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st: impact of bootstrapping on predicted probabilities of logisticregression models

From   "G. ter Riet" <[email protected]>
To   [email protected]
Subject   st: impact of bootstrapping on predicted probabilities of logisticregression models
Date   Fri, 03 Oct 2008 16:02:35 +0200

Dear Statalisters,
In medical research on prediction or diagnosis, we often use the bootstrap to calculate confidence intervals for an area under the curve, AUC, corresponding to a particular logistic regression model that is used for prediction of an event (e.g. death or some target illness). The AUC is a global measure for how well the model discriminates between those with an without an event. A program that does this might look as follows:

capture program drop rocb
program rocb, rclass
logit `1' `2' `3' `4' 
predict p
roctab `1' p
drop p
return scalar rocb = r(area)
bootstrap auc=r(rocb), reps(200): rocb  depvar indepvar1 indepvar2 indepvar3

What I should like to do, however, is to give readers of my paper an impression of the impact of bootstrapping, not just on the AUC, but on the distribution of predicted probabilities calculated from the logistic model since most clinicians are not that comfortable with AUCs of a ROC curve.  Suppose, my indepvars are all binary. Then I'd have 2^3=8 covariate patterns and potentially a unique predicted probability for each covariate pattern for each bootstrap sample. For each covariate pattern, I'd like to average the predicted probabilities across the 200 samples (and perhaps say something about their variability).
My programming abilities of Stata are not good enough to solve this efficiently. Any help I'd greatly appreciate. Of course any comments on whether you think the whole idea is worthwhile are welcome too.
Cheers, Gerben ter Riet (epidemiologist, AMC, Dept General Practice, Amsterdam, NL)
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