Quantifying and estimating additive measures of interaction from case-control data

Ola Hössjer, Lars Alfredsson, Anna Karin Hedström, Magnus Lekman, Ingrid Kockum, Tomas Olsson


In this paper we develop a general framework for quantifying how binary risk factors jointly influence a binary outcome. Our key result is an additive expansion of odds ratios as a sum of marginal effects and interaction terms of varying order. These odds ratio expansions are used for estimating the excess odds ratio, attributable proportion and synergy index for a case-control dataset by means of maximum likelihood from a logistic regression model. The confidence intervals associated with these estimates of joint effects and interaction of risk factors rely on the delta method. Our methodology is illustrated with a large Nordic meta dataset for multiple sclerosis. It combines four studies, with a total of 6265 cases and 8401 controls. It has three risk factors (smoking and two genetic factors) and a number of other confounding variables.


Additive odds model; attributable proportion; case-control data; expansion of odds ratios; interaction of risk factors; logistic regression

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DOI: http://dx.doi.org/10.15559/17-VMSTA77


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