lines, which define the tolerable location of an FN curve. However, to compare different risk reduction alternatives, one must be able to rank FN curves. The two main problems in doing this are that the FN curve contains multiple frequencies, and that there are usually large epistemic uncertainties about the curve. Since the mid 1970s, a number of authors have used the concept of “disutility” to summarize FN curves in which a family of disutility functions was defined with a single parameter controlling the degree of “risk aversion.” Here, we show it to be risk neutral, disaster averse, and insensitive to epistemic uncertainty on accident frequencies. A new approach is outlined that has a number of attractive properties. The formulation allows us to distinguish between risk aversion and disaster aversion, two concepts that have been confused in the literature until now. A two‐parameter family of disutilities generalizing the previous approach is defined, where one parameter controls risk aversion and the other disaster aversion. The family is sensitive to epistemic uncertainties. Such disutilities may, for example, be used to compare the impact of system design changes on group risks, or might form the basis for valuing reductions in group risk in a cost‐benefit analysis.     

软件项目风险管理中的敏感性分析研究

采用实证研究方式,应用EXPERT COCOMO模型与功能点分析模型(FPA)对某公司的M IS系统开发过程中所存在的风险进行分析。在对敏感性分析原理进行阐述之后,对某公司的管理信息系统的功能点进行了分析,并对其中所存在的风险进行了识别和量化,然后分别对分析能力(ACAP)、编程能力(PCAP)、可复用性(RU SE)3个主要风险因素的变动对项目的所产生的影响进行了敏感性分析。可望对管理信息系统开发决策中的风险分析有所帮助。     

Sensitivity Analysis of a Two-Dimensional Probabilistic Risk Assessment Model Using Analysis of Variance

This article demonstrates application of sensitivity analysis to risk assessment models with two-dimensional probabilistic frameworks that distinguish between variability and uncertainty. A microbial food safety process risk (MFSPR) model is used as a test bed. The process of identifying key controllable inputs and key sources of uncertainty using sensitivity analysis is challenged by typical characteristics of MFSPR models such as nonlinearity, thresholds, interactions, and categorical inputs. Among many available sensitivity analysis methods, analysis of variance (ANOVA) is evaluated in comparison to commonly used methods based on correlation coefficients. In a two-dimensional risk model, the identification of key controllable inputs that can be prioritized with respect to risk management is confounded by uncertainty. However, as shown here, ANOVA provided robust insights regarding controllable inputs most likely to lead to effective risk reduction despite uncertainty. ANOVA appropriately selected the top six important inputs, while correlation-based methods provided misleading insights. Bootstrap simulation is used to quantify uncertainty in ranks of inputs due to sampling error. For the selected sample size, differences in F values of 60% or more were associated with clear differences in rank order between inputs. Sensitivity analysis results identified inputs related to the storage of ground beef servings at home as the most important. Risk management recommendations are suggested in the form of a consumer advisory for better handling and storage practices.     

Adaptive Flood Risk Management Under Climate Change Uncertainty Using Real Options and Optimization

It is well recognized that adaptive and flexible flood risk strategies are required to account for future uncertainties. Development of such strategies is, however, a challenge. Climate change alone is a significant complication, but, in addition, complexities exist trying to identify the most appropriate set of mitigation measures, or interventions. There are a range of economic and environmental performance measures that require consideration, and the spatial and temporal aspects of evaluating the performance of these is complex. All these elements pose severe difficulties to decisionmakers. This article describes a decision support methodology that has the capability to assess the most appropriate set of interventions to make in a flood system and the opportune time to make these interventions, given the future uncertainties. The flood risk strategies have been explicitly designed to allow for flexible adaptive measures by capturing the concepts of real options and multiobjective optimization to evaluate potential flood risk management opportunities. A state‐of‐the‐art flood risk analysis tool is employed to evaluate the risk associated to each strategy over future points in time and a multiobjective genetic algorithm is utilized to search for the optimal adaptive strategies. The modeling system has been applied to a reach on the Thames Estuary (London, England), and initial results show the inclusion of flexibility is advantageous, while the outputs provide decisionmakers with supplementary knowledge that previously has not been considered.     

Expert Review on Poliovirus Immunity and Transmission

Successfully managing risks to achieve wild polioviruses (WPVs) eradication and address the complexities of oral poliovirus vaccine (OPV) cessation to stop all cases of paralytic poliomyelitis depends strongly on our collective understanding of poliovirus immunity and transmission. With increased shifting from OPV to inactivated poliovirus vaccine (IPV), numerous risk management choices motivate the need to understand the tradeoffs and uncertainties and to develop models to help inform decisions. The U.S. Centers for Disease Control and Prevention hosted a meeting of international experts in April 2010 to review the available literature relevant to poliovirus immunity and transmission. This expert review evaluates 66 OPV challenge studies and other evidence to support the development of quantitative models of poliovirus transmission and potential outbreaks. This review focuses on characterization of immunity as a function of exposure history in terms of susceptibility to excretion, duration of excretion, and concentration of excreted virus. We also discuss the evidence of waning of host immunity to poliovirus transmission, the relationship between the concentration of poliovirus excreted and infectiousness, the importance of different transmission routes, and the differences in transmissibility between OPV and WPV. We discuss the limitations of the available evidence for use in polio risk models, and conclude that despite the relatively large number of studies on immunity, very limited data exist to directly support quantification of model inputs related to transmission. Given the limitations in the evidence, we identify the need for expert input to derive quantitative model inputs from the existing data.     

Ethics, Decision Analysis, and Public Risk

In any analysis of a decision problem involving public risks, ethical implications are introduced. In some cases, these ethical implications may be introduced simply because an analysis is being done. Additional ethical implications may be inherently part of the methodology being utilized or introduced into the specific analysis of the decision problem. In this paper, we investigate where and how ethical implications enter when using the methodology of decision analysis to examine problems involving public risks. We conclude that the methodology of decision analysis is sufficiently robust to allow for numerous different ethical viewpoints to be accounted for in any specific analysis. Stated alternatively, decision analyses of public risks can be conducted in a manner consistent with utilitarianism, deontological theories, libertarianism, egalitarianism, and so forth. However, any specific analysis has embedded within it numerous ethical implications. This suggests that the careful ethical scrutiny of analyses involving the methodology of decision analysis should be placed on the specific application and not on the methodology per se or on the fact that an analysis is undertaken.     

A Matrix-Based Approach to Uncertainty and Sensitivity Analysis for Fault Trees1

System unavailabilities for large complex systems such as nuclear power plants are often evaluated through use of fault tree analysis. The system unavailability is obtained from a Boolean representation of a system fault tree. Even after truncation of higher order terms these expressions can be quite large, involving thousands of terms. A general matrix notation is proposed for the representation of Boolean expressions which facilitates uncertainty and sensitivity analysis calculations.     

Sensitivity and Uncertainty Studies of the CRAC2 Computer Code

We have studied the sensitivity of health impacts from nuclear reactor accidents, as predicted by the CRAC2 computer code, to the following sources of uncertainty: (1) the model for plume rise, (2) the model for wet deposition, (3) the meteorological bin-sampling procedure for selecting weather sequences with rain, (4) the dose conversion factors for inhalation as affected by uncertainties in the particle size of the carrier aerosol and the clearance rates of radionuclides from the respiratory tract, (5) the weathering half-time for external ground-surface exposure, and (6) the transfer coefficients for terrestrial foodchain pathways. Predicted health impacts usually showed little sensitivity to use of an alternative plume-rise model or a modified rain-bin structure in bin-sampling. Health impacts often were quite sensitive to use of an alternative wet-deposition model in single-trial runs with rain during plume passage, but were less sensitive to the model in bin-sampling runs. Uncertainties in the inhalation dose conversion factors had important effects on early injuries in single-trial runs. Latent cancer fatalities were moderately sensitive to uncertainties in the weathering half-time for ground-surface exposure, but showed little sensitivity to the transfer coefficients for terrestrial foodchain pathways. Sensitivities of CRAC2 predictions to uncertainties in the models and parameters also depended on the magnitude of the source term, and some of the effects on early health effects were comparable to those that were due only to selection of different sets of weather sequences in bin-sampling.     

Modeling Poliovirus Transmission in Pakistan and Afghanistan to Inform Vaccination Strategies in Undervaccinated Subpopulations

Due to security, access, and programmatic challenges in areas of Pakistan and Afghanistan, both countries continue to sustain indigenous wild poliovirus (WPV) transmission and threaten the success of global polio eradication and oral poliovirus vaccine (OPV) cessation. We fitted an existing differential‐equation‐based poliovirus transmission and OPV evolution model to Pakistan and Afghanistan using four subpopulations to characterize the well‐vaccinated and undervaccinated subpopulations in each country. We explored retrospective and prospective scenarios for using inactivated poliovirus vaccine (IPV) in routine immunization or supplemental immunization activities (SIAs). The undervaccinated subpopulations sustain the circulation of serotype 1 WPV and serotype 2 circulating vaccine‐derived poliovirus. We find a moderate impact of past IPV use on polio incidence and population immunity to transmission mainly due to (1) the boosting effect of IPV for individuals with preexisting immunity from a live poliovirus infection and (2) the effect of IPV‐only on oropharyngeal transmission for individuals without preexisting immunity from a live poliovirus infection. Future IPV use may similarly yield moderate benefits, particularly if access to undervaccinated subpopulations dramatically improves. However, OPV provides a much greater impact on transmission and the incremental benefit of IPV in addition to OPV remains limited. This study suggests that despite the moderate effect of using IPV in SIAs, using OPV in SIAs remains the most effective means to stop transmission, while limited IPV resources should prioritize IPV use in routine immunization.