A Bayesian approach to complex clinical diagnoses: a case‐study in child abuse

Summary.  Clinical diagnosis is often a complex task of decision making in the face of uncertainty. Diagnosis of child abuse is a particular example where misdiagnosis in either direction is very serious. We have developed a formal Bayesian methodology to quantify the intrinsic uncertainty in complex clinical diagnostic problems. The motivating case‐study was the diagnosis of abuse in an infant presenting with an acute life threatening event and oronasal haemorrhage (nosebleed). Since no direct evidence was available on the probability of abuse given an acute life threatening event and nosebleed, we used Bayes theorem to formulate the diagnosis in terms of prior and inverse conditional probabilities and adapted systematic review methodology and Bayesian evidence synthesis to estimate these and to propagate the associated uncertainty. The estimated probability of abuse was far more uncertain than might be supposed from either expert advice or an informal reading of the literature, and estimates depended crucially on assumptions that were made about the conditional independence of multiple signs of abuse. This highlights the importance of having a formal statistical methodology such as this to assist clinicians in reaching a diagnosis. The process that we worked through is likely to have wider application to other problems of complex clinical diagnosis.