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RE: st: confidence intervals for ratio of predictions-- bootstrap vs. parametric methods?


From   "Daniel Waxman" <dan@amplecat.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: confidence intervals for ratio of predictions-- bootstrap vs. parametric methods?
Date   Thu, 11 Oct 2007 10:23:47 -0400

Joseph, 

Thank you for the reply.  The thing is, the model fit seems to be quite
good, and it seems unlikely to me that another regression technique would
improve on it.  At the end of the day one is left with a set of predictions,
and the question of how to best describe their variability seems independent
of regression method, no?    

Since my model contains some complex terms (interaction terms and a dummy
variable that represents zero values of the continuous variable), I cannot
use many of the built in conveniences such as -adjust-.

The situation of the "red x's" was for only one of my many subsamples, and
in that case, I think that what bootstrap is telling me is that there aren't
enough cases distributed among the covariate patterns to give CIs that are
not zero or infinite.  I can live with that result for that one subsample
(if that is the correct conclusion).

In the other situations, the bootstrap gives CIs that do not cross 1, and my
most important question is ... assuming that my sample is a random draw from
the true population, is there any reason to think that there is a problem
with the bootstrapped CIs?  Or any easy explanation for why the parametric
CIs are so much worse if the bootstrapped ones are okay?

Daniel


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Joseph Coveney
Sent: Thursday, October 11, 2007 12:46 PM
To: Statalist
Subject: Re: st: confidence intervals for ratio of predictions-- bootstrap
vs. parametric methods?

Daniel Waxman wrote (excerpted):

A couple of months ago, Maarten Buis was kind enough to answer my questions:
How to correctly use -predictnl- to calculate confidence intervals for a
ratio of two adjusted predictions  (i.e. relative risk) after logistic
regression.

[redacted]

The problem is that these confidence intervals appear unreasonably wide, and
the lower bound can be negative, which is nonsensical.

So I did a bootstrap of the following program, and the bias-corrected
bootstraps give much happier results:
(note that I am bootstrapping the relative risk at a specific value of the
covariates (zero=1, zlog=`1') )

[redacted]

The sample sizes range from 1500 to 6000, with an event rate of ~ 1.5% -
3.5% depending on the population.  Most subjects are at low risk (i.e. the
distribution of the predictors is highly skewed).
Example of the different results: parametric: 3.1 (0.7 ,5.4); bc-bootstrap:
3.7 (2.2,7.4)

My questions:
1.  Can anybody explain why the results are so different, and whether the
bias-corrected bootstraps can reasonably be thought to be much closer to the
truth?
2.  If reporting parametric CIs, what to do when the results get negative?
3.  In one of my subpopulations, the bootstrap process returned a few red
'x's instead of dots, meaning, I think that in some samples, one of the
covariate patterns didn't exist or the regression couldn't be performed.  No
bc-CI was calculated.  Any thoughts on the real meaning of this?  (are the
CIs truly infinite?)

----------------------------------------------------------------------------
----

What do you get with, say, -glm . . . , family(binomial) link(log)-,
and -adjust- or -lincom , rrr-?

The topic of parameter estimates falling outside of the parameter space (and
by extension, their confidence intervals) when modeling risk ratio and risk
difference versus logit came up on the list in the past month or so.  It
seems like you're asking for trouble when modeling risk ratios in the
neighborhood of 1.5% event rates--the negative parametric lower confidence
limits and red Xs during bootstrapping seem to bear this out.  Is there a
reason why you cannot use the canonical link or, perhaps, the complementary
log-log link?

Joseph Coveney


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