Likelihood ratio

Authors
Affiliations

Doctor of Physical Therapy

B.S. in Kinesiology

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.

Citation

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