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To perform an *uncertainty analysis* is to determine how the
incomplete information about input values affects the results of your
calculations.

For instance, suppose that you knew that the incidence of a certain infection in a particular risk group was between 1 percent per year and 3 percent per year, and you knew that the population at risk was somewhere between 20000 and 50000 in size. Your lowest estimate for the expected number of new infections per year would be 0.01 times 20000, or 200, and your highest estimate would be 0.03 times 50000, or 1500. Based on this information you would then report that the expected number of new infections may range between 200 and 1500, and you have just performed a simple uncertainty analysis. Because we had incomplete information about the input parameters (the incidence rate, which was between 1 and 3 percent per year, and the population size at risk, which was between 20000 and 50000), the output we calculated (the expected number of new infections) was also uncertain (between 200 and 1500).

Uncertainty analysis can be more complex if you have many input parameters, and if you have partial information about each. We may have had several risk factors for the infection, together with uncertain relative risks for each, so that calculating the expected number of new infections would involve taking into account how many people were in each risk group and how strong the association with that risk factor and the infection is. The calculation becomes more complicated and there may be many more uncertain parameters. Or suppose that instead of simply an upper and lower bound for each input parameter, we had a best estimate also. For instance, our best estimate of the population size at risk in the above example were 38000, but our lower bound was still 20000 and our upper bound was still 50000.

One useful way of handling uncertainty analyses was developed by Iman, Conover and their colleagues. Called Latin Hypercube Sampling, it allows you to generate a large number of plausible collections of input parameters in a structured way. You then perform your calculation for each, and thus obtain a distribution of plausible results. The distribution of outputs reflects the uncertainty in your inputs. We implemented this method as an EPITool; go to the Latin Hypercube Page to learn more about it, and to generate your own Latin Hypercube samples.

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