# Bootstrap Confidence Bands/Simultaneous Confidence Intervals for GEE Logistic Model

I have a relatively complex logistic model I built using generalized estimating equations (GEE). The model is used to predict population mortality. I have gone about estimating the mortality in the population by (1) fitting a model to my data, (2) making individual-level predictions of mortality from the data, and finally by (3) taking the mean of these predictions. I am particularly interested in examining the shape of the model as I vary one predictor, holding all other variables constant. To this end, I need to calculate a confidence band around the population prediction function from my model. I can calculate population prediction intervals just fine (using the advice given by @Ben Bolker here Parametric Bootstrap without model refitting?), but now I'm trying to figure out how I might be able to bootstrap confidence bands/simultaneous confidence intervals instead of just bootstrap point-wise confidence intervals. Can anyone point me in the right direction?

• This does not involve the bootstrap, but the R rms package's contrast and Predict functions can provide simultaneous confidence intervals on cluster sandwich covariance based estimates, by assuming multivariate normality of $\hat{\beta}$. plot.Predict makes plots such as what you mentioned easy to do. – Frank Harrell Oct 14 '15 at 18:59
• Hi, @FrankHarrell, thanks for this reference. Can you tell me if rms will work for GEE models? I have the second edition of your book right here, but I don't see any GEE model examples. – StatsStudent Oct 25 '15 at 6:49
• rms implements GEE with working independence covariance assumptions. Fit the multiple record per subject model using any of the rms fitting functions then run the fit through robcov to get a robust cluster sandwich covariance estimator to take intra-subject correlation into account. Then contrast and Predict can compute simultaneous confidence regions based on assuming multivariate normality of the GEE $\hat{\beta}$. – Frank Harrell Oct 25 '15 at 11:58
• Awesome. Thanks for your guidance, @FrankHarrell. I'll give it a shot! Much appreciated! – StatsStudent Oct 25 '15 at 18:30