Likelihood ratios and the dependence of clinical evidence: should individual LRs be taken at face value?

Likelihood ratios (LRs) are often used to quantify the evidential weight of clinical findings. In diagnostic accuracy studies, however, LRs are typically reported for individual findings, not for conjunctions of findings. Since LRs for conjunctions of findings are often unavailable, influential Evidence-Based Diagnosis texts suggest that individual LRs may be multiplied to obtain joint LRs, but only under the assumption of approximate conditional independence. This assumption can be analytically convenient, but often implausible in clinical practice, where findings arise from shared pathophysiological mechanisms. This article examines the plausibility of this assumption and how a hidden dependence structure among clinical findings can affect the LR of their conjunction. To make this possible, we define the Coherence Factor ( Γ ) as the ratio between the association among findings under D and the corresponding association under ¬ D . It makes explicit the hidden dependence structure in the evaluation of joint LRs: it allows one to examine, in a formal way, the plausibility of the independence assumption, without replacing statistical approaches designed to account for it. In particular, this framework supports a more cautious interpretation of individual LRs by showing how using them at face value, whether individually or multiplicatively, presupposes a specific dependence structure, one rarely instantiated in clinical practice. The consequences of this analysis do not depend on whether physicians make calculations at the bedside, since it concerns how individual LRs should be interpreted in a Bayesian framework.