STOCHASTIC PROCESSES IN POPULATION GENETICS

这项研究提案的两个主要目的是(I)继续理论 关于确定抽样的一般原则的工作，以及(2)适用 疾病遗传参数估计的这些原则 与人类白细胞抗原有关。 第一个主要目标将特别集中在条件反射问题上。 在确证抽样中。众所周知，正确的分析必须 最低限度以确定要求为条件； 例如，如果仅在家庭中至少有一个兄弟姐妹的情况下才调查该家庭 受疾病的影响，参数的概率 估计必须以这一要求为条件。然而，它现在似乎来自 目前的研究表明，在许多情况下，进一步的条件反射是可能的， 不会在估算过程中引入任何偏差，从而导致 遗传基因估计的标准误差只有微小的增加 参数，但它可以消除经常讨论的描述 (可能不精确的)确定过程。这种可能性将是 追求各种模式，以及在什么情况下 这种类型的条件条件是可能的(因为它是已知的 并不是所有的条件化过程都具有刚才描述的特性。) 进一步的理论工作将考虑通过使用 依赖共享单倍型的评估程序中的特定人类白细胞抗原 变外显度的特点及其对性能的影响 估计。 第二个主要目标将是应用估计的条件形式 刚才描述的是参数的最大似然估计 与人类白细胞抗原相关的疾病。已经编写了适当的计算机程序 并在参数已知的情况下使用人造“数据”进行测试。在……里面 具体地说，已经检查了附加形式的条件作用 在这种情况下，删除确定问题。这些节目现在将是 用于实际数据，尤其用于可能是任意的数据 过去已经对确定模型做出了假设。

The two main aims of this research proposal are (i) to continue theoretical work on the general principles of ascertainment sampling, and (ii) to apply these principles to the estimation of genetic parameters of a disease linked to HLA. The first main aim will focus in particular on the problem of conditioning in ascertainment sampling. It is well known that a correct analysis must condition, at the very least, on the requirement for ascertainment; for example, if a family is investigated only if at least one sib in the family is affected by a disease, the probabilities from which the parameters are estimated must condition on this requirement. However, it now appears from present research that in many cases further conditioning is possible which does not introduce any bias into the estimation procedure, which causes only minor increases in the standard errors of estimates of genetic parameter and yet which can remove the much-discussed problem of describing the (perhaps imprecise) ascertainment process. This possibility will be pursued for a variety of models, and the circumstances under which conditioning of this type is possible will be delimited (since it is known that not all conditioning processes have the properties just described.) Further theoretical work will consider the information gained by the use of specific HLA antigens in estimation procedures relying on shared haplotype characteristics and the effects of variable penetrance on properties of estimates. The second main aim will be to apply the conditional forms of estimation just described to the maximum likelihood estimation of parameters for HLA-linked diseases. The appropriate computer programs have been written and tested using artificial "data" where the parameters are known. In particular it has been checked that the additional forms of conditioning do remove ascertainment problems in this case. The programs will now be applied to real data, in particular to data where perhaps arbitrary assumptions on the ascertainment model have been made in the past.