This pair of charts bears the internal subcaption “Imperfect reference standard, conditionally independent tests.” The charts compare the naïve estimates of the sensitivity and specificity of a test to the true values, in two situations where the reference test is not perfect. In the left-hand chart, the specificity of the reference test (spref) is 90%; in the right-hand chart, the sensitivity of the reference test (seref is 80%). In both charts, prevalence (p) = 10%, the sensitivity of the index test (seindex) = 70%, and the specificity of the index test (spindex) = 80%. The lighter, horizontal reference lines are the true sensitivity (solid) and specificity (dashed) of the index test. The bold lines are the naïve estimates. The legend at the bottom of the figure provides additional explanation.

Figure 9-2Naïve estimates versus true values for the performance of the index test with an imperfect reference standard

Seindex and Spindex = sensitivity and specificity of the index test, respectively; Seref and Spref: sensitivity and specificity of the reference test, respectively; p: disease prevalence.

If the results of the index and reference tests are independent conditional on disease status, the naïve estimates for the performance of the index test are underestimates. The red (lighter) reference lines are the true sensitivity (solid) and specificity (dashed) of the index test. Note that the naïve estimate for the sensitivity and specificity of the index test approach the true values as the sensitivity and specificity of the reference test approaches 100%. In the left plot the naïve estimate of sensitivity does not reach 70% (the true value) when the sensitivity of the reference test, Seref, is 100%, because the specificity of the reference test is not perfect (Spref=90%). Similarly, on the plot on the right, the specificity of the index test does not reach the true value of 80% when the specificity of the reference test, Spref, is 100%, because the sensitivity of the reference test is not perfect (Seref=80%). The naïve estimates would be the same as the true values only if both the sensitivity and the specificity of the reference test are 100%.

From: Chapter 9, Options for Summarizing Medical Test Performance in the Absence of a “Gold Standard”

Cover of Methods Guide for Medical Test Reviews
Methods Guide for Medical Test Reviews [Internet].
Chang SM, Matchar DB, Smetana GW, et al., editors.

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