In the QTLD test, we model association as a fixed effect on the trait mean and we decompose the genotype scores into two components, b' and w', where we have added primes to distinguish the QTLD components from those defined in the QTDT method. We modify the QTDT allelic transmission scoring in a simple way: founder genotypes are included in the within-family component rather than in the between-family component. That is, for founders, w' is set to the observed genotype and b' is set to 0. With this change in the scoring algorithm, our decomposition of the genotype scores no longer results in between- and within-family components, although we retain the notation for consistency.
