At 08:36 23/10/03 -0400, Buzz Burhans wrote:
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....
If you fit a GLM (or extension of a GLM) with a log link, then the
exponentiated parameters are arithmetic means and their ratios. This is
true whether the Y-variable is a count variable or a continuous variable.
The ratios may be simple between-group ratios (in the case of categorical
X-variables) or ratios associated with a unit increase in an X-variable
(in the case of continuous X-variables). If the continuous X-variable is
itself a log to the base 2 of another variable (eg X=log_2(W)), then the
exponentiated parameter is a per-doubling ratio associated with a doubling
of W.
An alternative to fitting arithmetic means and their ratios might be to
transform the outcome data to logs and then use a GLM (or extended GLM)
with an identity link. The exponentiated parameters are then geometric
means and their ratios. For instance, the exponentiated intercept is a
geometric mean Y for zero X, and the exponentiated slopes are amounts by
which the geometric means are multiplied per unit increase in X. The
geometric mean is often a better proxy for the median than the arithmetic
mean if the data are positively skewed, eg viral loads, plasma
triglycerides and house prices. Another possibility is to power-transform
the data and use a GLM with the corresponding inverse-power link function
to estimate algebraic means and their differences, but I don't know many
people who do this.
Either way, it usually makes sense to centre the X-variates at a sensible
X-value, so that the exponentiated intercept will represent an arithmetic
or geometric mean expected at a sensible X-value instead of an arithmetic
or geometric mean expected at a zero X-value (except if a xzero X-value is
sensible). And, in general, the parameters presented with confidence
limits should be explicable in words to non-statisticians.
I hope this helps.
Roger
--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom
Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
or 020 7848 6605 International +44 20 7848 6605
Email: [email protected]
Website: http://www.kcl-phs.org.uk/rogernewson
Opinions expressed are those of the author, not the institution.
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