Additive Risk versus Additive Relative Risk Models

The distinction between additive risk models and additive relative risk models is important when nonadditivity is used as a criterion for interdependence of causal effects (causal interaction). I show here that, in stratified studies, additive relative risk models do not provide the often-assumed correspondence between additivity and absence of causal interaction. Under the causal models of Rothman and others, complete assessment of causal interaction requires that one fit additive risk models; in matched case-control studies, such fitting may require external information.