A Modified Version of The TDT
More recently, Wittkowski KM, Liu X. (2002/2004) proposed a modification to the TDT that can be more powerful under some alternatives, although the asymptotic properties under the null hypothesis are equivalent.
The motivating idea for this modification is the fact that, while the transmissions of both allele from parents to a child are independent, the effects of other filial genetic or environmental covariates on penetrance are the same for both alleles transmitted to the same child. This situation can be important if, for example, the genetic marker is linked to a disease locus with a strong selection against heterozygous individuals. This observation suggests to shift the statistical model from a set of independent transmissions to a set of independent children (see Sasieni (1997) for the corresponding problem in case-control association tests). While this observation does not affect the distribution under the null hypothesis of no linkage, it allows, for some disease models, to design a more powerful test.
In this modified TDT test the children are stratified by parental type and the modified test statistic becomes:
![\chi^2 = \frac{ \left_{PQ \sim QQ} + 2\times_{PQ \sim PQ} + _{PP \sim PQ} \right]^2}{_{PQ \sim QQ} + 4\times_{PQ \sim PQ} + _{PP \sim PQ}}](http://upload.wikimedia.org/math/a/9/b/a9bd254f1d426df99ba3cd1c9ccbb96b.png)
where is the number of PQ children from parents with the PQ and QQ types.
Read more about this topic: Transmission Disequilibrium Test
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