TDT with errors: a likelihood based approach. S.C. Heath, J. Ott. Lab Statistical Genetics, Rockefeller Univ, New York, NY.

   The Transmission/Disequilibrium Test (TDT) is a non-parametric test for linkage. It does not requires large families, and can have more power to detect small effect loci than conventional linkage analysis methods, and has therefore been proposed as a method for performing genome scans for complex disease loci.
    In the absence of genotype errors the TDT is an unbiased test for linkage. However, genotype errors lead to an inflation of the type I error rate whenever marker frequencies are unequal. We present a likelihood based approach for diallelic loci which tests whether the probability of transmission of a '1' allele from heterozygous parents to an affected child is different from 1/2. This is essentially the the same test as the TDT, but can allow for both genotype errors and missing genotype data. As well as the transmission probability (t), the likelihood depends on the genotype frequencies (p) and the error rate (e). These are often unknown, so the test uses their maximum likelihood estimates. To perform the test we calculate the likelihood ratio T=2 Log(p’,e’,t’)/Log(p•,e•,t=1/2), which under the null hypothesis is approximately distributed as a chi-squared variable with 1 df. This test is unbiased in the presence of errors or missing (at random) genotype data. If, however, the data has been 'cleaned' before analysis (i.e., families with Mendelian inconsistencies have been removed), then e will be estimated at 0, and the estimate of t will (normally) be biased. It is therefore important that the test is performed on the original data. If this is not possible then an alternative approach, which we will also discuss, is to use both affected and unaffected offspring, estimating the transmission probability separately for each class of offspring and testing whether the two probabilities differ.
    If TDT is to be a useful tool for detecting disease loci and given that genotype errors do exist, it will be necessary to use methods that either explicitly allow for errors or, at least, are robust to the presence of errors. It is hoped that the methods presented here will prove useful in this regard. This work was supported by NIH grants GM58757-01 (SCH) and HG00008 (JO).