Expected Value of Sample Information, Net Benefit of Sampling

A Pared-Down Example

Consider patients with a complaint that may signal a special endocrine disorder. The composition of the case stream is known (Table 1a), except [Page 482]that the sensitivity (Se) of a relevant imaging test is uncertain: It may be .60 or .80, giving rise to the question-marked numbers. The specificity (Sp) is .90.

Decisions have good and bad consequences. Here, we focus on human costs and, more specifically, on regret, that is, the “cost” of not treating the patient as one would were his or her condition fully known. As PVneg is high anyhow, the test negatives will always be treated by the wait-and-see policy, and either 16 or only 8 false negatives (out of 1,000 patients) will incur a regret B associated with a delayed clarification of their condition. There are 96 false positives that pay C units; this is the human cost of the invasive tests they must undergo. Obviously, this leaves two promising policies: W = wait and see (no need to test) or F = follow the test's advice.

Experts and ex-patients reach a consensus on C and B: C = 1 month (= 1/12 quality-adjusted life year, or QALY), B = 3.5 months. As an unfortunate result, the optimal policy depends on the unknown Se (see Table 1b): If Se is only .60, PVpos is too low to have any consequences, and W is optimal (as its cost of 140 is less than 152). If Se = .80, F is optimal (as 124 < 140).

Now assume that the endocrinologists after studying the literature decide that the two values for Se are equally likely: This gives rise to an a priori mean number of (16 + 8)/2 = 12 false negatives (see the third row of Table 1b marked “F (average)”), so F beats W with a narrow margin of 2 months (= 140 − 138).

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