# A short list of math/stats results useful in our work

#### Jan 25, 2007

A derivation for Armitage’s trend test for the 2×3 genotype table

#### Feb 6, 2007

A very short R code for testing HWE Measures of Linkage Disequilibrium :

[code lang="r"]

HWE.test=function(als, counts=apply(als, 1, sum)){

# als is an nx2 matrix of allele counts

no.als=2*nrow(als)

t1=table(counts)

p=(2*t1[1]+t1[2])/no.als

cat("p",p,"\n")

e0=p^2*no.als; e1=2*p*(1-p)*no.als; e2=(1-p)^2*no.als

es=c(e0, e1, e2)

chi.sq=sum((es-t1)^2/(es))

pchisq.new=1-pchisq(chi.sq, 1)

return(pchisq.new)

}

[/code]

#### March 15, 2007

In this section we show the derivation of D’ and the relationship between D’ and R.

- Part I: A Development of the LD Measure D’
- Part II: A Development of the LD Measure R
- Part III: The Relationship Between D’ and R

#### June 5, 2007

Some R code to do a quick sample size estimate for genetic association using case-control studies. Please note that this code contains a parameter that can be adjusted to allow sample size correction under the assumption that the p-values will be adjusted with the Bonferronni correction. A drawback is that the code assumes that the researcher knows the mode of inheritance of the trait.

June 6, 2007 Some R code to do a quick power curve for genetic association using case-control studies. Given the accepted probability of Type I error, disease prevalence, mode of inheritance, and sample size, this returns a curve of power vs. relative risk given 2 disease alleles. Please note that this code contains a parameter that can be adjusted to allow power estimate under the assumption that the p-values will be adjusted with the Bonferronni correction. A drawback is that the code assumes that the researcher knows the mode of inheritance of the trait. Result of running the code will be a graphic like the one shown below.