STOCHASTIC PROCESSES IN POPULATION GENETICS

本研究的两个主要目的是（一）继续理论研究 研究确定性抽样的一般原则，以及（ii）应用 这些原则的估计遗传参数的疾病 与HLA相关 第一个主要目标将特别集中在条件反射的问题上 在确定抽样中。 众所周知，正确的分析必须 条件，至少，对查明的要求; 例如，如果一个家庭只有在家庭中至少有一个同胞才被调查， 受疾病影响的概率， 估计必须以这一要求为条件。 然而，现在看来， 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， 不会在估计过程中引入任何偏差， 只有轻微增加的标准误差估计的遗传 参数，但它可以消除描述的问题， （可能是不精确的）确认过程。 这种可能性将是 追求各种模式，以及在何种情况下， 这种类型的条件是可能的将被界定（因为它是已知的 并不是所有的调节过程都具有刚才描述的性质。 进一步的理论工作将考虑通过使用 在依赖于共享单倍型的估计程序中的特异性HLA抗原 特性和可变折射率对特性的影响 估算 第二个主要目标是应用估计的条件形式 刚才描述的参数的最大似然估计 HLA相关疾病 已经编写了相应的计算机程序 并使用已知参数的人工“数据”进行测试。 在 特别地，已经检查了附加形式的条件作用确实 解决本案中的疑难问题。 这些节目现在将 应用于真实的数据，特别是可能是任意的数据， 过去曾对确定模式作出假设。

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.