In econometrics and related empirical fields, the local average treatment effect (LATE), also known as the complier average causal effect (CACE), is the effect of a treatment for subjects who comply with the experimental treatment assigned to their sample group. It is not to be confused with the average treatment effect (ATE), which includes compliers and non-compliers together. Compliance refers to the human-subject response to a proposed experimental treatment condition. Similar to the ATE, the LATE is calculated but does not include non-compliant parties. If the goal is to evaluate the effect of a treatment in ideal, compliant subjects, the LATE value will give a more precise estimate. However, it may lack external validity by ignoring the effect of non-compliance that is likely to occur in the real-world deployment of a treatment method. The LATE can be estimated by a ratio of the estimated intent-to-treat effect and the estimated proportion of compliers, or alternatively through an instrumental variable estimator.
The LATE was first introduced in the econometrics literature by Guido W. Imbens and Joshua D. Angrist in 1994, who shared one half of the 2021 Nobel Memorial Prize in Economic Sciences.[1][2] As summarized by the Nobel Committee, the LATE framework "significantly altered how researchers approach empirical questions using data generated from either natural experiments or randomized experiments with incomplete compliance to the assigned treatment. At the core, the LATE interpretation clarifies what can and cannot be learned from such experiments."[2]
The phenomenon of non-compliant subjects (patients) is also known in medical research.[3] In the biostatistics literature, Baker and Lindeman (1994) independently developed the LATE method for a binary outcome with the paired availability design and the key monotonicity assumption.[4] Baker, Kramer, Lindeman (2016) summarized the history of its development.[5] Various papers called both Imbens and Angrist (1994) and Baker and Lindeman (1994) seminal.[6][7][8][9]
An early version of LATE involved one-sided noncompliance (and hence no monotonicity assumption). In 1983 Baker wrote a technical report describing LATE for one-sided noncompliance that was published in 2016 in a supplement.[5] In 1984, Bloom published a paper on LATE with one-sided compliance.[10] For a history of multiple discoveries involving LATE see Baker and Lindeman (2024).[11]
^Imbens, Guido W.; Angrist, Joshua D. (March 1994). "Identification and Estimation of Local Average Treatment Effects" (PDF). Econometrica. 62 (2): 467. doi:10.2307/2951620. ISSN 0012-9682. JSTOR 2951620.
^ abThe Committee for the Prize in Economic Sciences in Memory of Alfred Nobel (2021-10-11). "Answering causal questions using observational data. Scientific Background on the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2021" (PDF).
^Moerbeek, M., & Schie, S. van. (2019). What are the statistical implications of treatment non‐compliance in cluster randomized trials: A simulation study. In Statistics in Medicine (Vol. 38, Issue 26, pp. 5071–5084). Wiley. https://doi.org/10.1002/sim.8351
^Baker, Stuart G.; Lindeman, Karen S. (1994-11-15). "The paired availability design: A proposal for evaluating epidural analgesia during labor". Statistics in Medicine. 13 (21): 2269–2278. doi:10.1002/sim.4780132108. ISSN 0277-6715. PMID 7846425.
^ abBaker, Stuart G.; Kramer, Barnett S.; Lindeman, Karen S. (2018-10-30). ""Latent class instrumental variables: A clinical and biostatistical perspective"". Statistics in Medicine. 38 (5): 901. doi:10.1002/sim.6612. ISSN 0277-6715. PMID 30761594.
^Swanson, Sonja A.; Hernán, Miguel A.; Miller, Matthew; Robins, James M.; Richardson, Thomas S. (2018-04-03). "Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes". Journal of the American Statistical Association. 113 (522): 933–947. doi:10.1080/01621459.2018.1434530. ISSN 0162-1459. PMC 6752717. PMID 31537952.
^Lee, Kwonsang; Lorch, Scott A.; Small, Dylan S. (2019-02-20). "Sensitivity analyses for average treatment effects when outcome is censored by death in instrumental variable models". Statistics in Medicine. 38 (13): 2303–2316. arXiv:1802.06711. doi:10.1002/sim.8117. ISSN 0277-6715. PMID 30785641. S2CID 73458979.
^Sheng, E (2019). "Estimating causal effects of treatment in RCTs with provider and subject noncompliance". Statistics in Medicine. 38 (5): 738–750. doi:10.1002/sim.8012. PMID 30347462. S2CID 53035814.
^Wang, L (2016). "Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variable". arXiv:1611.09925v4. {{cite journal}}: Cite journal requires |journal= (help)
^Bloom, Howard S. (April 1984). "Accounting for No-Shows in Experimental Evaluation Designs". Evaluation Review. 8 (2): 225–246. doi:10.1177/0193841X8400800205. ISSN 0193-841X.
^Baker, Stuart G.; Lindeman, Karen S. (2024-04-02). "Multiple Discoveries in Causal Inference: LATE for the Party". CHANCE. 37 (2): 21–25. doi:10.1080/09332480.2024.2348956. ISSN 0933-2480.
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