POWER STUDIES FOR THE TRANSMISSION DISEQUILIBRIUM TESTS WITH MULTIPLEALLELES/

Case-control studies compare marker-allele distributions in affected a nd unaffected individuals, and significant results suggest linkage but may simply reflect population structure. For markers with m alleles ( m greater than or equal to 2), a McNemar-like statistic, I, estimates the level of population association between marker and disease loci. T o test for linkage after significant case-control tests, within-family tests are performed. These operate on the contingency table, with i, jth element equal to the number of parents that transmit marker allele M(i) and do not transmit marker allele M(j) to an affected offspring. The dimension of the table is the number of alleles at the marker loc us. Three test statistics have recently been proposed in the literatur e: T-c compares symmetric pairs of cells (i, j) and (j, i), T-m compar es row and column totals for the same marker allele, and a likelihood ratio statistic T-l uses all the cells in the table. In addition, we c onsider a new statistic, T-mhet, that uses only the heterozygous paren ts and is approximately chi(2) With (m - 1) df. We use a Monte Carlo t est to guarantee valid tests and to demonstrate the inferiority of T-c and the equality of T-m and T-l in terms of power. The power of the T -mhet test is close but not always equal to the power of the T-m test. We also show that under the alternative hypothesis of linkage, T-m is approximately noncentral chi(2) with (m - 1) df and noncentrality par ameter 2N(T)(1 - 2 theta)I-2, when data on single affecteds in N-T fa milies are used. If the disease has a low population frequency, then I is estimated using the case-control statistic I. This offers a basis for choosing sample size, or choosing a marker system.