Several formal statistical descriptions of genotype imputation procedures for association analyses in families have now been published (15, 108) and the procedures to support genotype in imputation are implemented in packages such as MERLIN (2, 3) and MENDEL (52, 53). In principle, these procedures can be implemented using the infrastructure of the Lander-Green (48) or Elston-Stewart (29) algorithms, or one of the many other pedigree analysis algorithms, including those that are based on Monte Carlo sampling (38, 96). An important observation from these more formal treatments of the problem is that even when genotypes cannot be imputed with high confidence, partial information about the identity of each of the true underlying genotypes can be productively incorporated in association analysis (15, 108). For example, when genotypes are measured directly, observed allele counts are often used in regression analyses to estimate an additive effect for each marker (1, 8, 34). These observed allele counts are discrete and indicate the number of copies of the allele of interest (0, 1 or 2) carried by each individual. When genotypes are not measured directly, these
