Duke University Medical Center Library Online

Sensitivity, Specificity Likelihood Ratios Nomogram

Diagnosis:

	Disease Present	Disease Absent	Totals
Test Positive	a	b	a + b
Test Negative	c	d	c + d
Totals	a + c	b + d	a + b + c + d

2 X 2 Table Calculator

Click here to calculate the Likelihood ratio using the sensitivity and specificity.

Sensitivity = a / (a + c)
The proportion of people with the target disorder who have a positive test. For a test to be useful in ruling out a disease, it must have a high sensitivity.

Specificity = d/(b + d)
The proportion of people without the target disorder who have a negative test. For a test to be useful at confirming a disease, it must have a high specificity.

The Likelihood Ratio (LR) is the likelihood that a given test result would be expected in a patient with the target disorder compared to the likelihood that the same result would be expected in a patient without the target disorder.

Likelihood ratio - positive test result = sensitivity / (1 - specificity) or a/(a + c) / b/(b +d)
The LR of a positive test tells us how well a positive test result does by comparing its performance when the disease is present compared with when it is absent. The best test to use for ruling in a disease is the one with the largest likelihood ratio of a positive test.

Likelihood ratio - negative test result = (1 - sensitivity) / specificity or c/(a + c) / d/(b + d)
The LR of a negative test tells us how well a negative test result does by comparing its performance when the disease is absent compared with when it is present. The better test to use to rule out disease is the one with the smaller likelihood ratio of a negative test.

The LR is a way to incorporate the sensitivity and specificity of a test into a single measure. Since sensitivity and specificity are fixed characteristics of the test itself, the likelihood ratio is independent of the prevalence of the disease in the population. (This is not true for positive predictive value.)

LR is a ratio of likelihoods (or probabilities) for a given test. The first is the probability that a given test result occurs among people with disease. The second is the probability that the same test result occurs among people without disease. The ratio of these 2 probabilities (or likelihoods) is the LR. It measures the power of a test to change the pre-test into the post-test probability of a disease being present.

How much do LRs change disease likelihood?

LRs greater than 10 or less than 0.1	cause large changes
LRs 5 - 10 or 0.1 - 0.2	cause moderate changes
LRs 2 - 5 or 0.2 - 0.5	cause small changes
LRs less than 2 or greater than 0.5	cause tiny changes
LRs = 1.0	cause no change at all

Finding articles about a diagnostic test:

explode "sensitivity and specificity" (subject heading)
diagnosis (subheading)

References:

Sackett, D. Evidence-Based Medicine: How to Practice and Teach EBM. 2nd ed. (CD-ROM) Churchill Livingstone, 2000.
ACP Journal Club 1994 Jul-Aug:A10-A12.

Nomogram for interpreting diagnostic test results (Likelihood ratio)

In this nomogram, a straight line drawn from a patient's pre-test probability of disease (which is estimated from experience, local data or published literature) through the LR for the test result that may be used, will point to the post-test probability of disease.

Adapted from Fagan TJ. Nomogram for Bayes's theorem N Engl J Med Jul 31, 1975; 293(5):257. From Jaeschke, R. Users' guide to the medical literature: III. How to use an article about diagnostic test: B. What are the results and will they help me in caring for my patients? JAMA Mar 2, 1994; 271(9):703-7 [Permission granted to reproduce image.]

Interactive Nomogram from Centre for Evidence Based Medicine
Nomogram for using Likelihood Ratios (LRs) to convert pre-test probabilities into post-test probabilities for diagnostic test results with a known LR. [Works best in IE with Shockwave 10.1.]

References:

Sackett, DL. Evidence-Based Medicine: How to Practice and Teach EBB. 2nd ed. (CD-ROM) Churchill Livingstone, 2000.
Richardson, WS. Where Do Pretest Probabilities Come From? Evidence-Based Medicine May-June 4:68-69.
Gilbert, R. Assessing Diagnostic and Screening Tests: Part 1. Concepts. Western Journal of Medicine June 2001 174:405-409.
Frohna, JG. Fostering the Efficient, Effective Use of Evidence-based Medicine in the Clinic. 2nd ed. University of Michigan. March 2001.
Raglans, RA. Studying a Study and Testing a Test. 4th ed. Lippincott Williams & Wilkins, 2000.
ACP Journal Club 1994 Sept-Oct:A10-A12