Re: st: deriving a bootstrap estimate of a difference between two weighted regressions

["Ariel Linden, DrPH" <ariel.linden@gmail.com>]

There are at least two conceptual reasons why this process makes sense. 

First, assume a causal inference model which uses a weight (let's say an
"average treatment on the treated" weight) to create balance on observed
pre-intervention covariates (by setting the covariates to equal that of the
treated group). Let's say the second model is identical but uses an "average
treatment on controls" (ATC) weight. Assuming no unmeasured confounding, the
treatment variable(s) from both models will provide the treatment effect
estimate given the respective weighting purposes (holding covariates to
represent treatment or control group characteristics). Thus, measuring the
difference between the treatment effects in both models (which will need to
have either bootstrapped or other adjustment to the SE) can serve as a
sensitivity analysis (one of many approaches).

Second, and in a similar manner, one can test the effect of a mediator using
a weighting method for the original X-Y model, and second weight for the
X-M-Y model. In both cases, different weights must be applied to two
different regression models, and in both cases, the SE's will need to be
adjusted. Weights are used in these models in a similar context to those in
the first example - to control for confounding.

By the way, a user written program called sgmediation (search sgmediation)
does something similar to this but without the weights, so it may be
possible to replicate many of the steps (or add weights?). 

Thanks!

Ariel


Date: Sat, 31 Jul 2010 22:20:41 -0500
From: Stas Kolenikov <skolenik@gmail.com>
Subject: Re: st: deriving a bootstrap estimate of a difference between two
weighted regressions

I am not sure this is sensible. Leaving aside the issue whether comparing
two regressions with different weight is sensible, to begin with, I am used
to thinking about aweights as a result of -collapse-.
For your bootstrap procedure to resemble all the steps in the original
process, you would have to resample the raw data before -collapse- to get
both new numbers and new weights.

On Sat, Jul 31, 2010 at 7:54 PM, Ariel Linden, DrPH <ariel.linden@gmail.com>
wrote:
> Hi All,
>
> I would like to run two regressions (each using a different weight), 
> and then get the bootstrapped estimates of the difference. Neither 
> suest or sureg allows different weights to be used in the two models. 
> I thought that maybe there is a way of getting the resulting estimate 
> in a somewhat manual manner, but I don't know how. I am thinking something
like this:
>
>
> regress outcome treatment [aw = att]
> scalar ATT =  _b[ treatment]
>
> Regress outcome treatment [aw = atc]
> scalar ATC =  _b[ treatment]
>
> scalar difference= (ATT-ATC)
>
> Then bootstrap the scalar difference to get the mean, CI, etc.
>
> Any help is much appreciated!
>
> Ariel


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