Bonney G E
Department of Biostatistics, Fox Chase Cancer Center, Philadelphia, USA.
Am J Hum Genet. 1998 Oct;63(4):1202-15. doi: 10.1086/302057.
Ascertainment concerns the manner by which families are selected for genetic analysis and how to correct for it in likelihood models. Because such families are often neither drawn at random nor selected according to well-defined rules, the problem of ascertainment correction in the genetic analysis of family data has proved durable. This paper undertakes a systematic study of ascertainment corrections in terms of smaller distinct units, which will usually be sibships, nuclear families, or small pedigrees. Three principal results are presented. The first is that ascertainment corrections in likelihood models for family data can be made in terms of smaller units, without breaking up the pedigree. The second is that the appropriate correction for single ascertainment in a unit is the reciprocal of the sum of the marginal probabilities of all the persons relevant to its ascertainment, as if affected. The third result is a generalization of the single ascertainment-correction formula to k-plex ascertainment, in which each unit has k or more affecteds. The correction is the reciprocal of the sum of the joint probabilities of all distinct sets of k persons in the unit, as if they were all affected. In extended families, two additional ascertainment schemes will be considered and explicit formulas will be presented. One of these schemes is "uniform-proband-status ascertainment," in which nonmembers of a given unit have the same chance as members to become probands if they are affected; the other scheme is the "inverse law of ascertainment," in which the chance that nonmembers of a unit will become probands for that unit decreases with degree of relationship. Several specific recommendations are made for further study.
确定涉及选择用于基因分析的家庭的方式以及如何在似然模型中对其进行校正。由于此类家庭通常既不是随机抽取的，也不是根据明确的规则选择的，因此在家庭数据的基因分析中，确定校正问题一直存在。本文对以较小的不同单位（通常是同胞组、核心家庭或小系谱）进行的确定校正进行了系统研究。给出了三个主要结果。第一个结果是，家庭数据似然模型中的确定校正可以根据较小的单位进行，而无需拆分系谱。第二个结果是，对单位中单次确定的适当校正是与确定相关的所有人员（假设为受影响者）的边际概率之和的倒数。第三个结果是将单次确定校正公式推广到k重确定，其中每个单位有k个或更多受影响者。校正是该单位中所有不同的k人集合的联合概率之和的倒数，就好像他们都受影响一样。在大家庭中，将考虑另外两种确定方案并给出明确的公式。其中一种方案是“均匀先证者状态确定”，在这种方案中，如果给定单位的非成员受影响，他们成为先证者的机会与成员相同；另一种方案是“反向确定定律”，在这种方案中，单位非成员成为该单位先证者的机会随着亲属关系程度的增加而降低。针对进一步研究提出了一些具体建议。
