How to collect better estimations of a logistic model parameters, by using bootstrapping things ?

I presume an `IC' is a confidence interval, but what is an `IP'?

I think you need to think hard about the assumptions you want to make. The 
usual way to do logistic regression is via glm(), and the confint() 
function will give you confidence intervals based on profile likelihoods 
that are rather accurate (you need package MASS for this).

If you want to bootstrap you have to decide how.  Case-based resampling is 
the only easy way, and would be appropriate only if the 41 cases were a 
sample and not a design (and even then experts would argue for conditional 
inference).  Bootstrapping logistic regression for a design involves a lot 
of assumptions, and there is not much to suggest that bootstrapping will 
better than using confint().

As for model selection, step() will do it, but given your problem sizes it 
is really _at best_ an exploratory procedure for what extra data might be 
worth collecting.

How to collect better estimations of a logistic model parameters, by using bootstrapping things ?

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