Bayes’ Theorem, Medical Diagnostics and Nomograms

BayesTheoremNomogram4Last month Joe Marasco, Leif Roschier and I published an article on Bayes’ Theorem in The UMAP Journal that included a foldout of large circular nomograms for calculating the results from it. The article, Doc, What Are My Chances?, can be freely downloaded from the Modern Nomograms webpage, which also offers commercial posters of the two nomograms used to calculate Bayes’ Theorem (one for common cases and one optimized for calculating rare cases).

Bayes’ Theorem is a statistical technique that calculates a final posttest probability based on an initial pretest probability and the results of a test of a given discriminating power. Thomas Bayes (1701-1761) first suggested this method, and Pierre-Simon Laplace published it in its modern form in 1812. It has generated quite a bit of controversy from frequentists (who work from a null hypothesis rather than an initial posited probability), but this technique has become much more popular in modern times.

Among many other applications, this is a common technique used in evidence-based medicine, in which statistical methods are used to analyze the results of diagnostic tests. For example, a diagnostic test might have a sensitivity of 98%, or in other words, the test will return a positive result 98% of the time for a person having that disease. It might have a specificity of 95%, which means it will return a negative result 95% of the time for a person who does not have the disease. For a disease that has a prevalence (a pretest probability) of 1% in the general population, Bayes’ Theorem provides, say, the probability of a person having the disease with a positive test result. Pretty darn likely, right? Well, it turns out it’s about 16% because the false positives from the 99% who do not have the disease overwhelm the true positives from the 1% who have it. This is the basis for recent recommendations to stop PSA screening in men, for example, as expensive and counterproductive. But all this is described in detail in the article. Enjoy!

4 thoughts on “Bayes’ Theorem, Medical Diagnostics and Nomograms

  1. Hendrik B. December 12, 2014 / 4:36 am

    Because “it turns out it’s about 16% “, [we] “recommendations to stop PSA screening in men”

    So the gist is that PSA is screening is only 16% effective, and, because it’s so expensive, we’d better stop doing it. This seems a rather callous attitude towards those 1 in 6 men who have the disease, and the early diagnostic that might save their lives.

    I agree the application can serve as input on how to apply the screening, but simply concluding on its ineffectiveness and proposal to scrap it, seems heartless.


    • TW December 14, 2017 / 2:20 pm

      No, it means of, say, 1000 people told that they have failed the screening, only 160 will actually have the disease. The other 840 will have a very stressful experience for no reason. Isn’t that more callous?


  2. terry fagan October 19, 2019 / 7:02 pm

    joe, check out a nomogram for chf and bnp by peter mccullough md


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