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Published in: BMC Medical Research Methodology 1/2017

Open Access 01-12-2017 | Research article

G-computation of average treatment effects on the treated and the untreated

Authors: Aolin Wang, Roch A. Nianogo, Onyebuchi A. Arah

Published in: BMC Medical Research Methodology | Issue 1/2017

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Abstract

Background

Average treatment effects on the treated (ATT) and the untreated (ATU) are useful when there is interest in: the evaluation of the effects of treatments or interventions on those who received them, the presence of treatment heterogeneity, or the projection of potential outcomes in a target (sub-) population. In this paper we illustrate the steps for estimating ATT and ATU using g-computation implemented via Monte Carlo simulation.

Methods

To obtain marginal effect estimates for ATT and ATU we used a three-step approach: fitting a model for the outcome, generating potential outcome variables for ATT and ATU separately, and regressing each potential outcome variable on treatment intervention.

Results

The estimates for ATT, ATU and average treatment effect (ATE) were of similar magnitude, with ATE being in between ATT and ATU as expected. In our illustrative example, the effect (risk difference [RD]) of a higher education on angina among the participants who indeed have at least a high school education (ATT) was −0.019 (95% CI: −0.040, −0.007) and that among those who have less than a high school education in India (ATU) was −0.012 (95% CI: −0.036, 0.010).

Conclusions

The g-computation algorithm is a powerful way of estimating standardized estimates like the ATT and ATU. Its use should be encouraged in modern epidemiologic teaching and practice.
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Literature
1.
go back to reference Imbens GW. Nonparametric estimation of average treatment effects under exogeneity: a review. Rev Econ Stat. 2004;86:4–29.CrossRef Imbens GW. Nonparametric estimation of average treatment effects under exogeneity: a review. Rev Econ Stat. 2004;86:4–29.CrossRef
2.
go back to reference Heckman JJ, Vytlacil E. Policy-Relevant Treatment Effects. Am Econ Rev. 2001;91:107–11.CrossRef Heckman JJ, Vytlacil E. Policy-Relevant Treatment Effects. Am Econ Rev. 2001;91:107–11.CrossRef
3.
go back to reference Robins JM. Marginal Structural Models versus Structural nested Models as Tools for Causal inference. In: Halloran ME, Berry D, editors. Stat. Model. Epidemiol. Environ. Clin. Trials. New York: Springer; 2000. p. 95–133.CrossRef Robins JM. Marginal Structural Models versus Structural nested Models as Tools for Causal inference. In: Halloran ME, Berry D, editors. Stat. Model. Epidemiol. Environ. Clin. Trials. New York: Springer; 2000. p. 95–133.CrossRef
4.
go back to reference Robins J. A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect. Math Model. 1986;7:1393–512.CrossRef Robins J. A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect. Math Model. 1986;7:1393–512.CrossRef
5.
go back to reference Robins JM, Robins JM, Hernán MA, Hernán MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology. 2000;11:550–60.CrossRefPubMed Robins JM, Robins JM, Hernán MA, Hernán MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology. 2000;11:550–60.CrossRefPubMed
6.
go back to reference Daniel RM, Cousens SN, De Stavola BL, Kenward MG, Sterne JAC. Methods for dealing with time-dependent confounding. Stat Med. 2013;32:1584–618.CrossRefPubMed Daniel RM, Cousens SN, De Stavola BL, Kenward MG, Sterne JAC. Methods for dealing with time-dependent confounding. Stat Med. 2013;32:1584–618.CrossRefPubMed
7.
go back to reference Snowden JM, Rose S, Mortimer KM. Implementation of G-computation on a simulated data set: demonstration of a causal inference technique. Am J Epidemiol. 2011;173:731–8.CrossRefPubMedPubMedCentral Snowden JM, Rose S, Mortimer KM. Implementation of G-computation on a simulated data set: demonstration of a causal inference technique. Am J Epidemiol. 2011;173:731–8.CrossRefPubMedPubMedCentral
8.
go back to reference Keil AP, Edwards JK, Richardson DB, Naimi AI, Cole SR. The parametric g-formula for time-to-event data: intuition and a worked example. Epidemiology. 2014;25:889–97.CrossRefPubMedPubMedCentral Keil AP, Edwards JK, Richardson DB, Naimi AI, Cole SR. The parametric g-formula for time-to-event data: intuition and a worked example. Epidemiology. 2014;25:889–97.CrossRefPubMedPubMedCentral
9.
go back to reference Taubman SL, Robins JM, Mittleman MA, Hernán MA. Intervening on risk factors for coronary heart disease: an application of the parametric g-formula. Int J Epidemiol. 2009;38:1599–611.CrossRefPubMedPubMedCentral Taubman SL, Robins JM, Mittleman MA, Hernán MA. Intervening on risk factors for coronary heart disease: an application of the parametric g-formula. Int J Epidemiol. 2009;38:1599–611.CrossRefPubMedPubMedCentral
10.
11.
go back to reference Nianogo RA, Wang MC, Wang A, Nobari TZ, Crespi CM, Whaley SE, et al. Projecting the impact of hypothetical early life interventions on adiposity in children living in low-income households. Pediatr Obes. 2016. doi:10.1111/ijpo.12157.PubMed Nianogo RA, Wang MC, Wang A, Nobari TZ, Crespi CM, Whaley SE, et al. Projecting the impact of hypothetical early life interventions on adiposity in children living in low-income households. Pediatr Obes. 2016. doi:10.​1111/​ijpo.​12157.PubMed
12.
go back to reference Cole SR, Frangakis CE. The consistency statement in causal inference: a definition or an assumption? Epidemiology. 2009;20:3–5.CrossRefPubMed Cole SR, Frangakis CE. The consistency statement in causal inference: a definition or an assumption? Epidemiology. 2009;20:3–5.CrossRefPubMed
15.
go back to reference Efron B, Tibshirani R. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Stat Sci. 1986;1:54–75.CrossRef Efron B, Tibshirani R. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Stat Sci. 1986;1:54–75.CrossRef
17.
go back to reference Wang A, Stronks K, Arah OA. Global educational disparities in the associations between body mass index and diabetes mellitus in 49 low-income and middle-income countries. J Epidemiol Community Health. 2014;68:705–11.CrossRefPubMed Wang A, Stronks K, Arah OA. Global educational disparities in the associations between body mass index and diabetes mellitus in 49 low-income and middle-income countries. J Epidemiol Community Health. 2014;68:705–11.CrossRefPubMed
18.
20.
go back to reference Bang H, Robins JM. Doubly robust estimation in missing data and causal inference models. Biometrics. 2005;61:962–72.CrossRefPubMed Bang H, Robins JM. Doubly robust estimation in missing data and causal inference models. Biometrics. 2005;61:962–72.CrossRefPubMed
21.
go back to reference Vansteelandt S, Keiding N. Invited commentary: G-computation--lost in translation? Am J Epidemiol. 2011;173:739–42.CrossRefPubMed Vansteelandt S, Keiding N. Invited commentary: G-computation--lost in translation? Am J Epidemiol. 2011;173:739–42.CrossRefPubMed
22.
go back to reference Sato T, Matsuyama Y. Marginal structural models as a tool for standardization. Epidemiology. 2003;14:680–6.CrossRefPubMed Sato T, Matsuyama Y. Marginal structural models as a tool for standardization. Epidemiology. 2003;14:680–6.CrossRefPubMed
Metadata
Title
G-computation of average treatment effects on the treated and the untreated
Authors
Aolin Wang
Roch A. Nianogo
Onyebuchi A. Arah
Publication date
01-12-2017
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2017
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/s12874-016-0282-4

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