Diagnostic test evaluation

Instructions: enter the number of cases in the diseased group that test positive (a) and negative (c); and the number of cases in the non-diseased group that test positive (b) and negative (d).

Next click the Test button.

 Disease        
TestPresentn  Absentn  Total
PositiveTrue Positive a=
  False Positive b=
 a + b
NegativeFalse Negative c=
  True Negative d=
  c + d
Total a + c   b + d  

Results

Sensitivity
a
a + c
Specificity
d
b + d
Positive
Likelihood
Ratio
Sensitivity
100 - Specificity
Negative
Likelihood
Ratio
100 - Sensitivity
Specificity
Disease
prevalence
a + c
a + b + c + d
(*)
Positive
Predictive
Value
a
a + b
(*)
Negative
Predictive
Value
d
c + d
(*)

Definitions

  • Sensitivity: probability that a test result will be positive when the disease is present (true positive rate).
    = a / (a+c)
  • Specificity: probability that a test result will be negative when the disease is not present (true negative rate).
    = d / (b+d)
  • Positive likelihood ratio: ratio between the probability of a positive test result given the presence of the disease and the probability of a positive test result given the absence of the disease, i.e.
    = True positive rate / False positive rate = Sensitivity / (1-Specificity)
  • Negative likelihood ratio: ratio between the probability of a negative test result given the presence of the disease and the probability of a negative test result given the absence of the disease, i.e.
    = False negative rate / True negative rate = (1-Sensitivity) / Specificity
  • Positive predictive value: probability that the disease is present when the test is positive.
    = a / (a+b)
  • Negative predictive value: probability that the disease is not present when the test is negative.
    = d  / (c+d)

Sensitivity, specificity, positive and negative predictive value as well as disease prevalence are expressed as percentages for ease of interpretation.

(*) Note

If the sample sizes in the positive (Disease present) and the negative (Disease absent) groups do not reflect the real prevalence of the disease, then the Positive and Negative predicted values cannot be estimated and you should ignore those values.

Alternatively, when the disease prevalence is known then the positive and negative predictive values can be calculated using the following formula's based on Bayes' theorem:

and

Literature

  • Gardner IA, Greiner M (2006) Receiver-operating characteristic curves and likelihood ratios: improvements over traditional methods for the evaluation and application of veterinary clinical pathology tests. Veterinary Clinical Pathology 35:8-17. [Abstract]
  • Parshall MB (2013) Unpacking the 2 x 2 table. Heart & Lung 42:221-226. [Abstract]
  • Zweig MH, Campbell G (1993) Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clinical Chemistry 39:561-577. [Abstract]
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