Issues in the application of Bayes' Theorem to child abuse decision making

Proposals for the application of Bayes' Theorem as an aid to child abuse decision making are discussed critically. Subsequently, two examples of the application of research findings concerning signs of child abuse to decision making are demonstrated, using data from research studies of signs of physical abuse and sexual abuse. The calculation of the probability of the presence of abuse using Bayes' Theorem is described, given prevalence information and specific indicators of abuse. In addition, a method for describing the degree of imprecision in estimates of the probability of abuse is discussed. Specific issues that affect the valid application of research findings within Bayes' Theorem are discussed, including estimates of the prevalence or base rate of child abuse, sensitivity and specificity of diagnostic signs, and the independence of information that is combined in Bayes' Theorem. Recommendations for addressing these issues when Bayes' Theorem is applied to child abuse decision making are discussed, including assessment of the independence of indicators that are combined in Bayes' Theorem, suitable bases for estimating the prevalence of abuse, and the calculation of imprecision in probability estimates of abuse.