[R] How to compare the effect of a variable across regression models?

[Frank Harrell]

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.
>
>
>
>
> 	[[alternative HTML version deleted]]
>
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