I am a scientist and while I can analyze data, I am not a statistician and I frequently take the authors at their word that stats models are being used correctly. Can a stats pro explain IPTW and also why truncation of weights is sometime used?
In: Mathematics
Disclaimer: not a statistician, but a social science grad student with an overdeveloped interest in methods. But, having just reread a bunch of papers to be sure, I’m reasonably certain about this explanation.
IPTW is an application of propensity scoring (see [Rosenbaum and Rubin 1983](https://academic.oup.com/biomet/article-abstract/70/1/41/240879) or the many primers that followed) proposed by [Rosenbaum](https://www.tandfonline.com/doi/pdf/10.1080/01621459.1987.10478441?casa_token=EFH_naBuP_cAAAAA:ikXjNF8JY5udB3pVQNHjZmPmUQbw5o693NrPGwt_KNvu-YnJ2kFXWi9fy5TGkMSP8gjdX-tsMhrx) as a method of adjusting for observed confounders.
The basic idea is that by weighting each observation in a sample using the inverse of its probability of receiving some treatment, one can create a “pseudo-population” in which outcomes are conditioned on treatment, but *not* on observed confounding covariates.
If the pseudo-population is correctly constructed (i.e. the estimated propensity score is satisfactory w.r.t. ignorability and other underlying assumptions), then the IPTW model recovers the basic form of an experiment — which is the foundational idea behind quasi-experimental methods like propensity scoring, regression discontinuity, etc. The estimated treatment effect, then, should be the effect of treatment depending *only* on treatment.
Truncation is a way of handling weird weights in scenarios like the above. If an observation receives treatment but has a low probability of treatment based on observed covariates, the weight assigned to them gets quite large; vice versa for those who are likely to receive treatment but do not. Truncation, in a simple form, either discards these outlying weights or coerces them to some quantile of the weight range as chosen by the researcher (similar to how you might drop outlying observations in regression modeling). Truncation biases the estimated treatment effect, but also decreases its variance — usually it is up to the researcher to decide what an acceptable tradeoff is in this respect.
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