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Proc Natl Acad Sci USA. Vaccination with partial knowledge of external effectiveness

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  • Proc Natl Acad Sci USA. Vaccination with partial knowledge of external effectiveness

    Vaccination with partial knowledge of external effectiveness (Proc Natl Acad Sci USA, abstract, edited)
    Vaccination with partial knowledge of external effectiveness

    1. Charles F. Manski 1

    Author Affiliations
    1. Department of Economics and Institute for Policy Research, Northwestern University, Evanston, IL 60208
    1. Contributed by Charles F. Manski, December 30, 2009 (sent for review October 26, 2009)


    Economists studying public policy have generally assumed that the relevant planner knows how policy affects population behavior. Planners typically do not possess all of this knowledge, so there is reason to consider policy formation with partial knowledge of policy impacts. Here I consider choice of a vaccination policy when a planner has partial knowledge of the effect of vaccination on illness rates. To begin, I pose a planning problem whose objective is to minimize the utilitarian social cost of illness and vaccination. The consequences of candidate vaccination rates depend on the extent to which vaccination prevents illness. I study the planning problem when the planner has partial knowledge of the external-response function, which expresses how the illness rate of unvaccinated persons varies with the vaccination rate. I suppose that the planner observes the illness rate of a study population whose vaccination rate has been chosen previously. He knows that the illness rate of unvaccinated persons weakly decreases as the vaccination rate increases, but he does not know the magnitude of the preventive effect of vaccination. In this setting, I first show how the planner can eliminate dominated vaccination rates and then how he can use the minimax or minimax-regret criterion to choose an undominated vaccination rate.

    * partial identification
    * planning under ambiguity
    * social interactions
    * vaccination policy

    * 1E-mail:
    * Author contributions: C.F.M. designed research, performed research, and wrote the paper.
    * This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2009.
    * The author declares no conflict of interest.
    * ↵?Although vaccination researchers have generally not studied policy choice as a problem of planning with partial knowledge, they have often performed sensitivity analyses in which they determine optimal policy under alternative assumptions. See, for example, ref. 12. Sensitivity analysis can be instructive, but it does not provide a criterion for choice with partial knowledge.
    * ↵?Use of the term ambiguity to describe the absence of a basis for assertion of a subjective probability distribution appears to have originated in ref. 13. The term uncertainty was used in refs. 14, 15, and some modern authors refer to ambiguity as Knightian uncertainty. Other authors have used ignorance as a synonym for ambiguity (16), whereas still others refer to robust Bayesian analysis (17) or imprecise probabilities (18).
    * ↵?Decision theorists have also suggested blending the minimax and minimax-regret criteria with the expected utility model. A decision maker who feels able to assert a partial distribution on the states of nature can minimize maximum expected cost or minimize maximum expected regret. These ideas have a long history in the literature on statistical decision theory, which refers to them as the Γ-minimax and Γ-minimax regret criteria (17). The Γ-minimax approach has recently drawn attention from economists, such as in refs. 32 and 33.
    * ↵?This assumption may be particularly credible when the study population is a recent cohort of the population now about to be treated, within which treatments were randomly assigned. However, the assumption is not innocuous. If the study population differs from the treatment population in size or social structure, or if assignment to vaccination was nonrandom, its external-response function may differ as well.
    * ↵‖Decision theorists have sometimes asserted preeminence for maximization of expected utility (minimization of expected cost here), asserting not only that a decision maker might use this decision criterion but that he should do so. Reference is often made to representation theorems deriving the expected utility criterion from consistency axioms on hypothetical choice behavior, famously in refs. 31 and 35. However, I have argued that the theorems of axiomatic decision theory should not be viewed as prescriptive (36).
    <cite cite="">Vaccination with partial knowledge of external effectiveness ? PNAS</cite>