This is a confusing topic that is at times difficult to wrap one’s head around. We likely created some confusion around the topic during lecture so here is a stepwise are the key points. So, let’s walk through.
When do I use Bayesian Statistics?
Believe it or not, you likely already use them on a day to day basis–you probably just don’t quantify them as much. Every time you make your differential diagnosis, you determine what you think the likelihood is of a particular diagnosis (ie – pretest probability). You make decisions on which test to order all the time based on that. Then, you use the sensitivity and specificity of the test to determine if that diagnosis is ruled out or if you want to pursue another test (ie – post test probability).
What are Bayesian Statistics?
First, let’s go over some definitions. Don’t memorize all of this right off the bat. Feel free to refer back to it.
Pre-test Probability: probability of a patient having a particular diagnosis. Sum of all pretest probabilities on the differential is 1.
Post-test Probability: probability of a patient having a particular diagnosis, adjusted for the results of the test performed.
Likelihood Ratio (LR): the ratio that changes our initial estimate of the likelihood that a patient has a condition (ie – pretest probability) to a more accurate estimate (ie – post test probability)
Positive LR: likelihood ratio for a positive test result
= Sensitivity / (1 – Specificity)
aka: probability of a aka: probability of having a positive test on a patient with a disease / probability of having a positive test in a patient without the disease
Negative LR: likelihood ratio for a negative test result
= (1 – Sensitivity) / Specificity
aka: probability of having a negative test in a patient with a disease / probability of a negative test in a patient without the disease
Bayes theorem merely states that the post test probability is affected by the pre-test probability and the likelihood ratio of the test you performed.
How do I use Bayesian Statistics?
Now that we’ve gone over the definitions, let’s walk through how you’d use Bayesian Statistics when diagnosing a patient on the floors.
1. Assess your pretest probability of the patient having Disease X. Two Primary Methods:
Use your gestalt. That is, your clinical judgment.
Note: This is susceptible to bias (eg – priming of recent experiences, traumatic/emotional experiences, insufficient weight on new evidence) and random error.
Evidence. Complementary Approaches
Use Clinical Decision Rules / Prediction Rules
Ex: Well’s, C spine rules, Ottawa foot and ankle rules
Find research with patients with the same clinical problem. These studies list the frequency of diagnoses and odds ratios based on certain characteristics.
2. Find or calculate the Likelihood Ratio.
Find in the literature or in UptoDate the likelihood ratio of your test being positive (+LR) or negative (-LR). If you cannot find this, the sensitivity and specificity can easily be used to calculate it (see calculations above)
3. Calculate your Post-Test Probability.
This is likely where the confusion arose in lecture. We didn’t have time to put up the Fagan Nomogram during lecture but I’m sure it will help elucidate.
In a nutshell, the left hand side is the pretest probability. In the center you’ll find the likelihood ratio. On the right is the post-test probability.
To use the nomogram, take a ruler and line it up with your pre-test probability and the calculated likelihood ratio. Draw a line into the third column to find your post-test probability!
See examples below!
Example: Pulmonary Embolism
Check back soon!
JAMA User’s Guide to the Medical Literature: Essentials of Evidence Based Clinical Practice