When math legitimizes knowledge: a step by step approach to Bayes’ rule in diagnostic reasoning

INTRODUCTION: Many mistakes in clinical practice arise from confusing the probability of a positive test in those with the disease and the probability of having the disease in those who test positive. This misunderstanding leads to overestimating disease probability, diagnosing diseases in healthy individuals, ordering invasive diagnostic tests, and prescribing unnecessary treatments, resulting in unjustified adverse effect, psychological stress, and increased cost. Probabilistic reasoning is an essential skill to mitigate this confusion, and Bayes theorem is an important tool to accomplish this goal. OBJECTIVE: To present a step-by-step demonstration of Bayes' formula for positive and negative predictive values, fostering understanding and enabling its adoption in evidence-based medicine education and clinical practice as a supporting tool in the decision-making process. METHODS: In this article, we explain the difference between deductive and inductive thinking and how diagnostic reasoning is predominantly inductive, where evidence (the test result) is used to predict the cause (the presence of disease), a path that involves reverse probability, for which our reasoning is hazier. Through a clinical example involving the diagnosis of systemic lupus erythematosus, we use the Bayesian framework as a tool to help understand the difference between sensitivity/specificity (forward probability; deductive) and positive/negative predictive values (reverse probability: inductive). CONCLUSIONS: Excellent doctors are masters at applying Bayesian reasoning without using any formulas: they understand that the most important component of the diagnostic process is the reasoning that originates it and the resulting clinical decision depends on interpreting results considering their interaction with the context, not in isolation. Bad clinical reasoning results in bad clinical decisions, despite how accurate the diagnostic test: garbage in, garbage out. We hope our step-by-step approach to Bayes' rule can help demystify this powerful statistical tool and strengthen the idea that the value of a diagnostic test is directly proportional to the quality of clinical reasoning that led to its request.