American Research Journal of Humanities and Social Sciences Original Article ISSN 2378-7031 Volume 1, Issue2, Apr-2015 www.arjonline.org 14 The Benefits of Applying Bayes’ Theorem in Medicine David Trafimow 1 Department of Psychology, MSC 3452 New Mexico State University, P. O. Box 30001 Las Cruces, NM 88003-8001 Abstract: The present article provides a very basic introduction to Bayes’ theorem and its potential implications for medical research. This introduction was written to be accessible to medical researchers without much mathematical background in general or without much background in Bayesian mathematics specifically. I prove Bayesian equations from very basic probability theorems and also show how these basic theorems can aid medical researchers to make important discoveries without having to do much empirical work. In many cases, the necessary empirical work, including relevant epidemiological work, is already in the medical literature and important discoveries can be made merely by looking up that work and applying one of the Bayesian equations to be presented. I also demonstrate that the traditional null hypothesis significance testing procedure that currently dominates medical research is blatantly invalid; a Bayesian point of view suggests that researchers should not use this procedure. Finally, I discuss some special issues, including philosophical issues that pertain to using a Bayesian perspective in medicine. I. INTRODUCTION TO THE BAYESIAN SPECIAL ISSUE Any researcher who is knowledgeable about the famous theorem by Bayes cannot help but notice two unfortunate patterns when perusing the medical findings. First, there already is much valuable published information but researchers are unable to use that information to maximal advantage. For example, there have been countless epidemiological studies that provide the medical world with potentially useful base rate information about the prevalence of diseases. By combining epidemiological information with false positive and false negative rates gleaned from research on particular medical diagnostic procedures, Bayesian analysis renders it possible to compute important probabilities, such as the probability that a person has a disorder given the result of the diagnostic procedure. Critical discoveries such as this can be made simply by spending an hour finding the relevant studies, and spending three minutes using Bayes’ theorem to make the relevant computation. An important goal of the present article, and of this Special Issue more generally is to make accessible to medical researchers (a) that Bayesian analyses greatly expand the potential for making important discoveries in medicine and (b) that some Bayesian analyses are very easy to perform and even can be performed on the backside of an envelope. The second problem with medical researchers being unfamiliar with Bayesian analyses is that they depend too much on the null hypothesis significance testing procedure (p< .05). The procedure is flawed in basic ways that are obvious to a Bayesian but that are difficult to see from the point of view of a non-Bayesian. The organization of the present article will underscore both issues. I commence with a general introduction of Bayes’ theorem that should be easy for any medical researcher who has had rudimentary algebra to understand. Based on the introduction, the following sections discuss, in turn, how to exploit Bayes’ theorem even if one has very little mathematical background and the implications of the theorem for null hypothesis significance tests. Finally, there are auxiliary issues that remain to be discussed. II. INTRODUCTION TO BAYES’ THEOREM IN A MEDICAL CONTEXT Suppose that a researcher wishes to know the probability of a disorder given the result of a diagnostic procedure or test. I will use the following notation.  P(D): Base rate probability (proportion of cases in the relevant population) of the disorder.  P( ): Proportion of cases in the relevant population that do not have the disorder .  P(T): Probability of a positive result when a test or diagnostic procedure is performed.  P( T): Probability of a negative result when a test or diagnostic procedure is performed . 1 Corresponding Author: dtrafimo@nmsu.edu