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

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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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