Average treatment effect

The average treatment effect , even Middle treatment effect called ( English average treatment effect , short- ATE ) is a measure that is used to treatments or interventions in randomized compare experiments and medical tests. The mean treatment effect measures the mean difference in treatment outcomes between individuals assigned to the experimental group and individuals assigned to the control group. In a randomized random experiment (e.g. an experimental study), the “average treatment effect” can be estimated by comparing the arithmetic mean of the results of the experimental group with the arithmetic mean of the results of the control group. The average treatment effect is generally understood as a causal parameter (i.e., an estimate or a property of a population), which it is in the interests of the researcher to determine and which is constructed independently of the research design or the estimation procedure. There are many different approaches to estimating the average treatment effect in observational research and experimental research.

general definition

The term “treatment” has its origins in the early days of statistical analysis, medicine and agriculture. Over time, the term has been applied to a wide spectrum , including natural and social sciences, more specifically psychology , political science and economics , such as: B. Assessing the impact of a policy change. The specification of the treatment or the result plays a subordinate role in the estimation of the ATE, i.e. H. the calculation of the ATE only requires the condition that the treatment has been assigned to some units and not to others, however the specification of the treatment (e.g., a pharmaceutical product, a payment incentive, a policy change etc.) is for the definition and the mathematical ATE estimate insignificant.

Average treatment effect in the population

The mean treatment effect of the population is defined as the difference between the mean values of the subjects assigned the treatment and the control group:

{\ displaystyle \ tau: = {\ frac {1} {N}} \ sum _ {i = 1} ^ {N} (y_ {1i} -y_ {0i}) = {\ bar {y}} _ { 1i} - {\ bar {y}} _ {0i}}

${\ displaystyle N}$ : Population size
${\ displaystyle i}$ : Index for subjects
${\ displaystyle D_ {i} = 1}$ : Treatment
${\ displaystyle D_ {i} = 0}$ : Control unit
${\ displaystyle y_ {1i}}$ : Result when individual i was assigned to the experimental group ${\ displaystyle D_ {i} = 1}$
${\ displaystyle y_ {0i}}$ : Result when individual i was assigned to the control group ${\ displaystyle D_ {i} = 0}$

Average treatment effect among those treated

A derived from the average treatment effect term is the average treatment effect among subjects ( English average treatment effect on the treatet short ATT ). This measure is used in the Neyman-Rubin model of causal inference.

literature

Jeffrey M. Wooldridge: Policy Analysis with Pooled Cross Sections . In: Introductory Econometrics: A Modern Approach . Thomson South-Western, Mason, OH 2013, ISBN 978-1-111-53104-1 , pp. 438-443.
Guido W. Imbens, Donald B. Rubin: Causal Inference for Statistics, Social, and Biomedical Sciences Harvard University / Stanford University 2015

Individual evidence

↑ Imbens, GW & Rubin, DB (2015). Causal Inference for Statistics, Social and Biomedical Sciences: An Introduction. New York: Cambridge, p. 86

[1] Imbens, GW & Rubin, DB (2015). Causal Inference for Statistics, Social and Biomedical Sciences: An Introduction. New York: Cambridge, p. 86