PostTest Probability Calculator
The posttest 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 pretest and posttest 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 pretest 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 pretest and posttest 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 pretest probability (prevalence)?
It's much easier than it seems! 😱
Let's take a look at the equation we used in our posttest 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 posttest probability?
We'll need a few steps and up to 5 equations.
 Find out the prevalence (pretest probability) and the likelihood ratio.
💡 If you need to calculate any of these variables, check out the specific tutorials featured in Omni's posttest probability calculator.

Calculate the pretest odds
pretest odds = prevalence / (1 – prevalence)

Calculate the posttest odds.
posttest odds = pretest odds × likelihood ratio

..and finally, compute the posttest probability!
posttest probability = posttest odds / (1 + posttest odds)
🙋 Want to discover more? Check the Bayes theorem calculator!
FAQ
What's the difference between the pretest odds and pretest probability?
Pretest 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, pretest 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 pretest odds?
That'll be quick:

Find the prevalence (pretest probability).

Transform the probability to odds, using the equation featured in our posttest probability calculator:
pretest odds = prevalence / (1 – prevalence)

Hey, you're done. 🎉
How do I calculate posttest odds?
To calculate the posttest odds, follow these steps:

Find the prevalence (pretest probability).

Calculate the pretest odds using the equation:
pretest odds = prevalence / (1 – prevalence)

Find the desired likelihood ratio.

Use the very last equation:
posttest odds = pretest odds × likelihood ratio

That'd be it! It's all ready. 🎂