various error models [31]. As discussed above, multiple affected and unaffected siblings are often collected and used for both linkage and association analysis. The family-based association test (FBAT) generalized the TDT model on various phenotypic traits and multiple markers [32]–[36]. Instead of using data from only the heterozygous parents as in the TDT, the affected-family based controls (AFBAC) method [37] is developed to take advantage of all the parental information. But the trade-off of this setup is its vulnerability to population stratification as genotype frequencies are not irrelevant in this test [37], [38]. Another extension of the TDT, the pedigree disequilibrium test (PDT), is specifically designed for analyzing the Linkage Disequilibrium (LD, the non-random association of alleles at two or more loci) in general pedigrees, which has been successfully applied on a number of complex traits such as diabetes [38], [39]. Further, as a more powerful development to the PDT, the presence of linkage (APL) is used to handle diseases of late-onset [38], [40]. However, in spite of the divergences as well as the great promise of these TDT-type analyses [9], [24], [41], one primary limitation that most of these extensions encounter is the dependence on completeness of the genotype
