The Sample Average Treatment Effect
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.
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.
- 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, 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
- European Medicines Agency, Guideline on adjustment for baseline covariates in clinical trials. London, February (2015)Google Scholar
- R.A. Fisher, The Design of Experiments, (Oliver and Boyd Ltd, London, 1935)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
- 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)MathSciNetCrossRefGoogle Scholar
- R.J. Hayes, L.H. Moulton, Cluster Randomised Trials. (Chapman & Hall/CRC, Boca Raton, 2009)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, 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.
- 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
- 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.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