Effects of Implicit Parameters in Segregation Analysis

In human genetic analysis, data are collected through the so-called 'ascertainment procedure'. Statistically this sampling scheme can be thought of as a multistage sampling method. At the first stage, one or several probands are ascertained. At the subsequent stages, a sequential sampling scheme is applied. Sampling in such a way is virtually a nonrandom procedure, which, in most cases, causes biased estimation which may be intractable. This paper focuses on the underlying causes of the intractability problem of ascertained genetic data. Three types of parameters, i.e. target, design and nuisance parameters, are defined as the essences to formulate the true likelihood of a set of data. These parameters are also classified into explicit or implicit parameters depending on whether they can be expressed explicity in the likelihood function. For ascertained genetic data, a sequential scheme is regarded as an implicit design parameter, and a true pedigree structure as an implicit nuisance parameter. The intractability problem is attributed to loss of information of any implicit parameter in likelihood formulation. Several approaches to build a likelihood for estimation of the segregation ratio when only an observed pedigree structure is available are proposed.