[R] Cochran-Armitage

[David Winsemius]

On Dec 12, 2008, at 8:57 AM, Peter Dalgaard wrote:

> Chuck Cleland wrote:
>> On 12/12/2008 3:29 AM, robert-mcfadden at o2.pl wrote:
>>> Hello,
>>> Which package allows to use Cochrana-Armitage trend test? I tried  
>>> to search for but I found only package coin in which there is no  
>>> explicit function.
>>
>>  But there is this example in coin:
>>
>> ### Cochran-Armitage trend test for proportions
>> ### Lung tumors in female mice exposed to 1,2-dichloroethane
>> ### Encyclopedia of Biostatistics (Armitage & Colton, 1998),
>> ### Chapter Trend Test for Counts and Proportions, page 4578, Table 2
>> lungtumor <- data.frame(dose = rep(c(0, 1, 2), c(40, 50, 48)),
>>                        tumor = c(rep(c(0, 1), c(38, 2)),
>>                                  rep(c(0, 1), c(43, 7)),
>>                                  rep(c(0, 1), c(33, 15))))
>> table(lungtumor$dose, lungtumor$tumor)
>>
>> ### Cochran-Armitage test (permutation equivalent to correlation
>> ### between dose and tumor), cf. Table 2 for results
>> independence_test(tumor ~ dose, data = lungtumor, teststat = "quad")
>>
>>  See the following:
>>
>> http://finzi.psych.upenn.edu/R/library/coin/html/ 
>> ContingencyTests.html
>
>
> Also prop.trend.test().
>
> There seems to be a subtle difference, though:
>
>> independence_test(tumor ~ dose, data = lungtumor, teststat = "quad")
>
>        Asymptotic General Independence Test
>
> data:  tumor by dose
> chi-squared = 10.6381, df = 1, p-value = 0.001108
>
>
>> tt <- table(lungtumor$dose, lungtumor$tumor)
>> prop.trend.test(tt[,2],rowSums(tt))
>
>        Chi-squared Test for Trend in Proportions
>
> data:  tt[, 2] out of rowSums(tt) ,
> using scores: 1 2 3
> X-squared = 10.7157, df = 1, p-value = 0.001062
>
>
> Anyone have a guess at what the difference is? (Just curious.)

My guess is that this is the difference between a rank-correlation  
test and a score based linear correlation test. I just looked at  
chapter 13 of "Medical Uses of Statistics" in which Moses, Emerson and  
Hosseini describe using a Wilcoxon statistic to tackle this problem.  
That appears to be equivalent to the permutation method implemented in  
the independence_test(). The authors of coin call it an equivalent  
rather than a "faithful" implemention.

My examination of the Armitage formula in his "Statistical Methods in  
Medical Research" (which appears to be what you implemented in  
prop.trend.test) did not lead me to think it was a rank or permutation  
based method.

I don't have JSTOR access, but if you do, a relevant citation for the  
permutation method appears to be:
<http://www.jstor.org/pss/2530667>

-- 
David Winsemius, MD
Heritage Labs
>
>
> 	-pd
>
>
>>
>>  There also is an implementation in the GeneticsBase package
>> (Bioconductor).
>>
>>> Best,
>>> RobMac
>>>
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>>
>
>
> -- 
>   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
>  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
> (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45)  
> 35327918
> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45)  
> 35327907
>
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