Are major behavioral and sociodemographic risk factors for mortality additive or multiplicative in their effects?

All individuals are subject to multiple risk factors for mortality. In this paper, we consider the nature of interactions between certain major sociodemographic and behavioral risk factors associated with all-cause mortality in the United States. We develop the formal logic pertaining to two forms of interaction between risk factors, additive and multiplicative relations. We then consider the general circumstances in which additive or multiplicative relations might be expected. We argue that expectations about interactions among socio-demographic variables, and their relation to behavioral variables, have been stated in terms of additivity. However, the statistical models typically used to estimate the relation between risk factors and mortality assume that risk factors act multiplicatively. We examine empirically the nature of interactions among five major risk factors associated with all-cause mortality: smoking, obesity, race, sex, and educational attainment. Data were drawn from the cross-sectional NHANES III (1988-1994) and NHANES 1999-2010 surveys, linked to death records through December 31, 2011. Our analytic sample comprised 35,604 respondents and 5369 deaths. We find that obesity is additive with each of the remaining four variables. We speculate that its additivity is a reflection of the fact that obese status is generally achieved later in life. For all pairings of socio-demographic variables, risks are multiplicative. For survival chances, it is much more dangerous to be poorly educated if you are black or if you are male. And it is much riskier to be a male if you are black. These traits, established at birth or during childhood, literally result in deadly combinations. We conclude that the identification of interactions among risk factors can cast valuable light on the nature of the process being studied. It also has public health implications by identifying especially vulnerable groups and by properly identifying the proportion of deaths attributable to a risk factor.