Approaches to Uncertainty 

 Analysis 



Analysis of uncertainty in a risk assessment should address both quan- 

 titative and qualitative uncertainty. Quantitative uncertainty analysis 

 deals primarily with variation in numerical estimates of exposure and 

 risk that results from changing the values of variables in mathematical 

 models used to calculate the estimates (e.g., low-dose extrapolation 

 models). Characterization of variability in chemical measurements, 

 food consumption rates, and Carcinogenic Potency Factors (or RfDs) 

 and its effect on estimates of exposure and risk is an example of 

 quantitative uncertainty analysis. A quaUtative uncertainty analysis 

 includes primarily a summary of limitations of the data and the weight 

 of evidence for toxic effects of concern. A discussion of qujJitative 

 uncertainties should present information from IRIS on the level of 

 confidence that EPA places in each Carcinogenic Potency Factor and 

 RfD. 



General approaches to treatment of uncertainty in variables used in 

 risk analysis models include the following (Morgan 1984): 



• Perform analysis using single-value-best-estimates for model 

 variables without uncertainty analysis 



• Perform single-value-best-estimate analysis, with sensitivity 

 calculations and appropriate discussion of uncertainty 



• Estimate some measure of uncertainty (e.g., standard devia- 

 tion) for each model variable and use error propagation 

 methods to estimate uncertainty of final exposure or risk value 



• Characterize subjectively the probability distribution of each 

 model variable and propagate error through stochastic simula- 

 tion 



• Characterize important model variables using a parametric 

 model and perform risk analysis using various plausible values 

 of each of the variables 



• Determine upper and lower bounds on model variables to yield 

 order-of-magnitude estimates and range of possible answers. 



Morgan (1984) refers to the first two approaches as "single-value-best- 

 estimate analysis," to the second two as "probabilistic analysis," and to 

 the final two as "parametric/bounding analysis." The analytical 

 strategies listed above are in roughly descending order, based on the 

 amount of uncertainty in the model variables. Single-value-best-es- 

 timate analysis is appropriate when model variables are precisely 

 known. Bounding analysis is most appropriate when values of model 

 variables are not well-known. The techniques listed above do not 

 address model uncertainty, which must be handled by exploratory 

 examination of outcomes based on alternative model equations. 



The choice of a method for uncertainty analysis will depend on the 

 amount and quality of exposure data and on the study objectives. 

 Quantitative uncertainty analysis is applied mainly to exposure vari- 

 ables, such as contaminant concentration in fishery species and con- 

 sumption rate. Following U.S. EPA (1980b, 1984a, 1985a), an 



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