The Test is Not the Truth: One Week in the Lonely Life of a Bayesian Clinician

DAH from GPA or CPE/ESRD?

If there is one thing you should remember about clinical decision making it is this:  the test is not the truth.  A diagnostic test raises or decreases the prior or pre-test probability (PTP) of the disease under consideration.  The amount of increase or decrease in probability with a positive or negative test depends on the starting probability and the likelihood ratio of the test.  (LR+ = sensitivity/1-specificity; LR- = 1-sensitivity/specificity).  If we don't attend to the PTP of disease, serious diagnostic errors and therapeutic misadventures may result.  This is especially true when a low PTP disease is diagnosed on the basis of a test with poor sensitivity and specificity (and a LR not much greater than 1 or 2 or even 4 or 5).  Several examples of this came up a while back.

A woman presented with thunderclap headache and had recurrent seizures during initial evaluation.  A differential diagnosis was formulated and it included PRES (posterior reversible encephalopathy syndrome) with a PTP of about 20%.  Subarachnoid hemorrhage was excluded with CT and LP and the PTP of PRES rose to about 40% (since it occupied some of the probability space previously occupied by SAH once the latter was excluded.)  The subsequent MRI images were consistent with PRES.  Nonetheless, a vascular MRI was ordered to "exclude the possibility of cerebral vasculitis".  The problems are twofold.  First, the probability of PRES is now on the order of 70% if the sensitivity and specificity of MRI are on the order of 80%, and it is 85% if sensitivity and specificity are each 90%.  (Go ahead and plug some numbers into the calculator on the sidebar of the blog.)  This probability meets or exceeds the probability threshold to both consider the diagnosis made, and to take action based on it.  In this case inaction and supportive care are indicated.  Even if a vascular MRI were consistent with cerebral vasculitis, which has a PTP an order of magnitude or more less than PRES, the diagnosis is still PRES.  The truth is not in the test, the truth is in the rationally considered diagnostic process of which the test is one part.

Bayes' Theorem Explained, No Math Required

I was asked by a medical student to explain Bayes' Theorem.  This blog is about lack of common sense in medicine, so it follows that education about first principles will contribute to uncommon sense, and I will oblige.

Bayes' theorem is simply a long or holistic way of looking at the world, one which is more in keeping with reality than the competing frequentist approach.  A Bayesian (a person who subscribes to the logic of Bayes' Theorem) looks at the totality of the data, whereas a frequentist is concerned with just a specific slice of the data such as a test or a discrete dataset.  Frequentist hypothesis testing is where we get P-values from.  Frequentists are concerned with just the data from the current study.  Bayesians are concerned with the totality of the data, and they do meta-analyses, combining data from as many sources as they can.  (But alas they are still reluctant frequentists, because they insist on combining only frequentist datasets, and shun attempts to incorporate more amorphous data such as "what is the likelihood of something like this based on common sense?")

Consider a trial of orange juice (OJ) for the treatment of sepsis.  Suppose that 300 patients are enrolled and orange juice reduces sepsis mortality from 50% to 20% with P<0.001.  The frequentist says "if the null hypothesis is true and there is no effect of orange juice in sepsis, the probability of finding a difference as great or greater than what was found between orange juice and placebo is less than 0.001; thus we reject the null hypothesis."  The frequentist, on the basis of this trial, believes that orange juice is a thaumaturgical cure for sepsis.  But the frequentist is wrong.

Specious Ideas: Trending Troponins and Chasing Lactates

I want to use this post to discuss an article in this week's JAMA called Lactate in Sepsis, which I think is fatally flawed and misleading.  But first...

Several years ago on the Medical Evidence Blog I talked about cardiac troponins and how their use is often misguided.  Not long after this post a young woman e-mailed me to describe a diagnostic and therapeutic misadventure that ensued after an abnormal troponin was "discovered" during work-up for a urological problem.  This led to transfer to another facility via ambulance for a cardiac catheterization with multiple complications including stroke.  It was a sad and unfortunate tale, but I fear it is not too uncommon.

Troponin, like all tests, needs to be ordered on the basis of a clinical suspicion (prior probability) that, when combined with the likelihood ratio of the test using Bayes Theorem (see calculator on the right of the blog), results in a posterior probability of disease that crosses a decision threshold.  (Because of the woeful inadequacy of medical education in regards to basic decision theory, I would not be surprised if the majority of physicians cannot correctly describe priors, Bayes, posteriors, or decision thresholds.  But this is old news, and beyond the scope of this post.)  The low prior probability of acute coronary syndromes in critically ill patients with non-cardiac primary diagnoses (PE, AECOPD, sepsis, etc.) leads me to list "non-specific troponin increase in the setting of critical illness" as a problem (an artificially begotten one) in my assessments after colleagues regretfully order tests that should never have been ordered.  And I will defer discussion of all those d-dimers and the needless CT angiograms they engender, lest I descend into unmitigated belligerence.