David,
In the Cox and many other regression models, the effect of a variable
is context-dependent. There is an identifiability problem in what you
are doing, as discussed by
@ARTICLE{for95mod,
author = {Ford, Ian and Norrie, John and Ahmadi, Susan},
year = 1995,
title = {Model inconsistency, illustrated by the {Cox} proportional
hazards
model},
journal = Stat in Med,
volume = 14,
pages = {735-746},
annote = {covariable adjustment; adjusted estimates; baseline
imbalances;
RCT; model misspecification; model identification}
}
One possible remedy, which may not work for your goals, is to embed
all models in a grand model that is used for inference.
When coefficients ARE comparable in some sense, you can use the
bootstrap to get confidence bands for differences in regressor effects
between models.
Frank
Frank E Harrell Jr Professor and Chairman School of Medicine
Department of Biostatistics Vanderbilt University
On Fri, 13 Aug 2010, Biau David wrote:
Hello,
I would like, if it is possible, to compare the effect of a variable across
regression models. I have looked around but I haven't found anything. Maybe
someone could help? Here is the problem:
I am studying the effect of a variable (age) on an outcome (local recurrence:
lr). I have built 3 models:
- model 1: lr ~ age y = \beta_(a1).age
- model 2: lr ~ age + presentation variables (X_p) y = \beta_(a2).age +
\BETA_(p2).X_p
- model 3: lr ~ age + presentation variables + treatment variables( X_t)
y = \beta_(a3).age + \BETA_(p3).X_(p) + \BETA_(t3).X_t
Presentation variables include variables such as tumor grade, tumor size, etc...
the physician cannot interfer with these variables.
Treatment variables include variables such as chemotherapy, radiation, surgical
margins (a surrogate for adequate surgery).
I have used cph for the models and restricted cubic splines (Design library) for
age. I have noted that the effect of age decreases from model 1 to 3.
I would like to compare the effect of age on the outcome across the different
models. A test of \beta_(a1) = \beta_(a2) = \beta_(a3) and then two by two
comparisons or a global trend test maybe? Is that possible?
Thank you for your help,
David Biau.
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