A transmission disequilibrium test for general pedigrees that is robust to the presence of random genotyping errors and any number of untyped parents

Abstract

Two issues regarding the robustness of the original transmission disequilibrium test (TDT) developed by Spielman et al are: (i) missing parental genotype data and (ii) the presence of undetected genotype errors. While extensions of the TDT that are robust to items (i) and (ii) have been developed, there is to date no single TDT statistic that is robust to both for general pedigrees. We present here a likelihood method, the TDT(ae), which is robust to these issues in general pedigrees. The TDT(ae) assumes a more general disease model than the traditional TDT, which assumes a multiplicative inheritance model for genotypic relative risk. Our model is based on Weinberg's work. To assess robustness, we perform simulations. Also, we apply our method to two data sets from actual diseases: psoriasis and sitosterolemia. Maximization under alternative and null hypotheses is performed using Powell's method. Results of our simulations indicate that our method maintains correct type I error rates at the 1, 5, and 10% levels of significance. Furthermore, a Kolmorogov-Smirnoff Goodness of Fit test suggests that the data are drawn from a central chi2 with 2 df, the correct asymptotic null distribution. The psoriasis results suggest two loci as being significantly linked to the disease, even in the presence of genotyping errors and missing data, and the sitosterolemia results show a P-value of 1.5 x 10(-9) for the marker locus nearest to the sitosterolemia disease genes. We have developed software to perform TDT(ae) calculations, which may be accessed from our ftp site.

Figure 1

Plot of −log(P-value) for TDT_ae statistic applied to 16 SNP markers genotyped in Psoriasis study. In this figure, the dotted horizontal line (x = 2.34) is the threshold for significance at the 5% level of the value −log(P-value), after correcting for multiple testing using the FDR method.,

Figure 2

Plot of −log(P-value) for TDT_ae statistic (solid line) and original TDT (dotted line) applied to 28 microsatellite markers genotyped in Sitosterolemia study. In this figure, we compute P-values for the TDT_ae applied to microsatellite markers using the following formula: the TDT_ae statistic is computed by downcoding all alleles at a locus to two alleles; the allele of interest vs all other alleles. For a marker with i alleles, each of which appears at least 30 times, i tests are performed. We choose the maximum likelihood ratio test statistic among all alleles, and multiply the corresponding uncorrected P-value by the number of alleles tested. The product of this number and the uncorrected P-value is the corrected P-value, and this is value that we report (−log transformed).