On the definition of a confounder
Open accessAbstract
The causal inference literature has provided a clear formal definition of confounding expressed in terms of counterfactual independence. The literature has not, however, come to any consensus on a formal definition of a confounder, as it has given priority to the concept of confounding over that of a confounder. We consider a number of candidate definitions arising from various more informal statements made in the literature. We consider the properties satisfied by each candidate definition, principally focusing on (i) whether under the candidate definition control for all “confounders” suffices to control for “confounding” and (ii) whether each confounder in some context helps eliminate or reduce confounding bias. Several of the candidate definitions do not have these two properties. Only one candidate definition of those considered satisfies both properties. We propose that a “confounder” be defined as a pre-exposure covariate $C$ for which there exists a set of other covariates $X$ such that effect of the exposure on the outcome is unconfounded conditional on $(X,C)$ but such that for no proper subset of $(X,C)$ is the effect of the exposure on the outcome unconfounded given the subset. We also provide a conditional analogue of the above definition; and we propose a variable that helps reduce bias but not eliminate bias be referred to as a “surrogate confounder.” These definitions are closely related to those given by Robins and Morgenstern [Comput. Math. Appl. 14 (1987) 869–916]. The implications that hold among the various candidate definitions are discussed.
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A great deal of variability in cellular responses to treatment may be attributable to underlying confounding variation.
“A great deal of variability in cellular responses to treatment may be attributable to underlying confounding variation10.”
From Causal identification of single-cell experimental perturbation effects with CINEMA-OT (2023) · cites this paper as [10]
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“We may also employ clustering techniques, such as Leiden clustering [23] to group cells by similarity of treatment responses.”
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An empirical investigation on the relationship between design and architecture smells
Sharma, T., Singh, P., & Spinellis, D. D. (2020) · Empirical Software Engineering · doi:10.1007/s10664-020-09847-2 · Cited by 67 · see citing works
“While computing causality relationship between design and architecture smell instances over a period of time, there could be some confounding factors (VanderWeele and Shpitser 2013) that influence both design and architecture smell instances time-series.”
BackgroundWhat Is the Causal Interpretation of Sibling Comparison Designs?
Petersen, A. H., & Lange, T. (2019) · Epidemiology · doi:10.1097/ede.0000000000001108 · Cited by 60 · see citing works
RegressionExplorer: Interactive Exploration of Logistic Regression Models with Subgroup Analysis
Dingen, D., Veer, M. V. ’., Houthuizen, P., Mestrom, E. H. J., Korsten, E. H. H. M., Bouwman, R. A., & van Wijk, J. J. (2018) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2018.2865043 · Cited by 58 · see citing works
“More recently even this method is increasingly being criticized [27].”
BackgroundMethodGao, Y., Xiang, L., Yi, H., Song, J., Sun, D., Xu, B., Zhang, G., & Wu, X. (2025) · BMC Medicine · doi:10.1186/s12916-025-03957-8 · Cited by 54 · see citing works
Propensity scores using missingness pattern information: a practical guide
Blake, H. A., Leyrat, C., Mansfield, K. E., Seaman, S. R., Tomlinson, L. A., Carpenter, J. R., & Williamson, E. (2020) · Statistics in Medicine · doi:10.1002/sim.8503 · Cited by 49 · see citing works
Shantha, K. V. (2019) · Sustainability · doi:10.3390/su11051448 · Cited by 52 · see citing works
“However, the examination of the association of these socio-demographic variables with trading experience and self-reflection constructs reveals that these variables are not really confounders to be controlled in the analysis [48].”
BackgroundSeaport status, port access, and regional economic development in Indonesia
Yudhistira, M. H., & Sofiyandi, Y. (2017) · Maritime Economics & Logistics · doi:10.1057/s41278-017-0089-1 · Cited by 48 · see citing works
Masukume, G., O’Neill, S. M., Baker, P. N., Kenny, L. C., Morton, S., & Khashan, A. S. (2018) · Scientific Reports · doi:10.1038/s41598-018-33482-z · Cited by 46 · see citing works
Confounding and effect measure modification in reproductive medicine research
Correia, K. F. B., Dodge, L. E., Farland, L. V., Hacker, M. R., Ginsburg, E. S., Whitcomb, B. W., Wise, L. A., & Missmer, S. A. (2020) · Human Reproduction · doi:10.1093/humrep/deaa051 · Cited by 46 · see citing works
“More technical definitions of confounding and confounders can be found in Rothman (1986), Greenland (2001), Rothman et al. (2008), Vanderweele (2013) and Hernan & Robins (2019), among others.”
BackgroundInstrumental Variable Estimation with a Stochastic Monotonicity Assumption
Small, D. S., Tan, Z., Ramsahai, R. R., Lorch, S. A., & Brookhart, M. A. (2017) · Statistical Science · doi:10.1214/17-sts623 · Cited by 45 · see citing works
“Assume that BA1, BA2, CF-CA1, CF-CA-2, CF-CA-3, SCC-IVA1 and SCC-IVA2 hold for a U that satisfies (3) and that the following extended versions of SCC-IVA1 and (3) involving A hold: { Y(0), Y (1),A } ⊥ D|Z,U,(9) { Y(0), Y (1),U,A } ⊥ Z.(10) Then, EQ[A] (11) = E(DA|Z = 1) − E(DA|Z = 0) P (D = 1|Z = 1) − P(D = 1|Z = 0) .”
BackgroundInfluentialTowards Causal Benchmarking of Bias in Face Analysis Algorithms
Balakrishnan, G., Xiong, Y., Xia, W., & Perona, P. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-58523-5_32 · Cited by 45 · see citing works
Liu, T., Zhang, M., Rahman, M. L., Wang, X., Hinkle, S. N., Zhang, C., & Mueller, N. T. (2021) · Environment International · doi:10.1016/j.envint.2021.106508 · Cited by 45 · see citing works
“We defined confounders as covariates that have been associated with both chemical concentrations and BP/HDP, based on previous studies, but not in the causal pathway (VanderWeele and Shpitser, 2013).”
Commentary: Causal Inference for Social Exposures
Kaufman, J. S. (2019) · Annual Review of Public Health · doi:10.1146/annurev-publhealth-040218-043735 · Cited by 46 · see citing works
Matched Versus Unmatched Analysis of Matched Case-Control Studies
Wan, F., Colditz, G. A., & Sutcliffe, S. S. (2021) · American Journal of Epidemiology · doi:10.1093/aje/kwab056 · Cited by 42 · see citing works
A Model for Joint Probabilistic Forecast of Solar Photovoltaic Power and Outdoor Temperature
Ramakrishna, R., Scaglione, A., Vittal, V., Dall’Anese, E., & Bernstein, A. (2019) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2019.2954973 · Cited by 41 · see citing works
“The premise is that solar irradiation is the cause of both solar PV power and temperature and therefore acts as a cofounding or lurking variable [6].”
BackgroundA spotlight on cross-sectional research: Addressing the issues of confounding and adjustment
Asiamah, N., Mends-Brew, E., & Boison, B. T. K. (2019) · International Journal of Healthcare Management · doi:10.1080/20479700.2019.1621022 · Cited by 42 · see citing works
“In randomization, the researcher reduces confounding by randomly assigning study participants to control or/ and experimental groups [4,7].”
BackgroundMethodInfluentialLin, C., Lee, Y., Fang, W., Lou, Y.-S., Kuo, F.-C., Lee, C., & Lin, C. S. (2021) · Journal of Personalized Medicine · doi:10.3390/jpm11080725 · Cited by 39 · see citing works
“These relationships have led us to consider the possibility of confounding effects whenever these factors causally influence both ECG and HbA1c [56].”
BackgroundFogarty, C. B., & Small, D. S. (2015) · Journal of the American Statistical Association · doi:10.1080/01621459.2015.1120675 · Cited by 38 · see citing works
“In order for these factors to affect the performed inference (and hence, to be confounders in the sense of VanderWeele and Shpitser (2013)), these factors must also impact the treatment © American Statistical Association Figure .”
BackgroundCausal Interventional Training for Image Recognition
Qin, W., Zhang, H., Hong, R., Lim, E., & Sun, Q. (2021) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2021.3136717 · Cited by 36 · see citing works
Dzhambov, A. M., Dimitrova, V., Germanova, N., Burov, A., Brezov, D. S., Hlebarov, I., & Dimitrova, R. N. (2023) · Environmental Research · doi:10.1016/j.envres.2023.116087 · Cited by 37 · see citing works
Dietary factors and risk of mortality among patients with esophageal cancer: a systematic review
Sun, L. L., Yan, L., Liu, Z., Zhao, W., Zhang, C., Chen, Y.-M., Lao, X. Q., & Liu, X. (2020) · BMC Cancer · doi:10.1186/s12885-020-06767-8 · Cited by 33 · see citing works
“Without adjustments, confounding factors could lead to misinterpretation of the association between independent variables and dependent variables [35].”
BackgroundA non-technical explanation of the counterfactual definition of confounding.
Bours, M. (2020) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2020.01.021 · Cited by 30 · see citing works
Ling, Y., Upadhyaya, P., Chen, L., Jiang, X., & Kim, Y. (2022) · Journal of Biomedical Informatics · doi:10.1016/j.jbi.2022.104256 · Cited by 31 · see citing works
“It is one of the major sources of bias that can mislead us to draw a wrong conclusion that the treatment has effects on the outcome when it does not.[2] A statistical approach to reducing such bias in observational data for treatment effect estimation has long been studied in multiple disciplines.”
BackgroundEndometriosis is associated with pregnancy loss: a nationwide historical cohort study
Boje, A. D., Egerup, P., Westergaard, D., Bertelsen, M.-L. M. F., Nyegaard, M., Hartwell, D., Lidegaard, Ø., & Nielsen, H. S. (2023) · Fertility and Sterility · doi:10.1016/j.fertnstert.2022.12.042 · Cited by 31 · see citing works
Ruiz‐Tagle, A., Droguett, E. L., & Groth, K. M. (2021) · Risk Analysis · doi:10.1111/risa.13711 · Cited by 30 · see citing works
Lin, C. S., Lin, C., Lee, D.-J., Lee, C., Chen, S., Tsai, S., Kuo, F.-C., Chau, T., & Lin, S. (2021) · Journal of the Endocrine Society · doi:10.1210/jendso/bvab120 · Cited by 30 · see citing works
“Previous studies had shown correlations between age [38], K + [29], and ECG, raising the possibility of confounding effects on both the ECG and TPP [39].”
ResultStatistical Control Requires Causal JustificationPreprint
Wysocki, A. C., Lawson, K. M., & Rhemtulla, M. (2020) · doi:10.31234/osf.io/j9vw4 · Cited by 30 · see citing works
Forman‐Rabinovici, A., & Sommer, U. (2019) · Democratization · doi:10.1080/13510347.2019.1661993 · Cited by 29 · see citing works
Schuurman, N. K. (2023) · doi:10.31234/osf.io/7zgkx · Cited by 28 · see citing works
The Structure and Function of Experimental Control in the Life Sciences
Schickore, J. (2018) · Philosophy of Science · doi:10.1086/701952 · Cited by 27 · see citing works
Piaggio, D., Zarro, M., Pagliara, S. M., Andellini, M., Almuhini, A., Maccaro, A., & Pecchia, L. (2023) · American Journal of Infection Control · doi:10.1016/j.ajic.2023.03.005 · Cited by 33 · see citing works
“Addressing confounders is important to avoid misinterpretation of findings, due to spurious associations [35, 36].”
BackgroundDiagnostics for Confounding of Time-varying and Other Joint Exposures
Jackson, J. W. (2016) · Epidemiology · doi:10.1097/ede.0000000000000547 · Cited by 26 · see citing works
Using Causal Diagrams for Biomedical Research
Kyriacou, D. N., Greenland, P., & Mansournia, M. A. (2022) · Annals of Emergency Medicine · doi:10.1016/j.annemergmed.2022.08.014 · Cited by 26 · see citing works
Cheng, H. L., McGovern, M. P., Garneau, H. C., Hurley, B., Fisher, T., Copeland, M., & Almirall, D. (2022) · Implementation Science Communications · doi:10.1186/s43058-022-00306-1 · Cited by 25 · see citing works
“To reduce the possibility of bias (in the estimated effect of early engagement on outcomes) due to common correlates of the outcomes and engagement [50, 51], all models included two types of variables as baseline covariates: (i) a theory-informed list of pre-implementation variables that were hypothesized to be associ…”
MethodLeviton, A., Allred, E. N., Fichorova, R. N., O’Shea, T. M., Fordham, L. A., Kuban, K., & Dammann, O. (2018) · European Journal of Paediatric Neurology · doi:10.1016/j.ejpn.2018.01.018 · Cited by 24 · see citing works
Zhang, M., Michos, E. D., Wang, G., Wang, X., & Mueller, N. T. (2020) · JAMA Network Open · doi:10.1001/jamanetworkopen.2020.19046 · Cited by 23 · see citing works
Barberio, J., Ahern, T. P., MacLehose, R. F., Collin, L. J., Cronin-Fenton, D. P., Damkier, P., Sørensen, H. T., & Lash, T. L. (2021) · Clinical Epidemiology · doi:10.2147/clep.s313613 · Cited by 23 · see citing works
“in a minimally sufficient set of variables that will leave no open backdoor path between the exposure and the outcome.(2) Valid estimation of a causal effect of an”
BackgroundA calibration approach to transportability and data‐fusion with observational data
Josey, K., Yang, F., Ghosh, D., & Raghavan, S. (2022) · Statistics in Medicine · doi:10.1002/sim.9523 · Cited by 29 · see citing works
“If both Assumptions 8 and 9 are violated, then Si behaves like a surrogate confounder (VanderWeele and Shpitser, 2013) and omitting it from either the potential outcome models or the propensity score model may lead to biased effect estimates.”
BackgroundNuzzo, J. L., Finn, H. T., & Herbert, R. (2019) · Sports Medicine · doi:10.1007/s40279-019-01131-8 · Cited by 23 · see citing works
Jordan, S. E., Bromley, R., Damase‐Michel, C., Given, J. E., Komninou, S., Loane, M. A., Marfell, N., & Dolk, H. M. (2022) · International Breastfeeding Journal · doi:10.1186/s13006-022-00494-5 · Cited by 22 · see citing works
“The definition of confounderglossary most widely adopted is: “a factor associated with both the exposure and the outcome, and not part of the causal pathway from exposure to outcome” [8], blurring effects [7, 69, 70] (Table 1).”
BackgroundConfound-leakage: confound removal in machine learning leads to leakage
Hamdan, S., Love, B. C., von Polier, G. G., Weis, S., Schwender, H. R., Eickhoff, S. B., & Patil, K. R. (2022) · GigaScience · doi:10.1093/gigascience/giad071 · Cited by 23 · see citing works
“It is important to note that we use a practitioner-oriented operational definition of confounds as a set of variables suspected to share an unwanted effect with both the features and target, which does not imply a causal link as in more formal definitions [18].”
Xia, X., Jiang, B., Li, J., & Zhang, W. (2015) · Lifetime Data Analysis · doi:10.1007/s10985-015-9350-z · Cited by 21 · see citing works
“2009) that may be regarded as confounders (VanderWeele and Shpitser 2013).”
BackgroundA counterfactual approach to bias and effect modification in terms of response types
Suzuki, E., Mitsuhashi, T., Tsuda, T., & Yamamoto, E. (2013) · BMC Medical Research Methodology · doi:10.1186/1471-2288-13-101 · Cited by 21 · see citing works
“Recently, VanderWeele and Shpitser [29,30] further discussed the definition of a confounder.”
BackgroundInfluentialHe, J., Zhong, Y., Song, Y., Luo, J., Lin, C., Wu, Y., Pan, L., Cen, Y., Zhao, J., Gou, S., et al. (2025) · BMC Public Health · doi:10.1186/s12889-025-23383-y · Cited by 20 · see citing works
“Confounders (or covariates) are variables that impact both the outcome and grouping variables [32].”
Testing group differences for confounder selection in nonrandomized studies: flawed practice
Sourial, N., Vedel, I., Berre, M. L., & Schuster, T. (2019) · Canadian Medical Association Journal · doi:10.1503/cmaj.190085 · Cited by 20 · see citing works
CoCoA-diff: counterfactual inference for single-cell gene expression analysis
Park, Y., & Kellis, M. (2021) · Genome biology · doi:10.1186/s13059-021-02438-4 · Cited by 17 · see citing works
“We define that a variable can confound a disease label (W) and gene expressions (λ and Y) if (1) it is associated with the disease and gene expression variables and (2) it is still associated with the expression even after conditioning on the disease label [26].”
BackgroundEffects of statins and aspirin on HCC risk in alcohol-related cirrhosis: nationwide emulated trials
Kraglund, F., Christensen, D. H., Eiset, A. H., Villadsen, G. E., West, J., & Jepsen, P. (2023) · Hepatology Communications · doi:10.1097/hc9.0000000000000013 · Cited by 20 · see citing works
“Furthermore, most studies have not utilized a new user design, and prior studies have not specified the minimally sufficient adjustment set of confounders.[19] Two prior studies have investigated the effects of both statins and aspirin, and in both cases, the effect of statins was more protective.”
BackgroundSet-Based Tests for the Gene–Environment Interaction in Longitudinal Studies
He, Z., Zhang, M., Lee, S., Smith, J. A., Kardia, S. L. R., Roux, A. V. D., & Mukherjee, B. (2016) · Journal of the American Statistical Association · doi:10.1080/01621459.2016.1252266 · Cited by 20 · see citing works
Decoupling global biases and local interactions between cell biological variables
Zaritsky, A., Obolski, U., Gan, Z., Reis, C. R., Kadlecová, Z., Du, Y., Schmid, S. L., & Danuser, G. M. (2017) · eLife · doi:10.7554/elife.22323 · Cited by 20 · see citing works
“6 (VanderWeele and Shpitser, 2013) that must be eliminated for more accurate assessment of the true local interaction, but ignore the possibility that the global bias contains by-itself valuable mechanistic information to cell behavior.”
BackgroundTichelman, E., Warmink-Perdijk, W. D. B., Henrichs, J., Peters, L., Schellevis, F., Berger, M. Y., & Burger, H. (2021) · Midwifery · doi:10.1016/j.midw.2021.103045 · Cited by 21 · see citing works
Zawadzki, R. S., Grill, J. D., Gillen, D. L., & Initiative, A. F. T. A. D. N. (2023) · BMC Medical Research Methodology · doi:10.1186/s12874-023-01936-2 · Cited by 19 · see citing works
“[17][18] Alternatively, we may identify the treatment effect through an IV denoted as Z.”
Causal Etiology of the Research of James M. Robins
Richardson, T. S., & Rotnitzky, A. G. (2014) · Statistical Science · doi:10.1214/14-sts505 · Cited by 19 · see citing works
“As one example, he offered a precise mathematical definition for the informal epidemiologic concept of a “confounding variable” that has apparently stood the test of time (see VanderWeele and Shpitser, 2013).”
BackgroundWilson, A., Zigler, C. M., Patel, C. J., & Dominici, F. (2018) · Biometrics · doi:10.1111/biom.12860 · Cited by 18 · see citing works
“We consider a minimal set of covariates sufficient to satisfy (2) as the confounders (VanderWeele and Shpitser, 2013), denoted by C∗ ⊆ C.”
BackgroundMalec, S. A., Taneja, S. B., Albert, S. M., Shaaban, C. E., Karim, H. T., Levine, A. S., Munro, P., Callahan, T. J., & Boyce, R. D. (2023) · Journal of Biomedical Informatics · doi:10.1016/j.jbi.2023.104368 · Cited by 19 · see citing works
Conditional or unconditional logistic regression for frequency matched case‐control design?
Wan, F. (2022) · Statistics in Medicine · doi:10.1002/sim.9313 · Cited by 17 · see citing works
Methods Commentary: Uncovering Unobserved Data Patterns With Latent Variable Mixture Modeling
Berlin, K. S., Ankney, R. L., & Rybak, T. M. (2018) · Journal of Pediatric Psychology · doi:10.1093/jpepsy/jsy042 · Cited by 16 · see citing works
Yu, Y., Li, H., Sun, X., Liu, X., Yang, F., Hou, L., Liu, L., Yan, R., Yu, Y., Jing, M., et al. (2020) · American Journal of Epidemiology · doi:10.1093/aje/kwaa172 · Cited by 15 · see citing works
Chan, G., Sun, T., Stjepanović, D., Vu, G. T., Hall, W., Connor, J. P., & Leung, J. (2024) · Addiction · doi:10.1111/add.16442 · Cited by 15 · see citing works
Educational attainment by children with parental alcohol problems in Denmark and Finland
Raitasalo, K., Østergaard, J., & Andrade, S. B. (2020) · Nordic Studies on Alcohol and Drugs · doi:10.1177/1455072520968343 · Cited by 15 · see citing works
Leviton, A., Dammann, O., Allred, E. N., Joseph, R. M., Fichorova, R. N., O’Shea, T. M., & Kuban, K. (2018) · International Journal of Developmental Neuroscience · doi:10.1016/j.ijdevneu.2018.01.001 · Cited by 16 · see citing works
“Inflammation is a broad and complex phenomenon (VanderWeele and Shpitser, 2013; Zak and Aderem, 2015) and we have assessed only a very small part of it.”
BackgroundLong-term causal effects of far-right terrorism in New Zealand
Bulbulia, J. A., Afzali, M. U., Yogeeswaran, K., & Sibley, C. G. (2023) · PNAS Nexus · doi:10.1093/pnasnexus/pgad242 · Cited by 15 · see citing works
Using negative controls to adjust for unmeasured confounding bias in time series studies
Hu, J. K., Tchetgen, E. J. T., & Dominici, F. (2023) · Nature Reviews Methods Primers · doi:10.1038/s43586-023-00249-4 · Cited by 14 · see citing works
Patterns of resilient functioning in early life: Identifying distinct groups and associated factors
Cahill, S., Hager, R., & Shryane, N. M. (2023) · Development and Psychopathology · doi:10.1017/s0954579423001165 · Cited by 16 · see citing works
“All ACE predictors were entered into each regression model to capture the cumulative impact of all ACEs on resilience (VanderWeele & Shpitser, 2013).”
MethodAlMaghlouth, I. A., Pullenayegum, E., Gladman, D. D., Urowitz, M. B., & Johnson, S. R. (2020) · The Journal of Rheumatology · doi:10.3899/jrheum.200254 · Cited by 14 · see citing works
Marcello, M., Denham, J. W., Kennedy, A., Haworth, A., Steigler, A., Greer, P. B., Holloway, L. C., Dowling, J., Jameson, M., Roach, D., et al. (2020) · Frontiers in Oncology · doi:10.3389/fonc.2020.01174 · Cited by 14 · see citing works
“Age, prescribed dose, disease risk, cancer stage, baseline PSA concentration and number of treatment beams were patient baseline characteristics investigated as potential control variables in each model, attempting to eliminate their confounding influence at each voxel (30, 31).”
BackgroundMalec, S. A., Wei, P., Bernstam, E. V., Boyce, R. D., & Cohen, T. (2021) · Journal of Biomedical Informatics · doi:10.1016/j.jbi.2021.103719 · Cited by 14 · see citing works
Aarabi, G., Walther, C., Kaymaz, K., Spinler, K., Buczak‐Stec, E., König, H., & Hajek, A. (2021) · Aging Clinical and Experimental Research · doi:10.1007/s40520-021-02051-2 · Cited by 14 · see citing works
“In directed acyclic graphs (DAG) notation, our aim was to block the backdoor path (i.e., a non-causal path from X to Y ; usually common causes of X and Y [20]) between personality factors and regular dental visit attendance via sociodemographic and health-related factors.”
tipr: An R package for sensitivity analyses for unmeasured confounders
McGowan, L. D. (2022) · The Journal of Open Source Software · doi:10.21105/joss.04495 · Cited by 14 · see citing works
Marcello, M., Ebert, M. A., Haworth, A., Steigler, A., Kennedy, A., Joseph, D. J., & Denham, J. W. (2017) · Radiotherapy and Oncology · doi:10.1016/j.radonc.2017.10.021 · Cited by 14 · see citing works
Research Note: Causal inference
Herbert, R. (2020) · Journal of physiotherapy · doi:10.1016/j.jphys.2020.07.010 · Cited by 14 · see citing works
- Authors
- VanderWeele, T. J., & Shpitser, I.
- Affiliations
- Harvard University (US)
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2013-02-01
- Volume
- 41
- Issue
- 1
- Pages
- 196-220
- ISSN
- 0090-5364 (ISSN-L)
- 2168-8966
- PMC
- PMC4276366
- OpenAlex
- W2067177016
- Cited by
- 268
- References
- 46
- Citations by year
- 2026: 18 · 2025: 23 · 2024: 28 · 2023: 25 · 2022: 23 · 2021: 46 · 2020: 33 · 2019: 20 · 2018: 17 · 2017: 15 · 2016: 11 · 2015: 5 · 2014: 3 · 2013: 1
- FWCI
- 5.87
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Statistics (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- Collection of Biostatistics Research Archive (submittedVersion)
- Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
- Project Euclid (Cornell University) (submittedVersion)
- ePrints Soton (University of Southampton) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Institutes of Health (ES017876)
- National Institute of Environmental Health Sciences (R01ES017876, R56ES017876)
- Eunice Kennedy Shriver National Institute of Child Health and Human Development (R03HD060696)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- confounding, causal inference, unconfoundedness, covariate control
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