How would one handle that many factors? I am very curious what the techniques for doing so would be.

I'm no expert but my initial reaction would be that you need more than 5834 adults in a study that controls for all of those factors. We don't really know how household size, for example, would affect the results, so wouldn't you need a bunch of test data to analyze all of the combinations? Or did they only study people who are the same in most of them? (i.e. 45, male, with a household size of 4, nonsmoking, etc...)

Would love to hear from someone more informed on this than myself.