SciStat

# Diagnostic test

## Description

This procedure allows to calculate test characteristics such as sensitivity, specificity, positive and negative likelihood ratio, disease prevalence as well as positive and negative predictive value, from data entered in a 2x2 table.

## Required input

• Left column: the number of cases in the diseased group that test positive (a) and negative (b).
• Right column: the number of cases in the non-diseased group that test positive (c) and negative (d).

### Disease prevalence

If the sample sizes in the positive (Disease present) and the negative (Disease absent) groups do not reflect the real prevalence of the disease, you can enter the disease prevalence (expressed as a percentage) in the corresponding input box.

## Results

• 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.

• Negative predictive value: probability that the disease is not present when the test is negative.

• Accuracy: overall probability that a patient is correctly classified.

= Sensitivity × Prevalence + Specificity × (1 − Prevalence)

Positive and negative predictive value, and accuracy, are dependent on disease prevalence.

Sensitivity, specificity, positive and negative predictive value, disease prevalence, and accuracy, are expressed as percentages.

Confidence intervals for sensitivity, specificity and accuracy are "exact" Clopper-Pearson confidence intervals.

Confidence intervals for the likelihood ratios are calculated using the "Log method" as given on page 109 of Altman et al. 2000.

Confidence intervals for the predictive values are the standard logit confidence intervals given by Mercaldo et al. 2007.

## Literature

• Altman DG, Machin D, Bryant TN, Gardner MJ (Eds) (2000) Statistics with confidence, 2nd ed. BMJ Books.
• 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.
• Griner PF, Mayewski RJ, Mushlin AI, Greenland P (1981) Selection and interpretation of diagnostic tests and procedures. Annals of Internal Medicine 94:555-600.
• Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143:29-36.
• Mercaldo ND, Lau KF, Zhou XH (2007) Confidence intervals for predictive values with an emphasis to case-control studies. Statistics in Medicine 26:2170-2183.
• Metz CE (1978) Basic principles of ROC analysis. Seminars in Nuclear Medicine 8:283-298.
• 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.