The triangle test statistic (TTS): a test of genetic homogeneity using departure from the triangle constraints in IBD distribution among affected sib-pairs

The proportions of affected sibs sharing 2: 1 or 0 identical by descent par ental marker alleles have been shown to conform to the 'triangle constraint s' (Suarez, 1978 Holmans, 1993). It has also been shown (Dudoit & Speed. 19 99) that the constraints are verified provided certain assumptions hold. II I this study we explore a realistic situation in which the constraints fail due to the presence of a factor in which the sibs differ. a factor on whic h penetrance depends. This factor may be a characteristic of the trait (sev ere vs. mild form), or the presence/absence of an associated trait or an en vironmental factor. We show that under such situations, using the triangle constraints mali lead to important loss of power to detect linkage by the M LS test. me propose here an alternative approach in order to detect both li nkage and heterogeneity.