Probabilistic risk assessment model uncertainties

Probabilistic methods can be applied in dose-response assessment when there is an understanding of the important parameters and their relationships, such as identification of the key determinants of human variation (e.g., metabolic polymorphisms, hormone levels, and cell replication rates), observation of the distributions of these variables, and valid models for combining these variables. With appropriate data and expert judgment, formal approaches to probabilistic risk assessment can be applied to provide insight into the overall extent and dominant sources of human variation and uncertainty. 

A probabilistic risk assessment (PRA) deals with many types of uncertainties. In addition to the uncertainties associated with the model itself and model input, there is also the meta-uncertainty about whether the entire PRA process has been performed properly. Employment of sophisticated mathematical and statistical methods may easily convey the false impression of accuracy, especially when numerical results are presented with a high number of significant figures. But those who produce PR As, and those who evaluate them, should exert caution there are many possible pitfalls, traps, and potential swindles that can arise. Because of the potential for generating seemingly correct results that are far from the intended model of reality, it is imperative that the PRA practitioner carefully evaluates not only model input data but also the assumptions used in the PRA, the model itself, and the calculations inherent within the model. This chapter presents information on performing PRA in a manner that will minimize the introduction of errors associated with the PRA process. 

The remainder of the article is organized as follows In Section 2, the factor model, which is a typical CCF factor model, is briefly introduced. Uncertainties brought by P factors are discussed and serve as an inspiration of using modified models to deal with dependencies in PR A. The D-S evidence theory and evidential networks are briefly introduced in Section 3. The EN based approach is then discussed in detail in Section 4. In Section 5, a part of a practical probabilistic risk assessment is analyzed using the proposed approach. The conclusion is expressed in the end. 

As probabilistic exposure and risk assessment methods are developed and become more frequently used for environmental fate and effects assessment, OPP increasingly needs distributions of environmental fate values rather than single point estimates, and quantitation of error and uncertainty in measurements. Probabilistic models currently being developed by the OPP require distributions of environmental fate and effects parameters either by measurement, extrapolation or a combination of the two. The models predictions will allow regulators to base decisions on the likelihood and magnitude of exposure and effects for a range of conditions which vary both spatially and temporally, rather than in a specific environment under static conditions. This increased need for basic data on environmental fate may increase data collection and drive development of less costly and more precise analytical methods. 

Bayesian statistics are applicable to analyzing uncertainty in all phases of a risk assessment. Bayesian or probabilistic induction provides a quantitative way to estimate the plausibility of a proposed causality model (Howson and Urbach 1989), including the causal (conceptual) models central to chemical risk assessment (Newman and Evans 2002). Bayesian inductive methods quantify the plausibility of a conceptual model based on existing data and can accommodate a process of data augmentation (or pooling) until sufficient belief (or disbelief) has been accumulated about the proposed cause-effect model. Once a plausible conceptual model is defined, Bayesian methods can quantify uncertainties in parameter estimation or model predictions (predictive inferences). Relevant methods can be found in numerous textbooks, e.g., Carlin and Louis (2000) and Gelman et al. (1997). 

Formulating the assessment problem well is an essential foundation for risk assessment. The workshop considered how the use of probabilistic models and uncertainty analysis affects problem formulation and its main components the integration of available information, definition of the assessment endpoint, specification of the conceptual model, and planning of the analysis phase. 

For food allergens, validated animal models for dose-response assessment are not available and human studies (double-blind placebo-controlled food challenges [DBPCFCs]) are the standard way to establish thresholds. It is practically impossible to establish the real population thresholds this way. Such population threshold can be estimated, but this is associated with major statistical and other uncertainties of low dose-extrapolation and patient recruitment and selection. As a matter of fact, uncertainties are of such order of magnitude that a reliable estimate of population thresholds is currently not possible. The result of the dose-response assessment can also be described as a threshold distribution rather than a single population threshold. Such distribution can effectively be used in probabilistic modeling as a tool in quantitative risk assessment (see Section 15.2.5)... 

Risk assessment is proposed by formulating the usual risk metrics for analyzing Surveillance Requirement changes in the literature, as introduced in section 2.3. It is proposed treatment of model and parameter uncertainties based on traditional sensitivity studies and uncertainty assessment respectively, the latter based of the probabilistic approach for uncertainty formulation and propagation by standard Monte Carlo Sampling (MCS) technique. 

Kaplan (1997) proposes the so-called probability of frequency approach to risk assessment, based on a risk concept in line with risk definition C6 (R = P C), where subjective probabilities are used to express uncertainty about true frequen-tist probabilities. The assessment thus focuses on quantifying uncertainty about an underlying true risk, which is estimated. Kaplan s view is strongly tied to realism, as the risk description focuses on a true risk as determined by experts. Closely related perspectives are those where uncertainty is quantified around a true risk, such as in the traditional Bayesian perspective where uncertainty is quantified in relation to model parameters (Aven Heide 2009). Such uncertainty quantification can also be done using non-probabilistic representations of epistemic uncertainty (Helton Johnson 2011). These methods typicdly consider a risk problem in a highly mathematized form. 

The modeling of earthquake-induced damage to buildings can be either probabilistic or deterministic or, since seismic risk assessment is a multi-step process, a combination of both. The benefit of probabilistic analysis is that they can account for the many uncertainties associated with seismic risk assessments of building stocks. 

Most probabilistic assessments have tended to combine variability and parameter uncertainty, and not consider model or decision rule uncertainty. Recent guidance from the US National Academy of Sciences (NRC 1994), USEPA (1997), US DOE (Bechtel Jacobs Company 1998), and others (Hattis and Burmaster 1994 Hoffman and Hammonds 1994) has emphasized the importance of tracking variability and parameter uncertainty separately. Indeed, the USEPA (2000) states that the risk assessor should strive to distinguish between variability and uncertainty. Two major advantages of tracking variability and parameter uncertainty separately in an uncertainty analysis are... 

The use of uncertainty analysis and probabilistic methods requires systematic and detailed formulation of the assessment problem. To facilitate this, a) risk assessors and risk managers should be given training in problem formulation, b) tools to assist appropriate problem formulation should be developed, and c) efforts should be made to develop generic problem formulations (including assessment scenarios, conceptual models, and standard datasets), which can be used as a starting point for assessments of particular pesticides. 

These simulation models use probabilistic approaches, but are much more complex than the simply Monte Carlo models described above that have been used in exposure assessments. Monte Carlo analysis has been applied to simple spreadsheet calculations of dose using add-in software programs such as Risk or Crystal Ball. These analyses seek to understand the uncertainty and variation in the predictions of these simple dose models. In contrast, these new models are stand-alone computer... 

Monte Carlo analysis is a specific probabilistic assessment method that can be used to characterize health risks and their likelihood of occurrence based on a wide range of parameters (Shade and Jayjock 1997). The U.S. EPA s Stochastic Human Exposure and Dose Simulation (SHEDS) model allows for the quantification of exposures based on a probabilistic assessment of multiple exposure pathways and multiple routes of exposure (Mokhtari et al. 2006 US EPA 2003b). Additional applications of probabilistic techniques wiU be discussed in the section below on conducting an uncertainty analysis of reconstructed exposure values. 

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