Readers who are not familiar with decision analysis may wonder that with so many assumptions and estimates of parameters in even this simple example, how a decision analysis can produce a valid conclusion. The process of sensitivity analysis addresses the issue of validity by exploring the effects of the assumptions on the decision in a systematic fashion.
Sensitivity analysis answers the question: How sensitive is the recommended decision to the assumptions that we made in structuring and assigning numerical values to the model? In particular, the goal of sensitivity analysis is to understand whether changing the assumptions changes the decision alternative recommended by the model.
The decision analyst systematically explores the effect of changing the numerical parameters of a model. After each change, the analyst re-resolves the decision tree. In our example, the analyst could vary the values for the probability p or any of the parameters that underlie the values for the variables cfej, cb2, cb3, or cb4.
The decision analyst plots the results of sensitivity analyses on graphs. The simplest sensitivity analysis is a one-way sensitivity analysis. Figure 29.7 shows the effect of varying the cost of the boil-water advisory over the range of $0 per person per day to the level of $1 per person per day used in the base-case analysis.The graph plots the expected total costs (cost of water and of sickness) for the choices act now and wait. This one-way sensitivity analysis reveals that if the cost of bottled water consumed during a boil-water advisory is less than 13.92 cents per person per day (to the left of the intersection of the two lines depicted in Figure 29.7), then the decision should be to issue a boil-water advisory immediately because the expected costs (including both the cost of bottled water as well as the benefit of averted illness) are lower than the expected cost of waiting.
We also derived the threshold value for p at which the decision changes. For p = 0.2349, the decision act now and issue boil-water advisory is associated with smaller costs than the decision wait and collect more data.
A decision analyst can also perform two- and three-way sensitivity analysis. In a two-way sensitivity analysis, the results are plotted on a three-dimensional graph. One approach to perform a multivariate analysis is to assign distributions to the parameters, assume the distributions are independent, and then randomly sample the parameters from their respective distributions to generate a distribution over the expected utility of each decision option. For more detail description of these techniques, see von Winterfeldt and Edwards ( 1988).
The decision analysis process is iterative. The sensitivity analysis might identify model parameters, such as the cost estimate of a boil-water advisory, for which better estimates would be highly desirable. This discovery may lead to a deeper literature search, consultation with experts to refine the estimates or new research. Once the decision analyst and the decision maker agree that the process of model building is finished, then the next step is to make the final decision.
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