# ntdt.q: Computes power of a TDT study as a function of the... In powerpkg: Power analyses for the affected sib pair and the TDT design

## Description

Power for a TDT study will be highest when the frequency of the susceptibility allele (q) matches the frequency of the associated allele (m). We can now examine this by using the ntdt.q() function, which returns a table give the required sample sizes (and log sample sizes) for a range of values of q, at three different levels of ld. These levels are (1) the maximum (dmax), (2) 75% of the maximum (dmax.75), and (3) 50% of the maximum (dmax.50).

## Usage

 `1` ```ntdt.q(g, m, alpha = 5e-08, power = 0.8) ```

## Arguments

 `g` the genotype risk ratio for the susceptibility gene `m` the frequency of the marker allele in linkage disequilibrium with the susceptibility allele. `alpha` the Type 1 error rate `power` the desired power

## Details

We will use an R program that implements the power formulae of Abel and Muller-Myhsok (1998). These formulae allow one to quickly compute power of the TDT approach under a variety of different conditions. This R program was modeled on Martin Farrall's Mathematica notebook.

The power computations here use a simple genetic model with several aspects: (1) The disease locus has two alleles, A and a, with allele frequencies q and 1-q. The risk of disease follows a multiplicative model with genotype relative risks of g and g*g for the A/a and A/A subjects. (2) There is a perfectly linked marker with two alleles, with allele frequencies m and 1-m.

## Value

This function returns a table give the required sample sizes (and log sample sizes) for a range of values of q, at three different levels of ld. These levels are (1) the maximum (dmax), (2) 75% of the maximum (dmax.75), and (3) 50% of the maximum (dmax.50).

The results can be plotted using the plotNtdt function.

## Note

This R program was modeled on Martin Farrall's Mathematica notebook.

Daniel E. Weeks

## References

Abel L, Muller-Myhsok B. Maximum-likelihood expression of the transmission/disequilibrium test and power considerations. Am J Hum Genet. 1998 Aug;63(2):664-7.

Chen WM, Deng HW. A general and accurate approach for computing the statistical power of the transmission disequilibrium test for complex disease genes. Genet Epidemiol. 2001 Jul;21(1):53-67.

Iles MM. On calculating the power of a TDT study–comparison of methods. Ann Hum Genet. 2002 Jul;66(Pt 4):323-8.

Purcell S, Cherny SS, Sham PC. Genetic Power Calculator: design of linkage and association genetic mapping studies of complex traits. Bioinformatics. 2003 Jan;19(1):149-50.

`plotNtdt`, `ntdt`
 `1` ```ntdt.q(g=2,m=0.5,alpha=0.00000005,power=0.80) ```