Statistical models for genetics data are often surprisingly challenging, from several points of view: statistical, mathematical, and computational. The development of new methods for the analysis of such genetics data requires highly nontrivial statistical methods. Indeed, the thorough evaluation of existing methods also may demand advanced statistical and mathematical analysis, in addition to extensive computer simulation. This project is first investigating a simple, widely used test (the TDT) for detecting association and/or linkage from parent child data. The transmission/disequilibrium test (TDT) has widespread use in statistical genetics. It does not make any assumptions regarding mode of inheritance, penetrance rates, marker or disease allele frequencies or population stratification. It is understood to have high power for detecting association and/or linkage, and is very simple to apply. However, it does not directly estimate any of the underlying parameters in the allele transmission probability model, nor provide for follow-up estimation when the null model of no association or linkage as been rejected. This project is the first analysis to do, and thus to make standard allele transmission data useful in a way that is as broadly useful as pedigree linkage methods. We introduce a new parametrization of the model, and show that the TDT has in fact surprisingly low power over a broad range of the parameter space. Thus the usual TDT is useful only when both association and linkage are present, and this is a consequence of the previously unsuspected nature of the metric for testing the null model: it is a hyperbolic metric, not a simple Euclidean. Also, we derive maximum likelihood estimates for the model parameters, and introduce a parametric bootstrap confidence interval for the parameters. We show by simulation that the test of the null model generated by the intervals is uniformly more powerful than the customary TDT. We also discuss extensions to cases for which a parent genotype is missing, using the EM (expectation maximumization) and the MI (multiple imputation) algorithms. [1] Malley, Redner, Severini, Badner (1999). Estimation of Association and Linkage from Transmission/disequilibrium (TDT) Data. CIT Technical Report; to be submitted to American Journal of Human Genetics. - transmission/disequilibrium; tests for association/ tests for linkage
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