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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