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Free statistical calculators

Diagnostic test evaluation

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

Next click the Test button.

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

Results

Statistic Formula Value 95% CI
Sensitivity Sensitivity    
Specificity Specificity    
Positive Likelihood Ratio Positive Likelihood Ratio    
Negative Likelihood Ratio Negative Likelihood Ratio    
Disease prevalence Prevalence (*)
Positive Predictive Value Positive Predicitive Value   (*)  
Negative Predictive Value Negative Predicitive Value   (*)  

Definitions

  • Sensitivity: probability that a test result will be positive when the disease is present (true positive rate).
    = a / (a+b)
  • Specificity: probability that a test result will be negative when the disease is not present (true negative rate).
    = d / (c+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+c)
  • Negative predictive value: probability that the disease is not present when the test is negative.
    = d  / (b+d)

Sensitivity, specificity, positive and negative predictive value as well as disease prevalence are expressed as percentages for ease of interpretation. Their confidence intervals are "exact" Clopper-Pearson confidence intervals.

(*) 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:

Positive predictive value

and

Negative predictive value

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]
  • Griner PF, Mayewski RJ, Mushlin AI, Greenland P (1981) Selection and interpretation of diagnostic tests and procedures. Annals of Internal Medicine, 94, 555-600. [Abstract]
  • Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143, 29-36. [Abstract]
  • Metz CE (1978) Basic principles of ROC analysis. Seminars in Nuclear Medicine, 8, 283-298. [Abstract]
  • Zhou XH, NA Obuchowski, DK McClish (2002) Statistical methods in diagnostic medicine. New York: Wiley.
  • 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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