What is the difference between independence.test in R and Cochrane and Armitage trend test?

Question

What is the difference between independence.test in R and CATT (Cochrane and Armitage) tests?

How these tests are calculated? Where do we and how do we define x=0.0 0.5 1.0 (genetic studies) for both of the tests?

Answer 1

As a follow-up to my comment, if independence.test refers to coin::independence_test, then you can reproduce a Cochrane and Armitage trend test, as it is used in GWAS analysis, as follows:

> library(SNPassoc)
> library(coin)
> data(SNPs)
> datSNP <- setupSNP(SNPs,6:40,sep="")
> ( tab <- xtabs(~ casco + snp10001, data=datSNP) )
     snp10001
casco T/T C/T C/C
    0  24  21   2
    1  68  32  10
> independence_test(casco~snp10001, data=datSNP, teststat="quad",
                    scores=list(snp10001=c(0,1,2)))

Asymptotic General Independence Test

data:  casco by snp10001 (T/T < C/T < C/C) 
chi-squared = 0.2846, df = 1, p-value = 0.5937

This is a conditional version of the CATT. About scoring of the ordinal variable (here, the frequency of the minor allele denoted by the letter C), you can play with the scores= arguments of independence_test() in order to reflect the model you want to test (the above result is for a log-additive model).

There are five different genetic models that are generally considered in GWAS, and they reflect how genotypes might be collapsed: codominant (T/T (92) C/T (53) C/C (12), yielding the usual $\chi^2(2)$ association test), dominant (T/T (92) vs. C/T-C/C (65)), recessive (T/T-C/T (145) vs. C/C (12)), overdominant (T/T-C/C (104) vs. C/T (53)) and log-additive (0 (92) < 1 (53) < 2 (12)). Note that genotype recoding is readily available in inheritance functions from the SNPassoc package. The "scores" should reflect these collapsing schemes.

Following Agresti (CDA, 2002, p. 182), CATT is computed as $n\cdot r^2$, where $r$ stands for the linear correlation between the numerical scores and the binary outcome (case/control), that is

z.catt <- sum(tab)*cor(datSNP$casco, as.numeric(datSNP$snp10001))^2
1 - pchisq(z.catt, df = 1)  # p=0.5925

There also exist various built-in CATT functions in R/Bioconductor ecosystem for GWAS, e.g.

• CATT() from Rassoc, e.g.

  with(datSNP, CATT(table(casco, snp10001), 0.5)) # p=0.5925 
  

(additive/multiplicative)

• in snpMatrix, there are headed as 1-df $\chi^2$-test when you call single.snp.tests() (see the vignette); please note that the default mode of inheritance is the codominant/additive effect.

Finally, here are two references that discuss the choice of scoring scheme depending on the genetic model under consideration, and some issues with power/robustness

1. Zheng, G, Freidlin, B, Li, Z and Gastwirth, JL (2003). Choice of scores in trend tests for case-control studies of candidate-gene associations. Biometrical Journal, 45: 335-348.
2. Freidlin, B, Zheng, G, Li, Z, and Gastwirth, JL (2002). Trend Tests for Case-Control Studies of Genetic Markers: Power, Sample Size and Robustness. Human Heredity, 53: 146-152.

See also the GeneticsDesign (bioc) package for power calculation with linear trend tests.