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Modern Stochastics: Theory and Applications


Quantifying and estimating additive measures of interaction from case-control data
Volume 4, Issue 2 (2017), pp. 109–125
Pub. online: 26 April 2017      Type: Research Article      Open accessOpen 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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© 2017 The Author(s). Published by VTeX
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

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