[R] Cochran-Mantel-Haenszel problem

[Frank E Harrell Jr]

On Thu, 11 Dec 2003 14:42:07 +0100
<Arne.Muller at aventis.com> wrote:

> Hello,
> 
> I've tried to analyze some data with a CMH test. My 3 dimensional
> contingency tables are 2x2xN where N is usually between 10 and 100.
> 
> The problem is that there may be 2 strata with opposite counts (the 2x2
> contigency table for these are reversed), producing opposite odds ratios
> that cancle out in the overall statistics. These opposite counts are
> very important for my analysis, since they account for a dramatic
> difference.
> 
> Could you recommend alternative tests that take account for opposite
> counts? Would you suggest a different strategy to analyze such data?
> 
> 	thanks a lot for your suggestions,
> 
> 	Arne
> 

I'm not sure about your specific problem, but in general you might think
of this as a binary or multinomial logistic model with strata x treatment
interactions, and get pooled treatment main effect + interaction effects,
which are equivalent to testing whether treatment is associated with
response for ANY stratum (without cancellation when signs of effects are
reversed).  With the Design package, for example, you can do this easily
when the response is binary or ordinal:

library(Design)
f <- lrm(y ~ treat*strat)
anova(f)   # prints multiple d.f. test for treat as either main effect or
effect modifier

Of course when you allow for a more general model such as this, the power
is diluted into multiple degrees of freedom when the effects really do not
vary very much over strata.

Frank

---
Frank E Harrell Jr    Professor and Chair            School of Medicine
                      Department of Biostatistics    Vanderbilt University