# Post-Test Probability Calculator

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Anna Szczepanek, PhD
Last updated: Jun 05, 2023

The post-test probability calculator does not only supply you with its titular calculation; it also computes the pretest probability and works with the likelihood ratio formulas.

This tool will shortly explain all the magic behind the pre-test and post-test probability / odds calculations — we'll discuss all the little aspects connected to the subject, from the beginning to the end. 🧙

So, hop on board this Bayesian calculator — it's time to do some math!

## Sensitivity, specificity, and likelihood ratio formulas

💡 Don't forget to check our sensitivity and specificity calculator and accuracy calculator. They're both tools designed for this very specific topic.

Let's get through all the basic descriptions:

• Sensitivity — the number of people with the disease who received a positive test result, compared to the total number of people with the disease (regardless of test status). Measures how good the test is when we're looking for the disease.

sensitivity = TP / (TP + FN)

• Specificity — the number of people without the disease who received a negative test result, compared to the total number of people without the disease. Measures how good the test is when we want to exclude the disease.

specificity = TN / (FP + TN) • Likelihood ratio — we recognize two different types of likelihood ratios.

• The positive likelihood ratio (LR+) answers the question: What are the chances that a sick person will test positive?

positive likelihood ratio = sensitivity / (1 – specificity)

• The negative likelihood ratio (LR–) tells us: What are the chances that a healthy person will test negative?

negative likelihood ratio = (1 – sensitivity) / specificity

• Prevalence — also called the pre-test probability. We usually understand it as the percentage of people in a population who suffer from a certain disease.

Having discussed the basics, we are now ready to deal with the pre-test and post-test probability. Let's go!

💡 Despite their negative and positive names, both likelihood ratios can only take values greater than or equal to 0.

## How do I calculate pre-test probability (prevalence)?

It's much easier than it seems! 😱

Let's take a look at the equation we used in our post-test probability calculator:

prevalence = (TP + FN) / (TP + FN + FP + TN)

Where:

• TP stands for true positive cases. The patient has the disease and tested positive.
• FN is false negative. The patient has the disease, yet tested negative.
• TN is true negative. The patient does not have the disease and tested negative.
• FP is false positive. The patient does not have the disease, yet tested positive.

## How do I calculate post-test probability?

We'll need a few steps and up to 5 equations.

1. Find out the prevalence (pre-test probability) and the likelihood ratio.

💡 If you need to calculate any of these variables, check out the specific tutorials featured in Omni's post-test probability calculator.

1. Calculate the pre-test odds

pre-test odds = prevalence / (1 – prevalence)

2. Calculate the post-test odds.

post-test odds = pre-test odds × likelihood ratio

3. ..and finally, compute the post-test probability!

post-test probability = post-test odds / (1 + post-test odds)

🙋 Want to discover more? Check the Bayes theorem calculator!

## FAQ

### What's the difference between the pre-test odds and pre-test probability?

Pre-test probability is also called prevalence — it tells us how often a specific thing occurs in different situations.

E.g., The prevalence of hypertension is 29% — every 29 out of 100 people suffer from hypertension.

On the other hand, pre-test odds inform us about the ratio of how often the event occurs, versus how often the event doesn't occur.

E.g., The odds of having hypertension are 3.5 — you're over three times more likely to develop hypertension than not to develop it.

### How do I calculate pre-test odds?

That'll be quick:

1. Find the prevalence (pre-test probability).

2. Transform the probability to odds, using the equation featured in our post-test probability calculator:

pre-test odds = prevalence / (1 – prevalence)

3. Hey, you're done. 🎉

### How do I calculate post-test odds?

To calculate the post-test odds, follow these steps:

1. Find the prevalence (pre-test probability).

2. Calculate the pre-test odds using the equation:

pre-test odds = prevalence / (1 – prevalence)

3. Find the desired likelihood ratio.

4. Use the very last equation:

post-test odds = pre-test odds × likelihood ratio

5. That'd be it! It's all ready. 🎂

Łucja Zaborowska, MD, PhD candidate
Prevalence
Do you know the prevalence?
Yes
Prevalence
%
Likelihood ratio
Do you know the likelihood ratio?
Yes
Likelihood ratio (LR)
Results
Post-test probability
%
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