| The transmission disequilibrium test (TDT) was built on the early work of haplotype relative risks, to test linkage when association/linkage disequilibrium exists and to evaluate association/linkage disequilibrium when linkage is present. The method applies to nuclear families that have at least one heterozygous parent with one child who is affected by a single-locus bi-allelic recessive genetic disease. An array of extensions of this method, including likelihood approaches, has been developed to cope with more complicated family structures and more complex genetic models. In particular, there are several methods developed for nuclear families with two affected siblings. In all methods, no attempt has been made to estimate linkage and linkage disequilibrium parameters simultaneously.; In this thesis, we extend the TDT to a more general scenario that can include any disease and genetic model, can include affected sib pairs to build a test with 2 degrees of freedom, and can include general family structure without the assumption of independent transmission from the parents to their children. We consider nuclear families with at least one parent who is heterozygous at a bi-allelic marker locus and with two affected siblings. The genetic model is specified by penetrances and allele frequency.; The joint distribution of transmitting and non-transmitting a particular marker allele from a heterozygous parent to his affected children is computed. The probability distribution of the TDT is verified to be a special case. The likelihood is then derived for the transmission probabilities which are based on this joint distribution, including the families structured with one heterozygous parent as well as two heterozygous parents without the assumption of independent transmission from the parents to their children.; With this likelihood, maximum likelihood estimates for the parameters of interest, either the linkage and linkage disequilibrium parameters or the transmission probabilities can be obtained, as well as their confidence intervals/confidence region. Statistical tests, such as the score test and the maximum likelihood ratio test, can also be performed based on this likelihood. Power calculation is presented for the score test.; Simulated data from GAW 11 is used as an example to illustrate the method. |
