First, do a simple plot to begin with for each group and differences may be visually apparent. Then use ANOVA :-)

Form a model including group variable and risk factors. Include interaction terms and see if they are significant. In case they are significant then this would mean that the effect of a risk factor changes across groups (if this is what you are after).

Great, thank you for replying! I will try both approaches. 

ANOVA is just wrong. Your predicted variable is probability of bleeding, so you are right to be using logistic regression.

YOu are very wrong to be using stepwise methods. It produces prediction models that fail badly when applied to new data (and that's the point of clinical prediction – to be able to generalise to new clinical situations). Take a look at the Stata FAQ on stepwise methods. The consensus is that they are no substitute for theory.

http://www.stata.com/support/faqs/statistics/stepwise-regression-problems/

Likewise, don't waste time fooling around with interaction terms. If you have no hypothesis, don't do tests. You simply run the risk of spurious associations beginning to dominate your model.

If you are interested in clinical prediction, think about modern methods of heuristic prediction such as fast and frugal trees, which closely resemble actualy clincal decision making, use far fewer variables (important when clinical decisions are being made - who has time to collect information on ten patient variables and plug them into an equation??) and – very importantly – the generalise much better than traditional models.

I can really recommend Gigerenzer's paper, which I have linked here. It will get you thinking again about prediction!

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.439.1557&rep=rep1&type=pdf