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# re: RE: st: Diff-in-diff: how to account for treatment intensity, rather than just a treatment dummy?

 From "Ariel Linden, DrPH" To Subject re: RE: st: Diff-in-diff: how to account for treatment intensity, rather than just a treatment dummy? Date Mon, 13 Aug 2012 12:38:39 -0400

```Cam recommended an interesting article but it was short on practical
application.

I would suggest reading: Robins JM, Hernan MA, Brumback B. Marginal
structural models and causal inference in epidemiology. Epidemiol
2000;11:550-60.

This paper describes a propensity score weighting approach (with the inverse
probability of treatment weights). Section 6 describes multilevel treatment
(ordinal), which can be substituted with multinomial treatments (where the
treatments are not ordered). The simplest way of describing this is that
you'd first estimate the propensity score using mlogit (perhaps setting the
base outcome as the first treatment). You'd then use -predict- to get the
probabilities for each of the treatment levels. Next, you'd calculate the
IPT weight as being 1/probability of receiving the actual treatment (so if a
person received treatment "A", they would have a weight of 1/probA if
treatment=="A").

After you've done that, it is simply a matter of running the diff-in-diff
model using the weight:

Y= post-pre
T = treatment
X = other covariates

Regress Y T X [pweight = IPT], robust

Even though the X's have been used in the estimation of the propensity
score, it is generally a good idea to include them in the outcome model as
covariates as well. This is called "doubly robust"...

I hope this helps

Ariel

Date: Sun, 12 Aug 2012 22:15:28 -0400
From: Cameron McIntosh <cnm100@hotmail.com>
Subject: RE: st: Diff-in-diff: how to account for treatment intensity,
rather than just a treatment dummy?

The following may also be of interest:

Crown, W.H. (2010). There's a reason they call them dummy variables: a note
on the use of structural equation techniques in comparative effectiveness
research. Pharmacoeconomics, 28(10), 947-955.

Cam

> Date: Sun, 12 Aug 2012 15:20:59 -0700
> Subject: Re: st: Diff-in-diff: how to account for treatment intensity,
rather than just a treatment dummy?
> From: tirthankar.lists@gmail.com
> To: statalist@hsphsun2.harvard.edu
>
> "Second, if I do not find another way than to break the treatment
> variable D into 10 dummies, does anyone know how I could recover the
> mean ATT and its standard error? I guess I would need to weight the 10
> different ATTs that I got, but what should be the weights? How about
> number of treated observations in each treatment group?"
>
> The process you want is described in Imbens' 2000 Biometrika paper
> which proposes the Generalised Propensity Score [GPS]
> dx.doi.org/10.1093/biomet/87.3.706
> See page 708.
>
> T
>
> On Sun, Aug 12, 2012 at 2:36 PM, John Carey <johncarey196@gmail.com>
wrote:
> > Hi everyone!
> >
> > I have been working on a difference-in-differences strategy, and I was
> > hoping someone could clarify an important point for me.
> >
> > In the beginning, the treatment I am working on was not a dummy. It is
> > a discrete variable ("D") which ranges from 1 to 10 when observations
> > are treated, and equals 0 otherwise. For the sake of simplicity, I
> > turned it into a dummy, equal to 1 when the discrete variable is
> > strictly positive, and equal to 0 otherwise. That way, I was able to
> > use a few common diff-in-diff models (OLS regression and psmatch2).
> > Also, I should specify that I only have 2 periods (pre-treatment, and
> > post-treatment).
> >
> > However, I have been doing research about how to account for treatment
> > intensity, because I would like to take into account the fact that
> > being treated with 10 is not the same as being treated with 1.
> >
> > For now, I have created 10 dummies for each of the possible values of
> > the treatment variable, and I have run 10 different regressions (1
> > against 0; 2 against 0; 3 against 0...). However, it is not easy to
> > get a full picture with that process. First, I have very few treated
> > observations for some of the treatment values, and therefore inference
> > is an issue. Second, I have not found an easy way to compare the
> > treatment effects to each other, since I have compared each of them to
> > getting 0 unit of treatment.
> >
> > Therefore, here are two questions ;)
> >
> > First, do you know of any way to account for treatment intensity
> > without breaking the treatment variable into 10 dummies? Ideally, I
> > would like to be able to run one regression which would take it all
> > into account. Some sort of weighted ATT.
> > For instance, do you think it is possible to use a regular OLS
> > diff-in-diff equation, plug the treatment variable as a discrete
> > variable (as opposed to a dummy), and include as many group fixed
> > effects and there are treatment values? I would be tempted to write it
> > like this:
> > Yit = a + b[T=t1] + c1[D=1] + c2[D=2] + ... + c10[D=10] + d[T=t1]*[D] +
e
> > In that equaltion, I would let [D] range from 0 to 10, and d would be
> > the ATT. Do you think that makes sense?
> >
> > Second, if I do not find another way than to break the treatment
> > variable D into 10 dummies, does anyone know how I could recover the
> > mean ATT and its standard error? I guess I would need to weight the 10
> > different ATTs that I got, but what should be the weights? How about
> > number of treated observations in each treatment group? I thought
> > about doing that, but I stopped because the fact that treatment was
> > not randomly allocated made me think otherwise.
> >
> > Thank you everyone for your help, and I wish you a great week!
> > *
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```