Diagnosing physical abuse using Bayes' Theorem: a preliminary study

Objectives. To perform a preliminary study to compare the patterns of bruises in a physically abused group of children and a control group; to investigate whether these could be modelled statistically to enable probabilities of typical bruise patterns to be calculated; to apply Bayes' Theorem to find the probability that a child with a given bruise pattern has been the subject of physical abuse. Design. An observational study. Setting. Cardiff and Vale of Glamorgan. Subjects. Children who have suffered child physical abuse, 0–14 years. The diagnosis was confirmed at a case conference in all cases. A control group of 289 children who presented to the Accident and Emergency Department at the Cardiff Royal Infirmary after an accidental injury. Main outcome measures. The distribution bruise pattern in three regions of the body. The posterior probability of abuse for a given bruise pattern. Results. The bruise distribution in physically abused and control children was well described by a negative binomial distribution. There was a different distribution for the three different regions of the body in physically abused children. The bruising frequency and distribution for the physically abused group was very different from that of the controls. We were able to use parameters derived from these distributions to calculate posterior probabilities of physical abuse given a particular pattern of bruises using Bayes' Theorem. Conclusions. This preliminary study demonstrates that we can use Bayes' Theorem to combine prior probabilities of physical abuse with observed patterns of bruising in given children to obtain posterior probabilities of abuse. This principle has considerable potential for better diagnosis of the physically abused child. © 1998 John Wiley & Sons, Ltd.