I have a set of healthcare data in which I used GLM Gamma to model the healthcare spending. Then I am trying to put together the results in a style that is similar to this: http://onlinelibrary.wiley.com/doi/10.1038/oby.2005.175/full
My question is how should I aggregate back correctly after controlling for covariates (for example, age & gender) in the GLM Gamma model. For example, the research paper summaries total healthcare cost for each BMI level. But the actual model output would be something like this:
The following example is the exponential of coefficients of a GLM Gamma model, with Y = Healthcare spending. Covariates include AGE (40-, 40+), GENDER (Female, Male), BMI(Normal, Overweight, OBESE).
Average 2.5 % 97.5 % (Intercept) 15049.58 13122.79 17299.13 AGE_40+ 0.9295 0.8564 1.0088 GENDER_MALE 0.9652 0.8834 1.0546 BMI_OVERWEIGHT 0.8291 0.7610 0.9033 BMI_OBESE 0.4623 0.4232 0.5046
So the interpretation of this GLM Gamma output is that for female under 40 with normal BMI, their average healthcare spending is 15049.58 dollars. And for male under 40 with normal BMI, their average healthcare spending is $15049.58 * 0.9652, and so on so that average spending for each age|gender|BMI sub-group can be calculated. But how can we calculate the average spending of say, OBESE people, controlling for age and gender. I can't convince myself it is simply the sum of spending times count divided by total count for all OBESE people of all age and gender because that wouldn't be controlling age & gender?