Let us assume that someone has two dummy variables: Pneumonia (0/1) and Septicemia (0/1) and wants to use them as predictors for hospital mortality, controlling for comorbidities and age. So far so good.

Now: If we want to study the event of someone having developed pneumonia AND septicemia, and their cumulative effect on hospital mortality, we can express this 'event' as a composite variable: pneumonia*septicemia and run the regression again.

What if I have 50 different combinations of events and want to find the most "lethal" combination?

Eg. {pneumonia*septicemia}, {pneumonia*septicemia*shock}, {appendicitis*septicemia} etc etc. I would have to run 50 different BLRs, right?

Can you think of a more effective way to study the above problem? As we all know, in BLR, the O.Rs cannot be added the same way the linear regression does with the Y = b1*x + b2*y... works.