Relative risks, the probability of necessity, and attributable fractions

Epidemiologists are careful to describe their findings as "associations", and to avoid any causal language or claims. Arguably, this attempt to avoid reference to causal processes has become counterproductive. Explicitly stated or not, assumptions about causal processes are inherent in the formulation and interpretation of any statistical study. This article offers a bridge between established, extensively developed proportional hazard methods that are used to study longitudinal observational cohort data, and results for causal inference. In particular, it considers the burden of disease that would not have occurred, but for an exposure such as smoking. It shows how this "probability of necessity", relates to population attributable fractions, and how these quantities along with their confidence intervals, can be estimated using conventional proportional hazard estimates. The example may often apply to cohort studies that consider disease-risk in the absence of prior disease. More generally, equivalent estimates can often be constructed when there is sufficient understanding to postulate a model for the causal relationship between exposures, confounders, and disease-risk, as summarised in a directed acyclic graph (DAG).