THE PROBLEM OF ASCERTAINMENT FOR LINKAGE ANALYSIS

It is generally believed that ascertainment corrections are unnecessar y in linkage analysis, provided individuals are selected for study sol ely on the basis of trait phenotype and not on the basis of marker gen otype. The theoretical rationale for this is that standard linkage ana lytic methods involve conditioning likelihoods on all the trait data, which may be viewed as an application of the ascertainment assumption- free (AAF) method of Ewens and Shute. In this paper, we show that when the observed pedigree structure depends on which relatives within a p edigree happen to have been the probands (proband-dependent, or PD, sa mpling) conditioning on all the trait data is not a valid application of the AAF method and will result in asymptotically biased estimates o f genetic parameters (except under single ascertainment). Furthermore, this result holds even if the recombination fraction R is the only pa rameter of interest. Since the fod score is proportional to the likeli hood of the marker data conditional. on all the trait data, this means that when data are obtained under PD sampling the fod score will yiel d asymptotically biased estimates of R, and that so-called mod scores (i.e., lod scores maximized over both R and parameters theta of the tr ait distribution) will yield asymptotically biased estimates of R and theta. Furthermore, the problem appears to be intractable, in the sens e that it is not possible to formulate the correct likelihood conditio nal on observed pedigree structure. In this paper we do not investigat e the numerical magnitude of the bias, which may be small in many situ ations. On the other hand, virtually all linkage data sets are collect ed under PD sampling. Thus, the existence of this bias will be the rul e rather than the exception in the usual applications.