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

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

doi:10.15559/17-VMSTA77

Modern Stochastics: Theory and Applications

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

Volume 4, Issue 2 (2017), pp. 109–125

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

https://doi.org/10.15559/17-VMSTA77

Pub. online: 26 April 2017 Type: Research Article

Open 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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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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