# ntdt: Computes number of trios needed for a TDT study. In powerpkg: Power analyses for the affected sib pair and the TDT design

## Description

Calculation of how many TDT trios need to be studied in order to have an adequately powered TDT study. The user specifies the susceptibility gene allele frequency (q), the frequency of the marker allele (m) in linkage disequilibrium with the susceptibility allele, the strength of the linkage disequilibrium between marker and susceptibility allele (ld), the genotype risk ratio for the susceptibility gene (g), the desired power (power) and the type 1 error rate (alpha) allowing for multiple testing.

## Usage

 `1` ```ntdt(g, q, m, ld, power, alpha) ```

## Arguments

 `g` the genotype risk ratio for the susceptibility gene `q` the susceptibility allele frequency `m` the frequency of the marker allele in linkage disequilibrium with the susceptibility allele. `ld` the strength ofthe linkage disequilibrium between marker and susceptibility allele, on a scale of 0 to 1. `power` the desired power `alpha` the Type 1 error rate

## 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

 `nfam` The number of trios needed to obtain the desired power.

## 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 studyâ€“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.q`
 ```1 2 3 4``` ```## Compute the number of TDT trios would be needed under these conditions: ## q = 0.15; m = 0.25;ld= 0.45;g= 1.5;power =0.85;alpha =0.05; ntdt(q=0.15,m=0.25,ld=0.45,g=1.5,power=0.85,alpha = 0.05) ```