Dear fellow Allstatters,
I was wondering if someone could help with an analysis problem for my
thesis. I have a binary outcome (sick=0,1) and want to estimate the risk
difference for an exposure adjusted on covariates. I can do this with a glm
by specifying a binomial family and an identity link function.
However...my data are "hierarchical" with covariables measured at the
individual level and at a higher neighbourhood level and clustering of
participants within neighbourhoods. I am interested in one of the
neighbourhood-level exposures but need to use (I think) a generalized linear
mixed model with neighbourhood as a random effect. I cannot use
family=binomial(link=identity) for this model in R or SAS.
I have had to resort to some DIY statistics, which almost makes me uneasy!
So far I have tried family=poisson(link=log) and then back calculating the RD as
exp(intercept + beta for the exposure) - exp(intercept)
and bootstrapping this for the CIs. I have also tried with
family=binomial(link=logit) and an expit back calculation to get to a RD.
BUT I get RD's which are sufficiently different between the two approaches
to worry me.
Another try was Gaussian/identity based on a paper I read recently but I get
different RD's again!
One of my concerns is whether this approach is valid. I know that the
beta's will be shrunk by a function including their variance because of the
random effect and so I suspect that the different estimates could be due to
different variances in the error families. But I don't have the mathematics
to go further with this. Could this be the problem? Does anyone have some
advice on which is the best approach of these or if there are other
approaches which would be valid?
On the brave assumption that one of these approaches is valid, I oddly get
bootstrap 95%CIs (non-parametric resampling, straight percentile
calculations of the CIs) which do not include some coefficient estimates.
Any ideas on why this is happening would be greatly appreciated!
Apologies for the length of this message. Any (long or short) replies would
be most welcome.
Cheers.
David.
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