# RE: st: model-based standardization

 From "Garth Rauscher" To Subject RE: st: model-based standardization Date Tue, 5 Feb 2008 01:28:34 -0600

```Austin-problem solved, just like that. Thanks for the solution-Garth.

Garth Rauscher
Division of Epid/Bios (M/C 923)
UIC School of Public Health
1603 West Taylor Street
Chicago, IL 60612
ph: (312)413-4317
fx:  (312)996-0064
em: garthr@uic.edu

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols
Sent: Monday, February 04, 2008 11:30 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: model-based standardization

Garth,
I haven't looked at the ref you cite, but what you want is one of the
several quantities that economists refer to as marginal effects (see e.g.
the description of -margfx- and SE calcs at

Your code fails because you have not multiplied estimated coefficients by
variables.
logit Y X r2 r3 a2 a3
g p0=invlogit(_b[_cons]+ _b[r2]*r2+_b[r3]*r3+_b[a2]*a2+_b[a3]*a3)
g p1=invlogit(_b[_cons]+_b[X]+_b[r2]*r2+_b[r3]*r3+_b[a2]*a2+_b[a3]*a3)

but it's easier to use predict in any case:
ren X wasX
g X=0
predict pr0
replace X=1
predict pr1
drop X
ren wasX X

though you still have to make sure there are no neglected connections
between X and other variables (e.g. interactions).

To bootstrap, simply wrap it in a program:

prog dp
cap drop pr0 pr1 dp
logit Y X r2 r3 a2 a3
ren X wasX
g X=0
predict pr0
replace X=1
predict pr1
drop X
ren wasX X
g dp=pr1-pr0
mean pr0 pr1 dp
end
bs: dp

On Feb 4, 2008 11:11 PM, Garth Rauscher <garthr@uic.edu> wrote:
> [I tried to send this message to the listserv a few days ago but don't
> think it made it through so I am trying again. I apologize if this is
> a duplicate message.]
>
> Dear listserve members
>
> I am attempting to learn how to perform a model-based standardization
> with Stata, using the marginal or predictive margins method.  I would
> like to be able to estimate standardized probabilities and probability
> differences from logistic regression that are standardized to the
> distribution of modeled covariates. The idea is summarized in:
> "Greenland S. Model-based estimation of relative risks and other
> epidemiologic measures in studies of common outcomes and in
> case-control studies. Am J Epidemiol 2004;160:301-305." To the best of
> my understanding, the method involves estimating predictied
> probabilities of Y under two scenarios (e.g. x=1 and x=0). Assuming we
> have a dependent variable Y(0,1), an exposure of interest X(0,1), and
> covariates
> r2 r3 a2 a3 a4 a5, two sets of predicted probabiltiies could be:
>
> P0(x) based on the joint distribution of covariates, with X=0 assigned
> to everyone
> P1(x) based on the joint distribution of covariates, with X=1 assigned
> to everyone
> PD(x) as the difference in probabilities,  P1(x) - P0(x)
>
> Below is my code.
> logit Y X r2 r3 a2 a3 a4 a5
> // predicted xbetas after assigning all observations to X=0 g
> if0=_b[_cons]+_b[X]*0+_b[r2]+_b[r3]+_b[a2]+_b[a3]+_b[a4]+_b[a5]
> // predicted xbetas after assigning all observations to X=1 g
> if1=_b[_cons]+_b[X]*1+_b[r2]+_b[r3]+_b[a2]+_b[a3]+_b[a4]+_b[a5]
> // predicted probabilities
>       g p0x = invlogit(if0)
>       g p1x = invlogit(if1)
> I was expecting two new variables of predictied probabilities, p0x and
> p1x with a range of values that depended on covariates. However, I
> noticed that p0x and p1x each had only one value instead of a range of
> values as I had expected (see above).  Any clarification as to what I
> am doing incorrectly would be appreciated. I think my next task would
> have been to perform bootstrapping to get confidence intervals from
> the distribution of means for p0x, p1x and PD(x).
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```