I've been trying to understand what means "statistically adjusted" when comparing two variables. For example, when computing the odds ratio for a death after surgery in two hospitals, we compute the odds of death in one hospital, to the odds of death in the other hospital.
But, then let's say we want to "statistically adjust" (as the literature likes to call it) for other variables. For each variable we "statistically adjust" for, we will multiply the number of odds ratios by 2.
For example, we "statistically adjust" for whether or not the patients are healthy. This would mean that we would have two odds ratios:
- odds ratio for the patients in good health
- odds ratio for patients of poor health
Then lets say we adjust for patients of age >50 and patients of age < 50. Then, we have a total of 4 odds ratios, which is the cartesian product of age, and health.
How do I end up with one odds ratio comparing death rates in the two hospitals?
A resource that attempts to explain this is here: https://www.iwh.on.ca/wrmb/statistically-adjusted. It says that a statistician "will tell you that the odds ratio has been statistically adjusted to incorporate the effect of patient condition at the time of surgery, and is now 1.14". I do not understand how one value, 1.14, is able to summarize everything about multiple odds ratios. Thanks for helping me.