Reply to Laird et al.

To the Editors:Laird et al. (1998xThe sib transmission/disequilibrium test is a Mantel-Haenszel test. Laird, N, Blacker, D, and Wilcox, M. Am J Hum Genet. 1998; 63: 915Abstract | Full Text | Full Text PDFSee all References1998 [in this issue]) point out that the sib transmission/disequilibrium test (S-TDT) is identical in principle to the Mantel extension test for trend in multiple strata. We were not aware of this test and independently developed the S-TDT. Despite identity in theory, however, our test differs in practice from the Mantel extension test in two respects.First, unlike the Mantel extension test described by Rosner (1995xRosner, B. See all References1995) and its implementation in SAS programs as described by Laird et al. (1998xThe sib transmission/disequilibrium test is a Mantel-Haenszel test. Laird, N, Blacker, D, and Wilcox, M. Am J Hum Genet. 1998; 63: 915Abstract | Full Text | Full Text PDFSee all References1998), our approach makes a continuity correction in the z score calculation and thus provides a somewhat more accurate approximation of P values. The difference is substantial when the data consist of only a small number of families. For instance, in our numerical example of three families (Spielman and Ewens 1998xA sibship test for linkage in the presence of association: the sib transmission/disequilibrium test. Spielman, RS and Ewens, WJ. Am J Hum Genet. 1998; 62: 450–458Abstract | Full Text | Full Text PDF | PubMed | Scopus (511)See all References1998), the use of a continuity correction led us to a z score of 1.9839, which results in a two-sided P value of .0473. The SAS program computes a two-sided P value of .016, which is also the value computed by use of the formula of Rosner (1995xRosner, B. See all References1995). In this example, the exact P value can be found by exhaustive enumeration of all permutations of the data from the three families: it is 3/70=.0429, which is close to our value and is more than twice the value computed by the SAS program.Laird et al. (1998xThe sib transmission/disequilibrium test is a Mantel-Haenszel test. Laird, N, Blacker, D, and Wilcox, M. Am J Hum Genet. 1998; 63: 915Abstract | Full Text | Full Text PDFSee all References1998) comment that the SAS calculation does not include a continuity correction but imply that the StatXact computer program can compute exact P values for the S-TDT. In practice, no procedure can do this when the sample consists of data from a large number of families, since in such cases an exact calculation would involve an astronomically large number of permutations. For such cases, StatXact resorts to Monte Carlo methods by using samples taken at random from the large number of permutations possible. We ourselves used this procedure for the S-TDT (Spielman and Ewens 1998xA sibship test for linkage in the presence of association: the sib transmission/disequilibrium test. Spielman, RS and Ewens, WJ. Am J Hum Genet. 1998; 62: 450–458Abstract | Full Text | Full Text PDF | PubMed | Scopus (511)See all References1998).Second, instead of the square of the z statistic, which the Mantel extension test applies, we prefer to use the unsquared z statistic, because one of our aims is to provide a combined test for data from some families that are suitable for the S-TDT test and from some that are suitable for the TDT (Spielman and Ewens 1998xA sibship test for linkage in the presence of association: the sib transmission/disequilibrium test. Spielman, RS and Ewens, WJ. Am J Hum Genet. 1998; 62: 450–458Abstract | Full Text | Full Text PDF | PubMed | Scopus (511)See all References1998). The combined test is easily performed by use of the unsquared statistic but not by use of the squared statistic. A computer program that incorporates the continuity correction and that allows for the combination of the S-TDT and TDT procedures is now available at http://spielman07.med.upenn.edu/TDT.htm.