Post-Test Probability Calculator
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:
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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)
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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)
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Likelihood ratio — we recognize two different types of likelihood ratios.
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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)
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The negative likelihood ratio (LR–) tells us: What are the chances that a healthy person will test negative?
negative likelihood ratio = (1 – sensitivity) / specificity
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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.
- 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.
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Calculate the pre-test odds
pre-test odds = prevalence / (1 – prevalence)
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Calculate the post-test odds.
post-test odds = pre-test odds × likelihood ratio
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..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:
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Find the prevalence (pre-test probability).
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Transform the probability to odds, using the equation featured in our post-test probability calculator:
pre-test odds = prevalence / (1 – prevalence)
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Hey, you're done. 🎉
How do I calculate post-test odds?
To calculate the post-test odds, follow these steps:
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Find the prevalence (pre-test probability).
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Calculate the pre-test odds using the equation:
pre-test odds = prevalence / (1 – prevalence)
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Find the desired likelihood ratio.
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Use the very last equation:
post-test odds = pre-test odds × likelihood ratio
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That'd be it! It's all ready. 🎂