Establishing a Prior

It is one of the worst places you can find yourself as an emergency clinician: sitting right on the fence and feeling stuck between two choices you don't like. Are going to subject a patient to a large and unnecessary work up. Or are you going to ignore the voice in your head and hope you are not wrong in deferring testing.

A previously healthy 33 year old walks into your ED. No history of migraines. No trauma. They tell you:

"This headache started during a stressful meeting a few hours ago. It's different from anything I've had before. It's just pounding and my neck feels tight."

They're sitting up, well-appearing, vitals stable except for a slightly elevated blood pressure. No focal neuro deficits. They're worried—but not panicked. You find yourself wondering:

"Is this a tension headache—or the start of a nightmare?"

You think to yourself "well, there was no syncope…but it was sudden onset. Does a stressful meeting count as exertion?" As you run through these risk factors in your head, you are performing a calculation that dates back to 1763, described by a quiet English minister named Thomas Bayes.

Thomas Bayes' theorem in plain english states:

Your current suspicion multiplied by the strength of the evidence brings you to your new, updated suspicion.

More formally:

P(A∣B)=P(B)P(B∣A)⋅P(A)​

Where:

• P(A) is your **pre-test probability** — your initial suspicion
• P(B|A) is the test's performance — how likely you are to see that evidence if your suspicion is correct
• P(A|B) is your **post-test probability** — what you now believe after considering the evidence

You don't need to solve the math in real time—and most of us don't. But it helps to know that this is the logic underneath our clinical decisions. If you want to get a little sharper with it, the calculators on Bayes Razor can help you quickly plug in your gestalt and see how it shifts with key findings, bringing structure to what we're already doing intuitively.

Back to our patient. As you walk into the darkened room a very uncomfortable patient holding their forehead turns their head to the side to say hello when you greet them. "Maybe but probably not a SAH" your gut tells you. And this is the point where you should be asking yourself, how do I turn this feeling into "P(A)"

A good starting point is with an established prevalence. For example, the rate of SAH in patients presenting to the ED with headache is less than 1% -lets call it 0.3% since the actual number is a bit unclear from the literature¹. So, if you think that there is a 10% chance this patient has a bleed, you are saying that they are 33 times more likely than the average patient presenting with a headache. If that's what you think - great, start there. If that seems too high now that you know the actual prevalence you can adjust down and refine your prior probability. Adjusting your prior probability with testing/risk factors is covered in other essays, for now lets focus on establishing the best starting point possible.

Your past experiences matter—and they absolutely influence how you build a prior. Maybe you've had a patient who looked just like this one and turned out to have a devastating bleed. That memory sticks, and it might push your estimate higher. Or maybe you just read this and walked in to see a headache patient. Availability bias will likely increase your suspicion without you knowing. Perhaps the triage nurse is daring you to succumb to anchoring bias by writing "patient arrives with migraine x 2 hours." Biases can push your prior probability higher or lower than where you would objectively place it. It is very important to be aware of your biases and continually work on debiasing strategies.

Every decision you make starts with a hunch. Pre-test probability isn't just academic jargon; it's the clinical scaffolding for everything that comes next. The better your starting point, the better your judgment will hold up under pressure. Trust your gut, but train it. And when it counts, take the extra second to ask: "How likely do I really think this is?" taking into account prevalence, past experience, and potential biases.

**1.** Thunderclap Headache Syndrome Presenting to the Emergency Department: An International Multicentre Observational Cohort Study.

Roberts T, Horner DE, Chu K, et al.

Emergency Medicine Journal : EMJ. 2022;39(11):803-809. doi:10.1136/emermed-2021-211370.