Likelihood ratio

Authors

Affiliations

Nate Yomogida, B.S., SPT

Doctor of Physical Therapy

B.S. in Kinesiology

Chloë Kerstein, B.S., SPT

Doctor of Physical Therapy

B.A. in Neuroscience

The likelihood ratio is defined as the probability of obtaining a positive test result in a patient with the disease divided by the probability of obtaining a positive test result in a patient without the disease¹.

Calculation

\[ \textrm{+LR} = \frac{(\textrm{Probability of obtaining a positive test in a patient with the disease})}{\textrm{Probability of attaining a positive test in a person without the disease}} \]

\[ \textrm{+LR} = \frac{Sensitivity}{1 - Specificity} = \frac{(\textrm{True Positive Rate})}{(\textrm{False Positive Rate})} \]

Example

• Sensitivity: 82%
• Specificity: 96.3%

\[ \textrm{+LR} = \frac{Sensitivity}{1 - Specificity} = \frac{0.82}{1-0.963} = 22.2 \]

Since the +LR is “22.2”, this indicates that a person with the condition is 22.2x more likely to test positive than someone without the disease¹.

Likelihood ratio vs Sensitivity

The likelihood ratio is defined as the probability of obtaining a positive test result in a patient with the disease divided by the probability of obtaining a positive test result in a patient without the disease¹.

Sensitivity is the probability of obtaining a positive test result in a patient with the disease¹.

References

1.

Motulsky H. Intuitive Biostatistics: A Nonmathematical Guide to Statistical Thinking. 4th ed. Oxford University Press; 2018.