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.
