Estimating interaction on an additive scale between continuous determinants in a logistic regression model

• Published in: International journal of epidemiology Vol. 36; no. 5; pp. 1111 - 1118
• Main Authors: Knol, Mirjam J, van der Tweel, Ingeborg, Grobbee, Diederick E, Numans, Mattijs E, Geerlings, Mirjam I
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.10.2007; Oxford Publishing Limited (England)
• Subjects: additive; Adolescent; Adult; Age Factors; Aged; Aged, 80 and over; biologic; Biological and medical sciences; Body Mass Index; Child; continuous; Data Interpretation, Statistical; effect-modification; Humans; Hypertension - epidemiology; Hypertension - etiology; Interaction; Logistic Models; Medical sciences; Middle Aged; Miscellaneous; Netherlands - epidemiology; Public health. Hygiene; Public health. Hygiene-occupational medicine; relative excess risk; Netherlands; relative excess risk; Interaction; biologic; continuous; additive; effect-modification; Modification; Continuous; Evaluation scale; Determinant; Estimation; Relative risk; Logistic regression; Additive; Regression model; Public health
• ISSN: 0300-5771; 1464-3685
• DOI: 10.1093/ije/dym157

Background To determine the presence of interaction in epidemiologic research, typically a product term is added to the regression model. In linear regression, the regression coefficient of the product term reflects interaction as departure from additivity. However, in logistic regression it refers to interaction as departure from multiplicativity. Rothman has argued that interaction estimated as departure from additivity better reflects biologic interaction. So far, literature on estimating interaction on an additive scale using logistic regression only focused on dichotomous determinants. The objective of the present study was to provide the methods to estimate interaction between continuous determinants and to illustrate these methods with a clinical example. Methods and results From the existing literature we derived the formulas to quantify interaction as departure from additivity between one continuous and one dichotomous determinant and between two continuous determinants using logistic regression. Bootstrapping was used to calculate the corresponding confidence intervals. To illustrate the theory with an empirical example, data from the Utrecht Health Project were used, with age and body mass index as risk factors for elevated diastolic blood pressure. Conclusions The methods and formulas presented in this article are intended to assist epidemiologists to calculate interaction on an additive scale between two variables on a certain outcome. The proposed methods are included in a spreadsheet which is freely available at: http://www.juliuscenter.nl/additive-interaction.xls.