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Additive Interaction in Survival Analysis: Use of the Additive Hazards Model

Rod, Naja Hulveja; Lange, Theisb; Andersen, Ingelisea; Marott, Jacob Louisc; Diderichsen, Finna

doi: 10.1097/EDE.0b013e31825fa218

It is a widely held belief in public health and clinical decision-making that interventions or preventive strategies should be aimed at patients or population subgroups where most cases could potentially be prevented. To identify such subgroups, deviation from additivity of absolute effects is the relevant measure of interest. Multiplicative survival models, such as the Cox proportional hazards model, are often used to estimate the association between exposure and risk of disease in prospective studies. In Cox models, deviations from additivity have usually been assessed by surrogate measures of additive interaction derived from multiplicative models—an approach that is both counter-intuitive and sometimes invalid. This paper presents a straightforward and intuitive way of assessing deviation from additivity of effects in survival analysis by use of the additive hazards model. The model directly estimates the absolute size of the deviation from additivity and provides confidence intervals. In addition, the model can accommodate both continuous and categorical exposures and models both exposures and potential confounders on the same underlying scale. To illustrate the approach, we present an empirical example of interaction between education and smoking on risk of lung cancer. We argue that deviations from additivity of effects are important for public health interventions and clinical decision-making, and such estimations should be encouraged in prospective studies on health. A detailed implementation guide of the additive hazards model is provided in the appendix.

From the aSection of Social Medicine, Department of Public Health, University of Copenhagen, Copenhagen, Denmark; bSection of Biostatistics, Department of Public Health, University of Copenhagen, Copenhagen, Denmark; and cCopenhagen City Heart Study, Bispebjerg University Hospital, Copenhagen, Denmark.

Submitted 4 November 2011; accepted 15 March 2012; posted 22 June 2012.

Conflicts of interest and source of funding: There are no conflicts of interests. This work was supported by the Commission of Social Inequality in Cancer [grant no. SU08004] and the Danish Medical Research Council [grant no. 09-062115 to NHR].

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Correspondence: Naja Hulvej Rod, Department of Public Health, University of Copenhagen, Øster Farimagsgade 5, Postbox 2099, 1014 Copenhagen K, Denmark. E-mail:

© 2012 Lippincott Williams & Wilkins, Inc.