An alternative to direct matching or matching on propensity scores involves the use of the inverse of propensity scores in a weighted regression framework (Horvitz and Thompson (1952), known as inverse probability of treatment weighted (IPTW) regression where:

IPTW regression (with weights specified as above) specifically
estimates the average treatment effect (ATE) (Astin, 2011):

ATE = E[Y

_{1i}-Y_{0i}]
Inverse
probability of treatment weighting (IPTW) uses weights derived from the
propensity scores to create a pseudo
population such that the distribution of covariates in the population are
independent of treatment assignment. (Astin,2011). This is an appeal to the CIA and
Rosenbaum and Rubin’s propensity score theorem discussed
before. The
weighting scheme essentially ‘weights up’ control units to look like treatment
units (Stuart,2011).

**References**

Austin, P.(2011). An Introduction to Propensity Score Methods for
Reducing the Effects of Confounding in
Observational Studies.

*Multivariate Behav Research.*May; 46(3): 399–424.
Horvitz D. G. & Thompson D. J.(1952) . A
Generalization of Sampling Without Replacement From a Finite Universe. Journal of the American
Statistical Association, Vol. 47, No. 260 (Dec., 1952), pp. 663- 685

Maciejewski, M. L. & Brookhart, M.A. (2011).

*Propensity score**workshop*. Retrieved January 19,2013. Website: http://ahrqplexnet.sharepointspace.com/Webinars/PS_webinar_followup.pdf
Stuart ,E.(2011).Propensity score methods for
estimating causal effects: The why, when, and how . Johns Hopkins Bloomberg School of Public
Health. Department of Mental Health. Department of Biostatistics. Retrieved January 19,2013.
Website:
www.biostat.jhsph.edu/estuart

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