Decision analysis avoids this problem by distinguishing between probabilities and consequences of project alternatives. These are then combined in logical fashion to obtain, for each candidate project, an expected effectiveness or expected utility score. For the examples presented in Table 2.1, for instance, one may estimate the expected number of lives saved per year with the following equation:

Expected number of lives saved |
= |
potential number of lives saved |
× |
vaccine efficacy |
× |
vaccine coverage |
× |
probability of vaccine development. |

For vaccine A (Table 2.1), for example, the efficacy score is 75. Vaccine coverage combines information on ease of implementation and cost, which for vaccine A are “excellent” and “moderate,” respectively. Expert judgment might translate this into a score of 0.80 for vaccine coverage. The 0.70 estimate for the probability of successful development makes more explicit the entry “good” in Table 2.1. Thus,

Expected number of lives saved |
= |
(10,000) |
× |
(0.75) |
× |
(0.80) |
× |
(0.70) |

= |
4,200 per year. |

A similar calculation of expected values could be made for other valued consequences, such as days of morbidity averted, medical costs saved, and costs of development. These expected values for each consequence could be combined into a composite score using the methods illustrated in Table 2.2, with expected values of valued consequences as the weighted items rather than a mixture of consequences and probabilities.

More rigorous application of decision analysis would entail combining the valued consequences into a utility score for each possible scenario, prior to averaging out by the probabilities, rather than averaging out each valued consequence separately and then combining the averaged-out values. The two ways of performing these steps will give the same result as long as the rule for combining consequence scores (utilities) is linear and additive. If the combination rule were multiplicative, for example, the answers generally would differ.

Cost-effectiveness analysis is a formal method for selecting projects under a resource constraint. It requires that the constrained resource be identified (e.g., NIAID budget for new vaccine development or national expenditures on vaccinations) and that the resource burden of each candidate project be estimated. It also requires that a