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.

References

[1]

Agresti, A.: A survey of exact inference for contingency tables. Stat. Sci. 7(1), 131–153 (1992). MR1173420. doi:10.1214/ss/1177011454

[2]

Agresti, A.: Categorical Data Analysis, 3rd edn. Wiley, Hoboken, New Jersey (2013). MR3087436

[3]

Andersson, T., Alfredsson, L., Källberg, H., Zdravkovic, S., Ahlbom, A.: Calculating measures of biological interaction. Eur. J. Epidemiol. 20, 575–579 (2005). doi:10.1007/s10654-005-7835-x

[4]

Assman, S.F., Hosmer, D.W., Lemeshow, S., Mundt, K.A.: Confidence intervals for measures of interaction. Epidemiology 7(3), 286–290 (1996). doi:10.1097/00001648-199605000-00012

[5]

Breslow, N.E., Day, N.E.: In: Statistical Methods in Cancer Research. Volume 1. The Analysis of Case-Control Studies, Lyon, France (1980)

[6]

Casella, G., Berger, R.L.: In: Statistical Inference, Thompson Learning (2002)

[7]

Cree, B.: Multiple sclerosis genetics. In: Handb. Clin. Neurol., vol. 122, pp. 193–209 (2014). doi:10.1016/B978-0-444-52001-2.00009-1

[8]

Ebers, G.C., Sadovnick, A.D.: The geographic distribution of multiple sclerosis: a review. Neuroepidemiology 1993 (2013)

[9]

Efron, B.: Better bootstrap confidence intervals (with discussion). J. Am. Stat. Assoc. 82, 171–200 (1987). doi:10.1080/01621459.1987.10478410

[10]

Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Monogr. Stat. Appl. Probab., vol. 57. Chapman and Hall/CRC (1994). MR1270903. doi:10.1007/978-1-4899-4541-9

[11]

Eide, G.E.: Attributable fractions: fundamental concepts and their visualization. Stat. Methods Med. Res. 10, 159–193 (2001). doi:10.1177/096228020101000302

[12]

Greenland, S.: Additive risk versus additive relative risk models. Epidemiology 4(1), 32–36 (1993). doi:10.1097/00001648-199301000-00007

[13]

Hedström, A.K., Sundqvist, E., Bäärnhielm, M., Nordin, N., Hiller, J., Kockum, I., Olsson, T., Alfredsson, L.,: Smoking and two human leukocyte antigen genes interact to increase the risk for multiple sclerosis. Brain 134, 653–664 (2011). doi:10.1093/brain/awq371

[14]

Hedström, A.K., Katsoulis, M., Hössjer, O., Bomfim, I.L., Oturai, A., et al.: The interaction between smoking and HLA genes in multiple sclerosis; replication and refinement. Eur. J. Epidemiol. (2017), accepted for publication

[15]

Hosmer, D.W., Lemeshow, S.: Confidence interval estimation of interaction. Epidemiology 3(5), 452–456 (1992). doi:10.1097/00001648-199209000-00012

[16]

Hössjer, O., Kockum, I., Alfredsson, L., Hedström, A-K., Olsson, T., Lekman, M.: A new normalization and generalized definition of attributable proportion. Epidemiol. Methods (2017) (available online December 2016). doi:10.1515/em-2015-0028

[17]

Katsoulis, M., Bamia, C.: Moving from two- to multi-way interactions between binary risk factors on the additive scale. Submitted for publication (2017)

[18]

Knol, M.J., VanderWeele, T.J., Groenwold, R.H., Klungel, O.H., Rovers, M.M., Grobbee, D.E.: Estimating measures of interaction on an additive scale for preventive exposures. Eur. J. Epidemiol. 26, 433–438 (2011). doi:10.1007/s10654-011-9554-9

[19]

Lekman, M., Hössjer, O., Andrew, P., Källberg, H., Uvehag, D., Charney, D., Manji, H., Rush, J., McMahon, F., Moore, J., Kockum, I.: The genetic interacting landscape of 63 candidate genes in Major Depressive Disorder: an explorative study Biodata Min. 7, 19 (2014) (18 pages)

[20]

McCullagh, P., Nelder, J.: Generalized Linear Models, 2nd edn. Chapman & Hall, London (1989)

[21]

Multiple Sclerosis International Federation: Atlas of MS Survey (2013)

[22]

Olsson, T., Barcellos, L.F., Alfredsson, L.: Interactions between genetic, lifestyle and environmental risk factors for multiple sclerosis. Nat. Rev. Neurol. 13(1), 25–36 (2017). doi:10.1038/nrneurol.2016.187

[23]

Petti, S., Masood, M., Scully, C.: The magnitude of tobacco smoking-betel quid chewing drinking interaction effect on oral cancer in South-East Asia. A meta-analysis of observational studies PLoS ONE 8(11), e78999 (2013)

[24]

Prentice, R.L., Pyke, R.: Logistic disease incidence models and case-control studies. Biometrika 66(3), 403–411 (1979). doi:10.1093/biomet/66.3.403

[25]

Rothman, K.J.: The estimation of synergy or antagonism. Am. J. Epidemiol. 103, 506–511 (1976). doi:10.1093/oxfordjournals.aje.a112252

[26]

Rothman, K.J.: Epidemiology. An Introduction, 2nd edn. Oxford Univ. Press, N.Y. (2012)

[27]

Rothman, K.J., Greenland, S., Walker, A.M.: Concepts of interaction. Am. J. Epidemiol. 112, 467–470 (1980). doi:10.1093/oxfordjournals.aje.a113015

[28]

Skrondal, A.: Interaction as departure from additivity in case-control studies: a cautionary note. Am. J. Epidemiol. 158, 251–258 (2003). doi:10.1093/aje/kwg113

[29]

VanderWeele, T.J.: Reconsidering the denominator of the attributable proportion for interaction. Eur. J. Epidemiol. 28, 779–784 (2013). doi:10.1007/s10654-013-9843-6

[30]

VanderWeele, T.J., Robins, J.M.: Empirical and counterfactual conditions for sufficient cause interactions. Biometrika 95, 49–61 (2008). doi:10.1093/biomet/asm090

Full article Related articles

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

Metrics

since March 2018

708 Article info views	306 Full article views
340 PDF downloads	152 XML downloads

RSS

Authors

Abstract

References

Export citation

Copy and paste formatted citation

Download citation in file