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Modern Stochastics: Theory and Applications


Quantifying and estimating additive measures of interaction from case-control data
Volume 4, Issue 2 (2017), pp. 109–125
Pub. online: 26 April 2017      Type: Research Article      Open accessOpen Access
Received
22 March 2017
Revised
12 April 2017
Accepted
12 April 2017
Published
26 April 2017

Abstract

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.

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© 2017 The Author(s). Published by VTeX
Open access article under the CC BY license.

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

MSC2010
62F10 62F12 62F25 62J12 62P10

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