Tools › Statistics › Hypothesis Tests › Diagnostic Accuracy and Agreement › Example

Sensitivity and specificity of a new test against a reference standard with score confidence intervals (FDA guidance 2007, Table 2)

ToolDiagnostic Accuracy and Agreement
SourceU.S. Food and Drug Administration (2007). Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests. Guidance for Industry and FDA Staff, Center for Devices and Radiological Health, 13 March 2007. Appendix 7.1, Table 2, pp. 22–23.
LevelUndergraduate

Problem

One specimen from each of 220 subjects of the intended-use population is tested by a new test and by the reference standard. Fifty-one subjects have the condition and 169 do not; the new test is positive in 44 of the 51 and in 1 of the 169. Estimate the sensitivity and the specificity of the new test with two-sided 95 % score confidence intervals.

Inputs to Enter

  • Analysis: diagnostic test (2 × 2 table); comparator: reference standard; confidence 95 %
  • True positives 44, false positives 1, false negatives 7, true negatives 168
  • Prevalence left blank (predictive values at the sample's prevalence only)
Open the Diagnostic Accuracy and Agreement tool (loaded with this example)

Answers

  • Sensitivity 44/51 = 86.3 % (guidance: 86.3 %); Wilson score limits 74.3 % to 93.2 % (guidance: 74.3 %, 93.2 %); exact Clopper–Pearson limits 73.7 % to 94.3 %
  • Specificity 168/169 = 99.4 % (guidance: 99.4 %); Wilson score limits 96.7 % to 99.9 % (guidance: 96.7 %, 99.9 %); exact limits 96.7 % to 100.0 %
  • Prevalence in the sample 51/220 = 23.2 % (guidance p. 28: 23.2 %); positive predictive value 97.8 %, negative predictive value 96.0 %, accuracy 96.4 % at that prevalence
  • Positive likelihood ratio 145.8 (20.59 to 1,032), negative likelihood ratio 0.1381 (0.06938 to 0.2748), diagnostic odds ratio 1,056, Youden index 0.8568 (the tool's additions; the guidance prints none of these)

Notes

The tool's default inputs are this case; press Submit. Choosing Non-reference standard and entering the guidance's Table 4 (40, 5, 4, 171) gives its positive, negative and overall percent agreement of 90.9 %, 97.2 % and 95.9 % with the printed score limits (78.8 to 96.4, 93.5 to 98.8, 92.4 to 97.8 %).