AUTHOR AND EDITOR INFORMATION

Section 1 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

INTRODUCTION

Section 2 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

Diagnostic tests help physicians revise disease probability for their patients. All tests should be ordered by the physician to answer a specific question. The 5 main reasons for a diagnostic test are as follows:

• Establish a diagnosis in symptomatic patients. For example, an ECG to diagnose ST-elevation myocardial infarction (STEMI) in patients with chest pain.
• Screen for disease in asymptomatic patients. For example, a prostate-specific antigen (PSA) test in men older than 50 years.
• Provide prognostic information in patients with established disease. For example, a CD4 count in patients with HIV.
• Monitor therapy by either benefits or side effects. For example, measuring the international normalized ratio (INR) in patients taking warfarin.
• A test may be performed to confirm that a person is free from a disease. For example, a pregnancy test to exclude the diagnosis of ectopic pregnancy.

The criterion (reference) standard test definitively decides either presence or absence of a disease. Examples of criterion standard tests include pathological specimens for malignancies and pulmonary angiography for pulmonary embolism. However, criterion standard tests routinely come with drawbacks; they are usually expensive, less widely available, more invasive, and riskier. These issues usually compel most physicians to choose other diagnostic tests as surrogates for their criterion standard test. 

For example, venography, the criterion standard for vein thrombosis, is an invasive procedure with significant complications including renal failure, allergic reaction, and clot formation. These risks make venography less desirable than the alternative diagnostic test—venous duplex ultrasonography. The price most diagnostic tests pay for their ease of use compared with their criterion standard is a decrease in accuracy. How to account for this trade-off between diagnostic accuracy and patient acceptability is the subject of this article.

PRETEST AND POSTTEST PROBABILITY

Section 3 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

Every clinical encounter begins with an initial clinical impression, a subjective pretest probability of disease. The ultimate goal of all diagnostic testing is to refine this pretest probability to the point where the physician can confidently make a treat or no-treat decision. Each diagnostic test whether it is a symptom, sign, laboratory, or radiological examination results in a change in the physician’s probability of disease, the posttest probability. The degree to which a diagnostic test increases or decreases the probability of disease from pretest to posttest represents the clinical utility of the test as measured by its operating characteristics.

DEFINITIONS AND CALCULATIONS

Section 4 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

Clinical studies of diagnostic tests measure the accuracy of the test against its criterion standard.  

Table 1. Criterion Standard

Table 2. Definition of Terms

SENSITIVITY AND SPECIFICITY

Section 5 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

Different diagnostic tests for the same disease often trade sensitivity for specificity or vice versa. In general, the more sensitive a test is for a disease, the higher its false-positive rate, lowering its specificity. A test with a higher specificity will usually sacrifice sensitivity by increasing its false-negative rate. This makes a highly sensitive test ideal for a screening examination. While, highly specific tests are best in a confirmatory role.

Sensitivity and specificity are calculated vertically in a 2 X 2 table. Sensitivity is measured in patients definitively diagnosed with the disease, whereas specificity is only a function of those free of disease. Sensitivity contains no information about false-positive results, and specificity does not account for false-negative results. This limits the applicability of sensitivity and specificity in predicting disease when the physician is uncertain about the diagnosis. For example, a positive test result with 90% sensitivity does not predict a 90% probability of disease in a patient.

The mnemonics SnOut and SpIn provide some guidelines on how to interpret sensitivity and specificity for an individual patient. SnOut helps physicians to remember that a highly Sensitive test with a negative result is good at ruling-out the disease. SpIn reminds physicians that a highly Specific test with a positive result is good at ruling-in the disease. 

PREDICTIVE VALUES

Section 6 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

To estimate the posttest probability for an individual patient another statistic is needed. Predictive values are horizontally calculated operating characteristics, which incorporate both false-positive and false-negative results into disease probability. The positive predictive value (PPV) is the probability of a patient actually having the disease if the test result is positive. The probability of the patient being free of the disease after a negative test result is given by the negative predictive value (NPV).

Unfortunately, predictive values are not stable characteristics of diagnostic tests. The predictive values are dependent on the prevalence of disease among the population of interest. The same diagnostic test will have varying predictive values in different populations. Without knowing the disease prevalence in the population of interest, predictive values cannot be accurately estimated.

For example, chest CT angiography with venous runoff (CTA VN) has a sensitivity of 90% and specificity of 95%. In a patient with a high probability (78.4%) of a pulmonary embolism according to the Wells’ criteria, the CTA VN would produce a PPV of 99% and NPV of 72%. The same test given to a patient with a much lower pretest probability of pulmonary embolism (3.4%) would result in a PPV of 39% and NPV of 99%.

BAYES' THEOREM AND LIKELIHOOD RATIOS

Section 7 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

Bayes’ Theorem

Adapting a theory of conditional probability from the 18^th century statistician Thomas Bayes solves the problem of calculating posttest disease probability. This theory allows pretest probability to be separated from a term that describes the strength of the diagnostic test—likelihood ratio.

Bayes' theorem:  Posttest Odds = Pretest Odds X Likelihood Ratio

Likelihood Ratio

Likelihood ratios are proportions of probabilities. A likelihood ratio for a positive test result (LR+) is the ratio of the true positive rate (sensitivity) divided by the false-positive rate (1 - specificity). LR+ then can be thought of how much more likely the patient is to actually have the disease after a positive test result. 

Dividing the false-negative rate (1 - sensitivity) by the true negative rate (specificity) gives the likelihood ratio for a negative test result and provides the strength of a negative test result in convincing the physician the patient is free of disease.

Since likelihood ratios are calculated from sensitivity and specificity, LRs are stable operating test characteristics, unaffected by prevalence of disease.

A LR of 1.0 is a useless test because this result fails to change the opinion of probability of disease from pretest to posttest. LR+ are always greater than 1.0; the larger the number, the more likely is the patient to have the disease after a positive test result. LR- are always less than 1.0, with the smaller numbers signifying a lower risk for disease than pretest estimates.

Table 3.   Strength of the Test by Likelihood Ratio

USING BAYES' THEOREM

Section 8 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

Bayes' theorem:  Posttest Odds = Pretest Odds X Likelihood Ratio

ACKNOWLEDGMENTS

Section 9 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

The authors and editors of eMedicine gratefully acknowledge the contributions of previous author, Theodore Gaeta, DO, to the development and writing of this article.

MULTIMEDIA

Section 10 of 11  

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

Media file 1:  Fagan nomogram.
	View Full Size Image
Media type:  Chart

REFERENCES

Section 11 of 11

• Authors and Editors
• Introduction
• Pretest and Posttest Probability
• Definitions and Calculations
• Sensitivity and Specificity
• Predictive Values
• Bayes' Theorem and Likelihood Ratios
• Using Bayes' Theorem
• Acknowledgments
• Multimedia
• References

• Fagan TJ. Letter: Nomogram for Bayes theorem. N Engl J Med. Jul 31 1975;293(5):257. [Medline].
• Iannaccone R, Laghi A, Catalano C, Mangiapane F, Lamazza A, Schillaci A, et al. Computed tomographic colonography without cathartic preparation for the detection of colorectal polyps. Gastroenterology. Nov 2004;127(5):1300-11. [Medline].
• Mayor D. Essential Evidenced-Based Medicine. United Kingdom: Cambridge University Press; 2004:Chap 20-26.
• Stein PD, Fowler SE, Goodman LR, Gottschalk A, Hales CA, Hull RD, et al. Multidetector computed tomography for acute pulmonary embolism. N Engl J Med. Jun 1 2006;354(22):2317-27. [Medline].
• Wells PS, Anderson DR, Rodger M, Ginsberg JS, Kearon C, Gent M, et al. Derivation of a simple clinical model to categorize patients probability of pulmonary embolism: increasing the models utility with the SimpliRED D-dimer. Thromb Haemost. Mar 2000;83(3):416-20. [Medline].

Article Last Updated: Nov 26, 2007