Sampling correction in linkage analysis

In a linkage analysis that requires the estimation of parameters other than the recombination fraction, we can construct a pedigree likelihood that leads to consistent parameter estimators if the sampling procedures are known. In particular, it is necessary to identify the subset of pedigree members "relevant to sampling" (RS), where by sampling we mean both pedigree ascertainment through a proband combination and the selective inclusion of the sampled pedigrees in the data that are analyzed. If both these procedures are independent of the marker phenotypes and the model of trait inheritance is known, then no sampling or ascertainment correction is needed to obtain a consistent estimator of the recombination fraction. Otherwise, the correction can be of two types: sampling-model-based, in which the ascertainment and inclusion procedures are modeled and used in the likelihood expression, or sampling-model-free, in which the data RS are "conditioned out" without any modeling of the sampling procedures. In either case, the pedigree proband sampling frame must be identified.