### Abstract

Test-performance characteristics can be derived from a simple 2x2 table displaying the dichotomous relationship between a positive or negative test result and the presence or absence of a target disorder. Sensitivity and specificity, including a summary display of their reciprocal relationship as a receiver operating characteristics curve, are relatively stable test characteristics. Unfortunately, they represent an inversion of customary clinical logic and fail to tell us precisely what we wish to know. Predictive values, on the other hand, provide us with the requisite information but - because they are vulnerable to variation in disease prevalence - are numerically unstable. Likelihood ratios (LRs), in contrast, combine the stability of sensitivity and specificity to provide an omnibus index of test performance far more useful than its constituent parts. Application of Bayes' theorem to LRs produces the following summary equation: Clinically estimated pretest odds of diseasexLR=Posttest odds of disease. This simple equation illustrates a concordance between the mathematical properties of likelihood ratios and the central strategy underlying diagnostic testing: the revision of disease probability.

Original language | English (US) |
---|---|

Pages (from-to) | 391-397 |

Number of pages | 7 |

Journal | Annals of Emergency Medicine |

Volume | 31 |

Issue number | 3 |

DOIs | |

State | Published - 1998 |

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### ASJC Scopus subject areas

- Emergency Medicine

### Cite this

**Clinical utility of likelihood ratios.** / Gallagher, E. John.

Research output: Contribution to journal › Article

*Annals of Emergency Medicine*, vol. 31, no. 3, pp. 391-397. https://doi.org/10.1016/S0196-0644(98)70352-X

}

TY - JOUR

T1 - Clinical utility of likelihood ratios

AU - Gallagher, E. John

PY - 1998

Y1 - 1998

N2 - Test-performance characteristics can be derived from a simple 2x2 table displaying the dichotomous relationship between a positive or negative test result and the presence or absence of a target disorder. Sensitivity and specificity, including a summary display of their reciprocal relationship as a receiver operating characteristics curve, are relatively stable test characteristics. Unfortunately, they represent an inversion of customary clinical logic and fail to tell us precisely what we wish to know. Predictive values, on the other hand, provide us with the requisite information but - because they are vulnerable to variation in disease prevalence - are numerically unstable. Likelihood ratios (LRs), in contrast, combine the stability of sensitivity and specificity to provide an omnibus index of test performance far more useful than its constituent parts. Application of Bayes' theorem to LRs produces the following summary equation: Clinically estimated pretest odds of diseasexLR=Posttest odds of disease. This simple equation illustrates a concordance between the mathematical properties of likelihood ratios and the central strategy underlying diagnostic testing: the revision of disease probability.

AB - Test-performance characteristics can be derived from a simple 2x2 table displaying the dichotomous relationship between a positive or negative test result and the presence or absence of a target disorder. Sensitivity and specificity, including a summary display of their reciprocal relationship as a receiver operating characteristics curve, are relatively stable test characteristics. Unfortunately, they represent an inversion of customary clinical logic and fail to tell us precisely what we wish to know. Predictive values, on the other hand, provide us with the requisite information but - because they are vulnerable to variation in disease prevalence - are numerically unstable. Likelihood ratios (LRs), in contrast, combine the stability of sensitivity and specificity to provide an omnibus index of test performance far more useful than its constituent parts. Application of Bayes' theorem to LRs produces the following summary equation: Clinically estimated pretest odds of diseasexLR=Posttest odds of disease. This simple equation illustrates a concordance between the mathematical properties of likelihood ratios and the central strategy underlying diagnostic testing: the revision of disease probability.

UR - http://www.scopus.com/inward/record.url?scp=0031896226&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031896226&partnerID=8YFLogxK

U2 - 10.1016/S0196-0644(98)70352-X

DO - 10.1016/S0196-0644(98)70352-X

M3 - Article

C2 - 9506499

AN - SCOPUS:0031896226

VL - 31

SP - 391

EP - 397

JO - Annals of Emergency Medicine

JF - Annals of Emergency Medicine

SN - 0196-0644

IS - 3

ER -