Statistical analysis quantitative risk assessment

When conducting a quantitative risk assessment the analyst(s) must define its probabilistic basis, and in most cases this means either to use the classical frequency approach or the Bayesian approach. The classical statistical approach is and has been the most commonly used probabilistic basis in health care (Schneider 2006). This approach interprets a probability as the relative fraction of times the event considered occurs if the situation analyzed were hypothetically repeated an infinite munber of times. The imder-lying probability is unknown, and is estimated in the risk analysis. In the alternative, the Bayesian perspective, a probability is a measure of imcertainty about future events and outcomes (consequences), as seen through the eyes ofthe assessor(s) and based on his/her backgroimd information and knowledge at the time of the analysis. Probability is a subjective measure of imcertainty. 

Highly quantitative statistical micertainty analysis is usually not practical or necessary for Superfund site risk assessments for a nmnber of... 

The deviation scenarios found in the previous step of the risk analysis must be assessed in terms of risk, which consists of assigning a level of severity and probability of occurrence to each scenario. This assessment is qualitative or semi-quantitative, but rarely quantitative, since a quantitative assessment requires a statistical database on failure frequency, which is difficult to obtain for the fine chemicals industry with such a huge diversity of processes. The severity is clearly linked to the consequences of the scenario or to the extent of possible damage. It may be assessed using different points of view, such as the impact on humans, the environment, property, the business continuity, or the company s reputation. Table 1.4 gives an example of such a set of criteria. In order to allow for a correct assessment, it is essential to describe the scenarios with all their consequences. This is often a demanding task for the team, which must interpret the available data in order to work out the consequences of a scenario, together with its chain of events. 

Uncertainties inherent to the risk assessment process can be quantitatively described using, for example, statistical distributions, fuzzy numbers, or intervals. Corresponding methods are available for propagating these kinds of uncertainties through the process of risk estimation, including Monte Carlo simulation, fuzzy arithmetic, and interval analysis. Computationally intensive methods (e.g., the bootstrap) that work directly from the data to characterize and propagate uncertainties can also be applied in ERA. Implementation of these methods for incorporating uncertainty can lead to risk estimates that are consistent with a probabilistic definition of risk. 

The overall schematic for quantified health risk estimates in the analysis of U.S. EPA (2007) entailed combining concentration—response functions with blood lead distributional statistics generated for each of the three case studies to produce distributions of IQ loss estimates for each study population. Before the quantitative analyses of health risk were done via using differing concentration—response functions, the health risk portion in U.S. EPA s full-scale health risk assessment was evaluated to produce several statistical modeling and assessment steps for the risk metric, IQ point loss, in young children sustaining developmental neurotoxicity effects at various PbB estimates. 

Evidence synthesis is a term used for synthesis of results from diverse sources and covers a wide range of analysis approaches (Sutton and Abrams, 2001). Bayesian Evidence Synthesis (here denoted as BES) is a statistical framework for exphcitly modeling several related and connected sources of data, in which uncertainty in model parameters are incorporated (Jackson et al., 2013). BES can be seen as a complex meta-analysis (Sutton and Abrams, 2001), where complex means to consider multiple effects from an intervention. Classical meta-analyses are usually based on studies that directly have observed the effect of an intervention. A broader view on meta-analyses allows for studies on effects on a lower level which are combined with quantitative modelling to assess the effect of an intervention on a higher level. In this view, a risk assessment can be seen as a meta-analysis (Linkov et al., 2009). Opening up for a quantitative assessment (or complex computer) model to measure effects, makes it possible to synthesize evidence for effects which are difficult, if at all, to empirically observe. In the PVA example, there is for example no possibility of... 

This discussion uses a typical MC-simulation to illustrate the need of emphasizing foundational issues how to perceive risk and assure quality of the assessment procedure. Students in fields relying on the use of quantitative assessments, such as risk, reliability or system analysis, learn about MC-simulation and different ways to quantitatively describe uncertainty. It is important not to end there, but give the students, and future quantitative assessors, the ability to fully understand what this uncertainty represents and on what scientific principles it can be assessed. We would like to point at Bayesian Evidence Synthesis as a suitable framework to teach predictive statistical principles involving simulations from a computer model. BES is useful both in scientific research and risk assessment and can therefore close the gap between these two highly important processes of knowledge production. 

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