Suppose I have a binary outcome (disease/no disease and all subjects had the same period of exposure) and 2 or 3 (categorical) predictors.

I can obviously build a logistic regression model which describes the data, possibly including interaction terms, on a relative scale:

model<-glm(disease~sex*race*prematurity,family=binomial)

1) Is there any way to extract information on the absolute scale (ie instead of saying male sex has an OR = 2.0, saying that all else equal, males have a 5 percentage point higher rate of disease, or, given certain values of covariates, the difference in rates of disease between boys and girls is X (95% ci for difference = ...).  I know there are mantzel-hanzell methods for cummarizing contingency tables, but if I had several covariates I wanted to control for, this approach quickly loses its appeal.  A regression framework which allowed for inference on the absolute scale would be ideal (or perhaps I'm just forgetting something about logistic regression?)

2) Now suppose that the situation is such that males are at higher risk of disease than females but that the magnitude of this difference varies by degree of prematurity (ie the interaction of sex*prematurity was significant) and suppose further that the effect of this interaction is to diminish the difference between males and females as one becomes less and less premature until the difference between sexes in undetectable.  Is there a procedure for determining at what level of the prematurity factor the impact of sex becomes undetectable?

My thought was to test the hypothesis that the model coefficients involving sex (ie a main effect and sex*prematurity interaction coefficients at each level of prematurity) sum to zero and taking the first level of prematurity where this sum was not statistically greater than zero as the level of prematurity at which sex ceased to alter risk.  

Does this approach make sense?


3) Suppose now that for each level of race, the level of prematurity at which sex ceases to increase risk is different.  Can anyone suggest an approach which would allow one to say that the level of prematurity at which this occurred in each race was statistically different?

Thanks,
bimal

Bimal P Chaudhari, MPH
MD Candidate, 2011
Boston University
MS Candidate, 2010
Washington University in St Louis


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