Invariants and noninvariants in the concept of interdependent effects

In two of his publications [Causal and preventive interdependence: Elementary principles. Scand J Work Environ Health 8 (1982) 159-168 and Theoretical Epidemiology, John Wiley & Sons, New York, NY 1985], Miettinen put forth basic definitions of causal and preventive interdependence of effects involving binary exposure indicators and outcomes. This paper shows that the identification of interdependence using Miettinen's definitions varies with the choice of the reference categories for the exposures. In particular, Miettinen's concepts of synergism and antagonism are not invariant under exposure recoding. It is also shown that, when both exposures affect risk in some individuals, the effects will appear interdependent under some choice of referent. In the deterministic case, invariant properties of joint effects may be identified through the formation of equivalence classes of response types. In the stochastic case, invariant properties may be identified through the averaging of individual hazards, rather than risks. In both cases, additivity of risk or rate differences emerges as an elementary criterion for the independence of effects.