st: reporting log linked, linear, and fractional polynomial results

[Buzz Burhans <wsb2@cornell.edu>]

I would appreciate advice on effective ways of reporting on data for 
similar outcome types from the same trial  which have been modeled using 
different link functions. The outcomes (plasma metabolites in animals under 
two treatment regimes) are repeated measurements made over time proximate 
to parturition, and have variously different profiles of curvilinear 
increase or decrease.  Simply fitting linear polynomial models failed to 
adequately satisfy assumptions for residuals for some (but not all) 
outcomes, so while some were modeled as normally distributed with the 
identity link, others were modeled using gllamm with family(gamma) 
link(log), all using adaptive quadrature. I have used logistic regression 
previously with categorical outcomes, but am unclear about the log link to 
continuous variables. My questions are as follows:

1. How to report the results from disparate model types.  My initial 
thought is to 1) tabulate fitted values and confidence intervals at a set 
of representative times, with stars for significance of treatment 
difference , and accompany such a table with plots of fixed effect values 
(over the entire experimental period).

Does this make sense? I am not sure how to otherwise tabulate coefficients 
and se, since some refer to outcomes in the original metric, while the log 
linked ones refer to logged outcomes .

I also considered exponentiating the coefficients and ci, but confess to 
being a bit unsure about how to express their exponentiated interpretation, 
given that they are relative to continuous rather than categorical 
dependant variables.  Is it appropriate to suggest that the exponentiated 
coefficient describes the proportionate change in the (backtransformed) 
outcome?

The reporting is a bit further complicated by the fact that some of the 
dependant variables are fractional polynomial transformations as well, 
which helped construct a good model, but complicate expressing the 
interpretation.

In the past I have modeled such data using linear or nonlinear mixed effect 
models in S-Plus (lme and nlme), and reported separate tables for variables 
modeled using each; use of nonlinear models makes interpretation of the 
coefficients more intuitive; however, I wanted to stay in Stata, and there 
are not yet random effects models in Stata that can handle mixed random and 
fixed slopes other than gllamm, and I am unable to fit nonlinear models in 
gllamm.

I am appreciative of any thoughts on these matters.

Buzz Burhans



Buzz Burhans
wsb2@cornell.edu


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