# Post-Test Probability Calculator

Determines the probability of the presence of a condition after a diagnostic test.

Refer to the text below the tool for more information about the formulas used.

The post-test probability is used to define the proportion of patients testing positive who truly have the disease. This measure is similar to the positive predictive value but in contrast to the former, also includes a patient-based probability of having the disease.

`Pre-test odds = Prevalence / (1 – Prevalence)`

`Post-test odds = Pre-Test Odds x LR(r)`

`Post-test probability = Post-test odds / (1 + Post-test odds)`

Where LR(r) = likelihood ratio

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**Steps on how to print your input & results:**

1. Fill in the calculator/tool with your values and/or your answer choices and press Calculate.

2. Then you can click on the Print button to open a PDF in a separate window with the inputs and results. You can further save the PDF or print it.

Please note that once you have closed the PDF you need to click on the Calculate button before you try opening it again, otherwise the input and/or results may not appear in the pdf.

## Determining Post-Test Probability

The post-test probability may be defined as the proportion of patients testing positive who truly have the disease. This measure is similar to the positive predictive value but in contrast to the former, also includes a patient-based probability of having the disease.

To calculate post-test probability one can start from pre-test probability, also known as prevalence (P), which is used to determine the pre-test odds (the odds that the patient has the target condition, before the test is carried out):

`Pre-test odds = Prevalence / (1 – Prevalence)`

`Post-test odds = Pre-Test Odds x LR(r)`

`Post-test probability = Post-test odds / (1 + Post-test odds)`

Where LR(r) is the Likelihood ratio.

If prevalence is unknown, it may be determined from:

`Prevalence = (TP + FN) / (TP + FN + FP + TN)`

Where:

- TP = true positive;
- FN = false negative;
- FP = false positive;
- TN = true negative.

The likelihood ratio is defined as the probability of a given test result in a patient with the target condition divided by the probability of that same result in a person without the target condition. Likelihood ratios use sensitivity and specificity to determine two things, first how useful a diagnostic test is and second, how likely is that a patient has a disease.

The table below summarizes one suggested way to interpret likelihood ratios:

LR(r) |
Interpretation – relative to likelihood of disease |

>10 | Large and often conclusive increase |

5 – 10 | Moderate increase |

2 – 5 | Small increase |

1 – 2 | Minimal increase |

1 | No change |

0.5 – 1 | Minimal decrease |

0.2 – 0.5 | Small decrease |

0.1 – 0.2 | Moderate decrease |

<0.1 | Large and often conclusive decrease |

## References

Perera R, Heneghan C. Making sense of diagnostic test likelihood ratios. ACP J Club. 2007; 146(2): A8-9.

Parikh R, Parikh S, Arun E, Thomas R. Likelihood ratios: clinical application in day-to-day practice. Indian J Ophthalmol. 2009; 57(3):217-21.

Specialty: Research

Article By: Denise Nedea

Published On: October 10, 2020

Last Checked: October 10, 2020

Next Review: October 10, 2025