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!

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!

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.

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

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

2. Calculate the pre-test odds

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

3. Calculate the post-test odds.

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

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

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

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.

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. 🎉

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. 🎂