Diagnostic accuracy (2x2)

Shown in the app as diagnostic_accuracy. Part of the method reference, under Diagnostic accuracy and agreement.

When to use

Agreement of a BINARY test against a BINARY gold standard: sensitivity, specificity, PPV, and NPV (each with a confidence interval), the 2x2 counts, and disease prevalence.

What you provide

Test result, then reference standard: two categorical columns.

Options

Missing data

Complete case (listwise deletion)

Multiple comparisons

Not adjustable for this method. Where it makes post-hoc comparisons, the procedure applies its own correction.

Confidence level

Every interval in the result is reported at the level you choose:

Other methods under Diagnostic accuracy and agreement:

Worked examples

Celeus's result on a published or illustrative dataset, next to an independent computation and, where one exists, a published value. The data themselves are not reproduced here.

documented illustrative 2x2 screening fixture

Source: Illustrative or synthetic example data
Licence: illustrative fixture (not real patient data); the counts are an educational example
Reference: Illustrative screening-test 2x2 (TP=95, FP=90, FN=5, TN=810); textbook-style table, not real patient data

Quantity	Celeus	Independent computation	Published value	Agrees
Sensitivity	0.95	0.95	0.95	Yes
Specificity	0.9	0.9	0.9	Yes
Positive predictive value	0.513514	0.513514	-	Yes
Negative predictive value	0.993865	0.993865	-	Yes
Prevalence	0.1	0.1	0.1	Yes

illustrative 2x2 (abnormal/normal labels, positive chosen)

Source: Illustrative or synthetic example data
Licence: n/a (illustrative counts written for this check)
Reference: Illustrative 2x2 table (TP 231, FP 32, FN 27, TN 54) written for this check, not sourced data

Quantity	Celeus	Independent computation	Published value	Agrees
Sensitivity	0.895349	0.895349	-	Yes
Specificity	0.627907	0.627907	-	Yes
Positive predictive value	0.878327	0.878327	-	Yes
Negative predictive value	0.666667	0.666667	-	Yes
Prevalence	0.75	0.75	-	Yes
Positive likelihood ratio	2.40625	2.40625	-	Yes
Diagnostic odds ratio	14.4375	14.4375	-	Yes

illustrative 2x2 (test Positive/Negative, reference Disease/Healthy)

Source: Illustrative or synthetic example data
Licence: n/a (illustrative counts written for this check)
Reference: Illustrative 2x2 table (TP 231, FP 32, FN 27, TN 54) written for this check, not sourced data

Quantity	Celeus	Independent computation	Published value	Agrees
Sensitivity	0.895349	0.895349	-	Yes
Specificity	0.627907	0.627907	-	Yes
Positive predictive value	0.878327	0.878327	-	Yes
Negative predictive value	0.666667	0.666667	-	Yes
Prevalence	0.75	0.75	-	Yes
Positive likelihood ratio	2.40625	2.40625	-	Yes

illustrative 2x2 (coded 1 = abnormal, 2 = normal; category order puts 1 last)

Source: Illustrative or synthetic example data
Licence: n/a (illustrative counts written for this check)
Reference: Illustrative 2x2 table (TP 231, FP 32, FN 27, TN 54) written for this check, not sourced data

Quantity	Celeus	Independent computation	Published value	Agrees
Sensitivity	0.895349	0.895349	-	Yes
Specificity	0.627907	0.627907	-	Yes
Positive predictive value	0.878327	0.878327	-	Yes
Negative predictive value	0.666667	0.666667	-	Yes
Prevalence	0.75	0.75	-	Yes
Positive likelihood ratio	2.40625	2.40625	-	Yes

illustrative 2x2 with 12 index-test results missing (rows 1-6 and 300-305), 90% intervals

Source: Illustrative or synthetic example data
Licence: n/a (illustrative counts written for this check)
Reference: Illustrative 2x2 table (TP 231, FP 32, FN 27, TN 54) written for this check, not sourced data

Quantity	Celeus	Independent computation	Published value	Agrees
Sensitivity	0.892857	0.892857	-	Yes
Specificity	0.6	0.6	-	Yes
Positive predictive value	0.875486	0.875486	-	Yes
Negative predictive value	0.64	0.64	-	Yes
Prevalence	0.759036	0.759036	-	Yes
Positive likelihood ratio	2.23214	2.23214	-	Yes
Number of observations	332	332	-	Yes
Confidence interval for the sensitivity	0.855283, 0.923290	0.855283, 0.923290	-	Yes

synthetic example (a perfect 10/0/0/10 2x2)

Source: Illustrative or synthetic example data
Licence: n/a (synthetic data written for this check, not sourced)
Reference: Hand-authored synthetic fixture, not sourced or published data; the zero cells leave the likelihood ratios not estimable.

Quantity	Celeus	Independent computation	Published value	Agrees
Sensitivity	1	1	-	Yes
Specificity	1	1	-	Yes
Confidence interval for the sensitivity	0.691503, 1.000000	0.691503, 1.000000	-	Yes

documented illustrative 2x2 screening fixture (90% intervals)

Source: Illustrative or synthetic example data
Licence: illustrative fixture (not real patient data); the counts are an educational example
Reference: Illustrative screening-test 2x2 (TP=95, FP=90, FN=5, TN=810); textbook-style table, not real patient data

Quantity	Celeus	Independent computation	Published value	Agrees
Confidence interval for the sensitivity	0.897747, 0.980094	0.897747, 0.980094	-	Yes
Positive likelihood ratio	9.5	9.5	-	Yes

Validation report

References

Youden, W. J. (1950). Index for rating diagnostic tests. Cancer 3: 32-35. doi:10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3 doi:10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3
Clopper, C. J., Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26: 404-413. doi:10.1093/biomet/26.4.404 doi:10.1093/biomet/26.4.404
Simel, D. L., Samsa, G. P., Matchar, D. B. (1991). Likelihood ratios with confidence: sample size estimation for diagnostic test studies. Journal of Clinical Epidemiology 44: 763-770. doi:10.1016/0895-4356(91)90128-V doi:10.1016/0895-4356(91)90128-V