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

• Main Authors: Ola Hössjer, Lars Alfredsson, Anna Karin Hedström, Magnus Lekman, Ingrid Kockum, Tomas Olsson
• Format: Article
• Language: English
• Published: VTeX 2017-04-01
• Series: Modern Stochastics: Theory and Applications
• Subjects: Additive odds model; attributable proportion; case-control data; expansion of odds ratios; interaction of risk factors; Logistic regression
• Online Access: https://vmsta.vtex.vmt/doi/10.15559/17-VMSTA77
• ISSN: 2351-6046; 2351-6054

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.