The search for information — A patient perspective on multiple opinions

This paper describes the first dynamic formulation of the optimal strategy, from a patient perspective, for the search for additional information in the form of multiple opinions. The Mehrez and Gafni framework for choosing an optimal treatment from a patient perspective is employed to study the optimal search strategy for a representative individual who is an expected utility maximizer. Two different processes for gathering information regarding the probability of treatment success (P) are studied: In the first, physicians provide information in a yes or no (treatment) type of recommendation; in the second, physicians provide probabilistic information about the likelihood of success in the treatment. For the first system the optimal strategy is derived using an algorithm of an order O(n) (n is the number of opinions to be purchased from expert doctors) for a prior beta probability density function of P and a Bernoulli process of information gathering. EVSI (expected value of sample information) measures are incorporated into the Bayesian analysis to study this case and to obtain an upper bound on n∗ (the optimal number of opinions to be purchased). The approach developed here is different than the well known one provided by Raiffa and Schlaifer in 1961 and it enables us to present additional results regarding the optimal search strategy and how to identify it. For example, if (i) the process of information gathering is generated by a Bernoulli process, (ii) the natural conjurate prior distribution is beta, and (iii) the utility functions are linear functions of the probability of treatment success, then for each n, there exists at most one value of x (the number of experts recommending treatment) for which a search should continue. At this value the incremental increase of the individual's lifetime expected utility stemming from the decision to seek additional expert's opinion is positive. This observation might explain a reality where the likelihood of seeking a large number of opinions is very low. Furthermore, sufficient conditions for not initiating the information search process and on the range of n∗ are provided. In addition an analysis of the second process is provided and properties of the optimal strategy are studied. It is shown that the formulations of the two processes are equivalent and that they can be further analyzed through the two action space project selection problem studied by Mehrez and Stulman and others. A numerical comparison and a sensitivity analysis between the two processes for gathering information is presented. It is illustrated that for similar cost figures, the probability estimation procedure provides more information than the yes-no type recommendation to the patient.