Ascertainment adjustment: where does it take us?

It is commonly assumed that the parameter estimates of a statistical genetics model that has been adjusted for ascertainment will estimate parameters in the general population from which the ascertained subpopulation was originally drawn. We show that this is true only in certain restricted circumstances. More generally, ascertainment-adjusted parameter estimates reflect parameters in the ascertained subpopulation. In many situations, this shift in perspective is immaterial: the parameters of interest are the same in the ascertained sample and in the population from which it was drawn, and it is therefore irrelevant to which population inferences are presumed to apply. In other circumstances, however, this is not so. This has important implications, particularly for studies investigating the etiology of complex diseases.