Precision of sensitivity estimations in diagnostic test evaluations. Power functions for comparisons of sensitivities of two tests.

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Abstract
The precision of estimates of the sensitivity of diagnostic tests is evaluated. "Sensitivity" is defined as the fraction of diseased subjects with test values exceeding the 0.975-fractile of the distribution of control values. An estimate of the sensitivity is subject to sample variation because of variation of both control observations and patient observations. If gaussian distributions are assumed, the 0.95-confidence interval for a sensitivity estimate is up to +/- 0.15 for a sample of 100 controls and 100 patients. For the same sample size, minimum differences of 0.08 to 0.32 of sensitivities of two tests are established as significant with a power of 0.90. For some published diagnostic test evaluations the median sample sizes for controls and patients were 63 and 33, respectively. I show that, to obtain a reasonable precision of sensitivity estimates and a reasonable power when two tests are being compared, the number of samples should in general be considerably larger.