Murphy E A, Rosell M I, Rosell E M
Am J Med Genet. 1982 Oct;13(2):163-78. doi: 10.1002/ajmg.1320130208.
The theory of assessing genetic risk for rare autosomal recessive traits in the face of extensive consanguinity is explored. A general lemma is proved that justifies the partition of posterior probability and recursive incorporation of it, as a means of reducing the logic of analysis to steps of manageable complexity: the conditions are that either the components should be independent or that each component, as it is added, is conditioned on the occurrence of all earlier components. An example is given of a pedigree in which the tracing of a gene by the method of expected proportions is misleading, and another that points up the importance of the posterior information. Four classes of patterns are identified and appropriate methods devised for handling them: the single consanguineous loop, multiple mutually-external loops, nested loops, and multiple closures. The latter problem may be treated in general by the use of truncated generating functions, with or without the use of matrix methods.
探讨了在存在广泛近亲结婚情况下评估罕见常染色体隐性性状遗传风险的理论。证明了一个通用引理，该引理证明了后验概率的划分及其递归合并的合理性，以此作为将分析逻辑简化为具有可管理复杂性步骤的一种方法：条件是要么各组成部分应相互独立，要么每个组成部分在添加时都以所有早期组成部分的出现为条件。给出了一个系谱的例子，其中通过期望比例法追踪基因会产生误导，还给出了另一个强调后验信息重要性的例子。识别出四类模式，并设计了相应的处理方法：单一近亲循环、多个相互外部循环、嵌套循环和多重闭合。后一个问题通常可以通过使用截断生成函数来处理，可使用或不使用矩阵方法。
