Reconsidering the denominator of the attributable proportion for interaction
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Modified AP is independent of covariate adjustment.
“It is independent of covariate adjustment.29”
From Understanding of interaction (subgroup) analysis in clinical trials (2019) · cites this paper as [29]
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Cites
Rothman, K. J., Greenland, S. 1., & Lash, T. L. (1998) · Cited by 2,106 · see citing works
Confidence interval estimation of interaction
Hosmer, D. W., & Lemeshow, S. (1992) · Epidemiology · doi:10.1097/00001648-199209000-00012 · Cited by 1,239 · see citing works
VanderWeele, T. J., & Knol, M. J. (2014) · Epidemiologic Methods · doi:10.1515/em-2013-0005 · Cited by 1,127 · see citing works
Self-citationROTHMAN, K. J., GREENLAND, S., & WALKER, A. M. (1980) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a113015 · Cited by 851 · see citing works
Estimating measures of interaction on an additive scale for preventive exposures
Knol, M. J., VanderWeele, T. J., Groenwold, R. H. H., Klungel, O. H., Rovers, M. M., & Grobbee, D. E. (2011) · European Journal of Epidemiology · doi:10.1007/s10654-011-9554-9 · Cited by 776 · cited 1× · see citing works
“[11] suggested that the interpretation of measures like RERI were clearest when the effects of the each of the exposures in the absence of the other were positive and proposed a recoding strategy of exposures to ensure that that was so.”
Self-citationROTHMAN, K. J. (1976) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a112335 · Cited by 776 · see citing works
Schottenfeld, D. (2002) · American Journal of Epidemiology · doi:10.1093/aje/kwf028 · Cited by 627 · see citing works
Interaction as departure from additivity in case-control studies: a cautionary note
Skrondal, A. (2003) · American Journal of Epidemiology · doi:10.1093/aje/kwg113 · Cited by 180 · cited 2× · see citing works
“would still obtain the same attributable proportion measure of AP 1⁄4 33:3 %: Third, Skrondal [12] criticized Rothman’s original attributable proportion measure (and also RERI) because, in the presence of covariates, if the risks follow a linear risk model that is additive in the covariates, P(D = 1|X1 = x1, X2 = x2,…”
Sufficient cause interactions and statistical interactions
VanderWeele, T. J. (2009) · Epidemiology · doi:10.1097/ede.0b013e31818f69e7 · Cited by 163 · see citing works
Self-citation(1996) · PubMed · Cited by 141 · see citing works
VanderWeele, T. J., & Vansteelandt, S. (2011) · American Journal of Epidemiology · doi:10.1093/aje/kwr334 · Cited by 46 · see citing works
Self-citationRothman, K. J., Huybrechts, K. F., & Murray, E. J. (2024) · doi:10.1093/oso/9780197751541.001.0001 · Cited by 12 · see citing works
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VanderWeele, T. J., & Knol, M. J. (2014) · Epidemiologic Methods · doi:10.1515/em-2013-0005 · Cited by 1,127 · see citing works
“Alternatively, we might consider the proportion of the joint effects of both exposures together that is due to interaction (Rothman, 1986; VanderWeele, 2013).”
BackgroundSelf-citationThe Rotterdam Study: 2016 objectives and design update
Albert Hofman, D., Brusselle, G., Murad, S. D., van Duijn, C. M., Franco, O. H., Goedegebure, A., Ikram, M. A., Klaver, C. C. W., Nijsten, T. E. C., Peeters, R. P., et al. (2015) · European Journal of Epidemiology · doi:10.1007/s10654-015-0082-x · Cited by 382 · see citing works
Understanding of interaction (subgroup) analysis in clinical trials
Brankovic, M., Kardys, I., Steyerberg, E. W., Lemeshow, S., Markovic, M., Rizopoulos, D., & Boersma, E. (2019) · European Journal of Clinical Investigation · doi:10.1111/eci.13145 · Cited by 130 · see citing works
Greenland, S. (2014) · Annals of Epidemiology · doi:10.1016/j.annepidem.2014.11.005 · Cited by 107 · see citing works
Attributing Effects to Interactions
VanderWeele, T. J., & Tchetgen, E. J. T. (2014) · Epidemiology · doi:10.1097/ede.0000000000000096 · Cited by 105 · see citing works
Self-citationInteraction between passive smoking and two HLA genes with regard to multiple sclerosis risk
Hedström, A. K., Bomfim, I. L., Barcellos, L. F., Briggs, F. B. S., Schaefer, C. A., Kockum, I. S., Olsson, T. P., & Alfredsson, L. S. (2014) · International Journal of Epidemiology · doi:10.1093/ije/dyu195 · Cited by 83 · see citing works
“AP as defined by Rothman,(11) as defined by WanderWeele.(12) Adjusted for age, gender, ancestry, HLA-A*02 status and study.”
MethodInfluentialWhat matters most: quantifying an epidemiology of consequence
Keyes, K. M., & Galea, S. (2015) · Annals of Epidemiology · doi:10.1016/j.annepidem.2015.01.016 · Cited by 75 · see citing works
“A more rigorous focus on the absolute change in population health associated with exposures of interest has captured the attention of the methodologic literature [42,43], and several measures and indices with which to build from the solid risk factor work produced by the field in the last several decades have been dev…”
BackgroundSynergistic Association of House Endotoxin Exposure and Ambient Air Pollution with Asthma Outcomes
Mendy, A., Wilkerson, J., Salo, P. M., Weir, C. H., Feinstein, L., Zeldin, D. C., & Thorne, P. S. (2019) · American Journal of Respiratory and Critical Care Medicine · doi:10.1164/rccm.201809-1733oc · Cited by 59 · see citing works
“It suggests that an interaction is synergistic when positive or antagonistic when negative (27).”
BackgroundThe contribution of secondhand tobacco smoke exposure to pediatric multiple sclerosis risk
Lavery, A. M., Collins, B. N., Waldman, A. T., Hart, C. N., Bar‐Or, A., Marrie, R. A., Arnold, D. L., O’Mahony, J., & Banwell, B. (2018) · Multiple Sclerosis Journal · doi:10.1177/1352458518757089 · Cited by 47 · see citing works
Joint impact of polygenic risk score and lifestyles on early- and late-onset cardiovascular diseases
The China Kadoorie Biobank Collaborative Group, Sun, D., Ding, Y., Yu, C., Sun, D., Pang, Y., Pei, P., Yang, L., Millwood, I. Y., Walters, R. G., et al. (2024) · Nature Human Behaviour · doi:10.1038/s41562-024-01923-7 · Cited by 43 · see citing works
“…of high genetic risk and unfavourable lifestyle into three components—the proportions attributable to high genetic risk alone, unfavourable lifestyle alone and their interaction—and calculated the alternative attributable proportion (AP * ) for each component 44,45 (detailed in Supplementary Note).”
Wei, S., Tie, L., Liao, J., Liu, X., Du, M., Lan, S., Li, X., Li, C., Zhan, H., & Huang, C. (2020) · Plant and Soil · doi:10.1007/s11104-020-04498-0 · Cited by 41 · see citing works
“Supposing that there is no interaction, RERI and API are equal to 0 (Andersson et al. 2005; VanderWeele 2013).”
Muga, M. A., Owili, P. O., Hsu, C., & Chao, J. C.-J. (2019) · BMC Public Health · doi:10.1186/s12889-019-7686-0 · Cited by 28 · see citing works
Tanner, S., Thomson, S. M., Drummond, K. D., O’Hely, M., Symeonides, C., Mansell, T., Saffery, R., Sly, P. D., Collier, F., Burgner, D. P., et al. (2022) · Antioxidants · doi:10.3390/antiox11040659 · Cited by 27 · see citing works
“in the doubly exposed group that is due to the interaction [63] and the relative excess risk due to interaction (RERI), a measure of interaction on the additive scale for risk ratios [64].”
BackgroundZhang, Q., Meng, X., Luo, H., Yu, K., Li, A., Zhou, L., Chen, R., & Kan, H. (2024) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2024.173009 · Cited by 12 · see citing works
Hensel, A. L. J., & Gomaa, N. A. (2023) · PLoS ONE · doi:10.1371/journal.pone.0286006 · Cited by 10 · see citing works
“This measure was used to capture the proportion of the disease in the doubly exposed group that is due to the interaction between the two exposures [36].”
MethodHe, H., Pan, L., Ren, X., Wang, D., Du, J., Cui, Z. Q., Zhao, J., Wang, H., Wang, X., Liu, F., et al. (2022) · Frontiers in Nutrition · doi:10.3389/fnut.2022.806751 · Cited by 10 · see citing works
“AP was intended to capture the proportion of the disease in the doubly exposed group that is due to the interaction between the two exposures (17).”
BackgroundBentley, J. P., Ramachandran, S., & Salgado, T. M. (2021) · Research in Social and Administrative Pharmacy · doi:10.1016/j.sapharm.2021.04.020 · Cited by 6 · see citing works
A General Framework for and New Normalization of Attributable Proportion
Hössjer, O., Kockum, I. S., Alfredsson, L. S., Hedström, A. K., Olsson, T. P., & Lekman, M. (2016) · Epidemiologic Methods · doi:10.1515/em-2015-0028 · Cited by 5 · see citing works
“(12) to RRð1, 1Þ− 1, see Rothman (2012) and VanderWeele (2013).”
MethodKondracki, A. J., Li, W., Bursac, Z., Mokhtari, M., Reddick, B. K., & Barkin, J. L. (2022) · Journal of Clinical Medicine · doi:10.3390/jcm11175184 · Cited by 5 · see citing works
“Although interaction effects are generally examined using the risk ratios (RRs), the odds ratios (ORs) will approximate RRs when the outcome is rare (<10%) [29].”
BackgroundMethodElagali, A. E. M., Eisner, A., Tanner, S., Drummond, K. D., Symeonides, C., Love, C. J., Tang, M. L. K., Mansell, T., Burgner, D. P., Collier, F., et al. (2024) · International Journal of Hygiene and Environmental Health · doi:10.1016/j.ijheh.2024.114514 · Cited by 4 · see citing works
Lago-Sampedro, A. M., Oualla‐Bachiri, W., Maldonado‐Araque, C., Valdés, S., González-Molero, I., Doulatram‐Gamgaram, V. K., Delgado, E., Chaves, F. J., Castaño, L. A., Calle‐Pascual, A. L., et al. (2025) · Biomedicines · doi:10.3390/biomedicines13010160 · Cited by 3 · see citing works
Alternative Decompositions for Attributing Effects to Interactions
VanderWeele, T. J., & Tchetgen, E. J. T. (2015) · Epidemiology · doi:10.1097/ede.0000000000000263 · Cited by 3 · see citing works
Self-citationUmemura, Y., Yamakawa, K., Murao, S., Mitsuyama, Y., Ogura, H., & Fujimi, S. (2022) · Journal of Personalized Medicine · doi:10.3390/jpm12010044 · Cited by 3 · see citing works
“To capture the proportion of the joint effect attributable to additive interaction, we calculated relative excess risks due to interaction (RERI) and the attributable proportion [18].”
MethodA Unification of Mediation and Interaction
VanderWeele, T. J. (2014) · Epidemiology · doi:10.1097/ede.0000000000000121 · Cited by 654 · see citing works
Self-citationQuantifying and estimating additive measures of interaction from case-control data
Hössjer, O., Alfredsson, L. S., Hedström, A. K., Lekman, M., Kockum, I. S., & Olsson, T. P. (2017) · Modern Stochastics Theory and Applications · doi:10.15559/17-vmsta77 · Cited by 1 · see citing works
“Traditional definitions of attributable proportion have an unbounded negative range [18, 29, 19].”
BackgroundLiu, W., Yin, Y., You, Y., Guo, Y., Chai, S., Wang, W., Guan, X., Zhong, G., Yin, Z., Wen, Y., et al. (2026) · Environment International · doi:10.1016/j.envint.2026.110239 · Cited by 1 · see citing works
Moderation analysis with binary outcomes: Interactions on additive and multiplicative scales
Bentley, J. P., Ramachandran, S., & Salgado, T. M. (2022) · Elsevier eBooks · doi:10.1016/b978-0-323-91888-6.00039-9 · Cited by 1 · see citing works
Tobacco Smoke Exposure and Pediatric Multiple Sclerosis
Lavery, A. M. (2016) · TUScholarShare (Temple University)
Yang, K. Y., Chang, J., Qin, Q., Xiang, J., Wei, T., Yan, Y., & Tang, Y. (2024) · Research Square · doi:10.21203/rs.3.rs-4251416/v1
Akrami, R., Hadji, M., Rashidian, H., Nazemipour, M., Naghibzadeh‐Tahami, A., Ansari‐Moghaddam, A., Zendehdel, K., & Mansournia, M. A. (2024) · Global Epidemiology · doi:10.1016/j.gloepi.2024.100182
Comparative tuberculosis risk in healthcare and educational workers: occupational synergy
Lee, Y., Kim, H. W., Kim, J. S., Park, Y.-J., Kim, G., 김, 유., Park, G., & Myong, J. (2025) · ERJ Open Research · doi:10.1183/23120541.01005-2025
“Statistical interactions were assessed on the additive scale using the relative excess risk due to interaction (RERI), the attributable proportion (AP) and the synergy index (SI) [22, 23].”
Gao, Z., Li, Y., Liu, Z., Tuo, M., & Ren, C. (2026) · Circulation Population Health and Outcomes · doi:10.1161/circoutcomes.125.012113
Salter, A. R., Lancia, S., Kowalec, K., Fitzgerald, K. C., & Marrie, R. A. (2026) · Neurology Open Access · doi:10.1212/wn9.0000000000000116
李澍卿, Liu, J., zhang, T., Tan, X., chen, T., liu, J., Huang, L., & Li, W. (2026) · Research Square · doi:10.21203/rs.3.rs-10896387/v1
Sleep Duration Moderates the Association Between Bullying and Suicide Attempts Among US Adolescents
Narcisse, M., Wolff, J. C., Medeiros, K. G., & Barker, D. (2026) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph23101303
- Authors
- VanderWeele, T. J.
- Affiliations
- Harvard University (US)
- Corresponding author
- VanderWeele, Tyler J.
- Venue
- European Journal of Epidemiology
- Published
- 2013-09-14
- Volume
- 28
- Issue
- 10
- Pages
- 779-784
- ISSN
- 0393-2990 (ISSN-L)
- 1573-7284
- PMC
- PMC3882023
- OpenAlex
- W2049708264
- Cited by
- 36
- References
- 12
- Citations by year
- 2026: 5 · 2025: 2 · 2024: 5 · 2023: 1 · 2022: 5 · 2021: 1 · 2020: 1 · 2019: 3 · 2018: 1 · 2017: 1 · 2016: 2 · 2015: 3 · 2014: 6
- FWCI
- 3.24
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Licence
- www.springer.com/tdm (tdm)
- Locations
- European Journal of Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institute of Environmental Health Sciences (R01ES017876)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- additive interaction, attributable proportion, risk difference, potential outcomes framework, intervention targeting
- MeSH terms
- Data Interpretation, Statistical, Humans, Models, Statistical, Epidemiologic Research Design, Causality, Epidemiologic Studies
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