Abstract
Diagnostic tests allow better informed medical decisions when there is uncertainty about a patient’s health status and, therefore, about the desirability to undertake treatment. This paper studies the relation between the expected value of diagnostic information and a patient's risk aversion. We show that the ex ante value of diagnostic information increases with risk aversion for diseases with low prevalence, but decreases with risk aversion for diseases with high prevalence. On the other hand, the ex post value of diagnostic information always increases with the patient's degree of risk aversion.
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Notes
Allowing for imperfect tests would complicate the analysis and requires using different concepts of risk aversion. We leave this for future research.
Theorem 1 in Jewitt (1987, p. 75) is as follows: Let the distribution functions \(F\) and \(G\) cross exactly once, and suppose that \(G\) crosses \(F\) from below. It follows that \(\int u\mathrm{d}G\ge \int u\mathrm{d}F\) implies \(\int v\mathrm{d}G\ge \int v\mathrm{d}F\) whenever \(u\) and \(v\) are both increasing with \(v\) more risk averse than \(u\) in the sense of Arrow–Pratt.
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Bleichrodt, H., Crainich, D., Eeckhoudt, L. et al. Risk aversion and the value of diagnostic tests. Theory Decis 89, 137–149 (2020). https://doi.org/10.1007/s11238-020-09750-8
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DOI: https://doi.org/10.1007/s11238-020-09750-8