What does "p for trend" mean, exactly?

[Steve Simon, P.Mean Consulting]

I'm writing up a brief article for my email newsletter about the words
"p for trend" that appear in many abstracts. I sort of know how this
works. But I'm curious about specifics.

You could get a p for trend by including an independent variable as a
single degree of freedom continuous variable instead of a multiple
degree of freedom categorical variable. Or you could use a
non-parametric test like the Cochran-Armitage test. Are there other
approaches? Is there a common understanding of what "p for trend" implies?
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[Neil Shephard]

On 7 January 2013 16:41, Steve Simon, P.Mean Consulting <n...@pmean.com> wrote:
> I'm writing up a brief article for my email newsletter about the words "p
> for trend" that appear in many abstracts. I sort of know how this works. But
> I'm curious about specifics.
>
> You could get a p for trend by including an independent variable as a single
> degree of freedom continuous variable instead of a multiple degree of
> freedom categorical variable. Or you could use a non-parametric test like
> the Cochran-Armitage test. Are there other approaches? Is there a common
> understanding of what "p for trend" implies?

I've always understood it in terms of the Cochran-Armitage test
although I'd tend to use "test for trend" rather than "p for trend".
This is within the area of statistical genetics where diploid
genotypes might be considered ordered categorical (AA, Aa, aa) and
you're looking to see if there is an increasing effect size with the
number of copies of a particular allele.

Neil

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"To kill an error is as good a service as, and sometimes even better
than, the establishing of a new truth or fact" - Charles Darwin

Neil Shephard
Clinical Trials Research Unit
University of Sheffield

[Frank Harrell]

And I'll add that this test should now be considered obsolete for most purposes.  There are other approaches that don't assume linearity in the proportions over (arbitrary) category numbers 1, 2, 3, ...

Frank

[SteveDrD]

On Monday, January 7, 2013 5:00:04 PM UTC-5, Frank Harrell wrote:

And I'll add that this test should now be considered obsolete for most purposes.  There are other approaches that don't assume linearity in the proportions over (arbitrary) category numbers 1, 2, 3, ...

Frank

 

And yet the analysis of carcinogenicity tests still depends largely on two tests of this type: Cochran-Armitage and Peto, and toxicologists just don't seem to want to move on.

 

Steve Denham

[Steve Simon, P.Mean Consulting]

On 1/7/2013 4:00 PM, Frank Harrell wrote:

> And I'll add that this test should now be considered obsolete for
> most purposes. There are other approaches that don't assume
> linearity in the proportions over (arbitrary) category numbers 1, 2,
> 3, ...

Don't leave me in suspense! What are the other approaches?

[Frank Harrell]

One can reverse the problem and use a proportional odds model to predict ordered category as a function of the binary Y.

I see the test for trend abused over and over in epidemiology where a continuous variable is grouped into quintiles and then a test for trend is done against quintile numbers.  I can't imagine a more ridiculous approach.

Frank