observedtoexpected

Observed-to-expected, often abbreviated as O/E, is a statistical ratio that compares the number of events actually observed in a study to the number expected under a predefined model or reference population. It is used to assess whether observed event counts differ meaningfully from what is anticipated under baseline assumptions.

Calculation and interpretation: O/E is calculated as observed events divided by expected events (O / E). The exact meaning of the expected count depends on the context and model: in epidemiology, E is derived from age-, sex-, and time-adjusted population rates applied to the study cohort; in genetics, E may come from context-dependent mutational rates; in quality control, E is based on historical defect rates. An O/E greater than 1 indicates more events than expected (enrichment), while an O/E less than 1 indicates fewer events (deficit). An O/E near 1 suggests concordance with the model. Confidence intervals are commonly reported, often using Poisson assumptions for the observed count or model-based methods to reflect uncertainty in E.

Applications and caveats: O/E ratios are widely used in epidemiology to evaluate disease risk, in genetics to assess mutational burden, and in clinical quality assessment to gauge deviations from baseline performance. They depend on an accurate and appropriate specification of the expected count; misestimation can lead to misleading conclusions. Additionally, issues such as overdispersion, confounding, and exposure misclassification can affect interpretation.

Related measures include the standardized mortality ratio (SMR) and standardized incidence ratio (SIR), both of which are specific forms of the observed-to-expected concept. See also incidence rate ratios and risk ratios for alternative comparative metrics.