Skip to main content
SpringerLink
Log in

The Sample Average Treatment Effect

  • Chapter
  • First Online:
Targeted Learning in Data Science

Part of the book series: Springer Series in Statistics ((SSS))

  • 5607 Accesses

Abstract

In cluster randomized trials (CRTs), the study units usually are not a simple random sample from some clearly defined target population. Instead, the target population tends to be hypothetical or ill-defined, and the selection of study units tends to be systematic, driven by logistical and practical considerations. As a result, the population average treatment effect (PATE) may be neither well defined nor easily interpretable. In contrast, the sample average treatment effect (SATE) is the mean difference in the counterfactual outcomes for the study units. The sample parameter is easily interpretable and arguably the most relevant when the study units are not sampled from some specific super-population of interest. Furthermore, in most settings the sample parameter will be estimated more efficiently than the population parameter.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Logistic fluctuation can also be used for a continuous outcome that is bounded in [a, b] by first applying the following transformation to the outcome: Y ∗ = (Y − a)∕(b − a). Use of logistic regression over linear regression can provide stability under data sparsity and/or with rare outcomes (e.g., Gruber and van der Laan 2010b).

References

  • A. Abadie, G. Imbens, Simple and bias-corrected matching estimators for average treatment effects. Technical Report 283. NBER Working Paper (2002)

    Google Scholar 

  • L. Balzer, M. Petersen, M.J. van der Laan, Adaptive pair-matching in randomized trials with unbiased and efficient effect estimation. Stat. Med. 34(6), 999–1011 (2015)

    Article  MathSciNet  Google Scholar 

  • L. Balzer, J. Ahern, S. Galea, M.J. van der Laan, Estimating effects with rare outcomes and high dimensional covariates: Knowledge is power. Epidemiol. Methods. 5(1), 1–18 (2016a)

    Google Scholar 

  • L.B. Balzer, M.L. Petersen, M.J. van der Laan, the SEARCH Collaboration, Targeted estimation and inference of the sample average treatment effect in trials with and without pair-matching. Stat. Med. 35(21), 3717–3732 (2016c)

    Google Scholar 

  • E. Bareinboim, J. Pearl, A general algorithm for deciding transportability of experimental results. J. Causal Inf. 1(1), 107–134 (2013)

    Google Scholar 

  • C. Beck, B. Lu, R. Greevy, nbpMatching: functions for optimal non-bipartite optimal matching (2016). https://CRAN.R-project.org/package=nbpMatching

  • M.J. Campbell, A. Donner, N. Klar, Developments in cluster randomized trials and statistics in medicine. Stat. Med. 26, 2–19 (2007)

    Article  MathSciNet  Google Scholar 

  • W.G. Cochran, Analysis of covariance: its nature and uses. Biometrics 13, 261–281 (1957)

    Article  MathSciNet  Google Scholar 

  • S.R. Cole, E.A. Stuart, Generalizing evidence from randomized clinical trials to target populations: the ACTG 320 trial. Am. J. Epidemiol. 172(1), 107–115 (2010)

    Article  Google Scholar 

  • D.R. Cox, P. McCullagh, Some aspects of analysis of covariance. Biometrics 38(3), 541–561 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  • European Medicines Agency, Guideline on adjustment for baseline covariates in clinical trials. London, February (2015)

    Google Scholar 

  • R.A. Fisher, Statistical Methods for Research Workers, 4th edn. (Oliver and Boyd Ltd., Edinburgh, 1932)

    MATH  Google Scholar 

  • R.A. Fisher, The Design of Experiments, (Oliver and Boyd Ltd, London, 1935)

    Google Scholar 

  • L.S. Freedman, M.H. Gail, S.B. Green, D.K. Corle, The COMMIT Research Group, The Efficiency of the matched-pairs design of the community intervention trial for smoking cessation (COMMIT). Control. Clin. Trials 18(2), 131–139 (1997)

    Article  Google Scholar 

  • R. Greevy, B. Lu, J.H. Silber, P. Rosenbaum, Optimal multivariate matching before randomization. Biostatistics 5(2), 263–275 (2004)

    Article  MATH  Google Scholar 

  • H. Grosskurth, F. Mosha, J. Todd, E. Mwijarubi, A. Klokke, K. Senkoro, P. Mayaud, J. Changalucha, A. Nicoll, G. ka-Gina, J. Newell, K. Mugeye, D. Mabey, R. Hayes, Impact of improved treatment of sexually transmitted diseases on HIV infection in rural Tanzania: randomised controlled trial. Lancet 346(8974), 530–536 (1995)

    Google Scholar 

  • S. Gruber, M.J. van der Laan, A targeted maximum likelihood estimator of a causal effect on a bounded continuous outcome. Int. J. Biostat. 6(1), Article 26 (2010b)

    Google Scholar 

  • J. Hahn, On the role of the propensity score in efficient semiparametric estimation of average treatment effects. Econometrica 2, 315–331 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • E. Hartman, R. Grieve, R. Ramsahai, J.S. Sekhon, From sample average treatment effect to population average treatment effect on the treated: combining experimental with observational studies to estimate population treatment effects. J. R. Stat. Soc. Ser. A 178(3), 757–778 (2015)

    Article  MathSciNet  Google Scholar 

  • R.J. Hayes, L.H. Moulton, Cluster Randomised Trials. (Chapman & Hall/CRC, Boca Raton, 2009)

    Google Scholar 

  • D.G. Horvitz, D.J. Thompson, A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc. 47, 663–685 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  • K. Imai, Variance identification and efficiency analysis in randomized experiments under the matched-pair design. Stat. Med. 27(24), 4857–4873 (2008)

    Article  MathSciNet  Google Scholar 

  • K. Imai, G. King, C. Nall, The essential role of pair matching in cluster-randomized experiments, with application to the Mexican universal health insurance evaluation. Stat. Sci. 24(1), 29–53 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • G.W. Imbens, Nonparametric estimation of average treatment effects under exogeneity: a review. Rev. Econ. Stat. 86(1), 4–29 (2004)

    Article  MathSciNet  Google Scholar 

  • G. Imbens, D.B. Rubin, Causal Inference for Statistics, Social, and Biomedical Sciences (Cambridge University Press, New York, 2015)

    Book  MATH  Google Scholar 

  • N. Klar, A. Donner, The merits of matching in community intervention trials: a cautionary tale. Stat. Med. 16(15), 1753–1764 (1997)

    Article  Google Scholar 

  • B. Lu, R. Greevy, X. Xu, C. Beck, Optimal nonbipartite matching and its statistical applications. Am. Stat. 65(1), 21–30 (2011)

    Article  MathSciNet  Google Scholar 

  • K.L. Moore, M.J. van der Laan, Covariate adjustment in randomized trials with binary outcomes: targeted maximum likelihood estimation. Stat. Med. 28(1), 39–64 (2009b)

    Google Scholar 

  • J. Neyman, Sur les applications de la theorie des probabilites aux experiences agricoles: Essai des principes (In Polish). English translation by D.M. Dabrowska and T.P. Speed (1990). Stat. Sci. 5, 465–480 (1923)

    Google Scholar 

  • J. Pearl, Causal diagrams for empirical research. Biometrika 82, 669–710 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Pearl, Causality: Models, Reasoning, and Inference, 2nd edn. (Cambridge, New York, 2009a)

    Google Scholar 

  • R Development Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna (2016). http://www.R-project.org.

  • J.M. Robins, A new approach to causal inference in mortality studies with sustained exposure periods–application to control of the healthy worker survivor effect. Math. Modell. 7, 1393–1512 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • J.M. Robins, A. Rotnitzky, L.P. Zhao, Estimation of regression coefficients when some regressors are not always observed. J. Am. Stat. Assoc. 89(427), 846–866 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • P.R. Rosenbaum, D.B. Rubin, The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41–55 (1983b)

    Google Scholar 

  • M. Rosenblum, M.J. van der Laan, Simple, efficient estimators of treatment effects in randomized trials using generalized linear models to leverage baseline variables. Int. J. Biostat. 6(1), Article 13 (2010b)

    Google Scholar 

  • D.B. Rubin, Comment: Neyman (1923) and causal inference in experiments and observational studies. Stat. Sci. 5(4), 472–480 (1990)

    Article  MATH  Google Scholar 

  • P. Schochet, Estimators for clustered education RCTs using the Neyman model for causal inference. J. Educ. Behav. Stat. 38(3), 219–238 (2013)

    Article  Google Scholar 

  • C. Shen, X. Li, L. Li, Inverse probability weighting for covariate adjustment in randomized studies. Stat. Med. 33, 555–568 (2014)

    Article  MathSciNet  Google Scholar 

  • J.M. Snowden, S. Rose, K.M. Mortimer, Implementation of g-computation on a simulated data set: demonstration of a causal inference technique. Am. J. Epidemiol. 173(7), 731–738 (2011)

    Article  Google Scholar 

  • E.A. Stuart, S.R. Cole, C.P. Bradshaw, P.J. Leaf, The use of propensity scores to assess the generalizability of results from randomized trials. J. R. Stat. Soc. Ser. A 174(Part 2), 369–386 (2011)

    Google Scholar 

  • M. Toftager, L.B. Christiansen, P.L. Kristensen, J. Troelsen, Space for physical activity-a multicomponent intervention study: study design and baseline findings from a cluster randomized controlled trial. BMC Public Health 11, 777 (2011)

    Article  Google Scholar 

  • A.A. Tsiatis, M. Davidian, M. Zhang, X. Lu, Covariate adjustment for two-sample treatment comparisons in randomized clinical trials: a principled yet flexible approach. Stat. Med. 27, 4658–4677 (2008)

    Article  MathSciNet  Google Scholar 

  • M.J. van der Laan, J.M. Robins, Unified Methods for Censored Longitudinal Data and Causality (Springer, Berlin Heidelberg New York, 2003)

    Book  MATH  Google Scholar 

  • M.J. van der Laan, S. Rose, Targeted Learning: Causal Inference for Observational and Experimental Data (Springer, Berlin, Heidelberg, New York, 2011)

    Book  Google Scholar 

  • M.J. van der Laan, D.B. Rubin, Targeted maximum likelihood learning. Int. J. Biostat. 2(1), Article 11 (2006)

    Google Scholar 

  • M.J. van der Laan, L.B. Balzer, M.L. Petersen, Adaptive matching in randomized trials and observational studies. J. Stat. Res. 46(2), 113–156 (2013a)

    Google Scholar 

  • L. Watson, R. Small, S. Brown, W. Dawson, J. Lumley, Mounting a community-randomized trial: sample size, matching, selection, and randomization issues in PRISM. Control. Clin. Trials 25(3), 235–250 (2004)

    Article  Google Scholar 

  • K. Zhang, D.S. Small, Comment: the essential role of pair matching in cluster-randomized experiments, with application to the Mexican universal health insurance evaluation. Stat. Sci. 25(1), 59–64 (2009)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

Research reported in this chapter was supported by Division of AIDS, NIAID of the National Institutes of Health under award numbers R01-AI074345, R37-AI051164, UM1AI069502 and U01AI099959. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

Author information

Authors and Affiliations

  1. Department of Biostatistics and Epidemiology, School of Public Health and Health Sciences, University of Massachusetts - Amherst, 416 Arnold House, 715 North Pleasant St, Amherst, MA, 01003, USA

    Laura B. Balzer

  2. Division of Epidemiology and Division of Biostatistics, University of California, Berkeley, 101 Haviland Hall, #7358, Berkeley, CA, 94720, USA

    Maya L. Petersen

  3. Division of Biostatistics and Department of Statistics, University of California, Berkeley, 101 Haviland Hall, #7358, Berkeley, CA, 94720, USA

    Mark J. van der Laan

Authors
  1. Laura B. Balzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maya L. Petersen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mark J. van der Laan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laura B. Balzer .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Balzer, L.B., Petersen, M.L., van der Laan, M.J. (2018). The Sample Average Treatment Effect. In: Targeted Learning in Data Science. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-65304-4_12

Download citation

Publish with us

Policies and ethics

Search

Navigation