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September 1989

Clear Heads and Bayesian Tales: Predictive Value and the Coin Toss?

Am J Dis Child. 1989;143(9):1000-1001. doi:10.1001/archpedi.1989.02150210016008

Sir.—Drs Halperin and Doyle, in their response to a recent letter,1 made an assertion that deserves clarification. They stated that"... diagnosing ITP [idiopathic thrombocytopenic purpura] on the basis of a positive serologic test would be as accurate as flipping a coin," given a positive predictive value of approximately 50%. The statement is accurate in this context, since they were referring to data gathered on a population of patients' sera that had a prevalence of ITP of approximately 50%.2 In general, however, using a coin flip as a screening test does not produce a fixed positive predictive value of 50%. Instead, it produces a positive predictive value equal to the prevalence of the disease in the population tested.

The distinction is important. If we choose a disease, for example, with a 5% prevalence, then a coin flip will give a positive predictive value of 5%. If, however, another

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