Conceptual problems in the definition and interpretation of attributable fractions.

We have argued that the concept of attributable fraction requires separation into the concepts of excess fraction, etiologic fraction, and incidence-density fraction. These quantities do not necessarily approximate one another, and the etiologic fraction is not generally estimable without strong biologic assumptions. For these reasons, care is needed in deciding which (if any) of the concepts is appropriate for a particular application. It appears that the excess fraction (like incidence proportion) will be most relevant in situations that require only consideration of whether disease occurs by a particular time. In situations that require consideration of when disease occurs, direct measures of effect on incidence time may be as relevant as or more relevant than any attributable fraction. To avoid technical complications, we have not discussed additional problems of causal attribution that can arise when exposure has multiple levels or is sustained over time, and the estimation problems that can arise when considering case-control studies, competing risks, or differential censoring. For more detailed discussions of such problems and proposed solutions, see references 11-20.