An Alternative Foundation for the Planning and Evaluation of Linkage Analysis

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Abstract
The lod score, which is based on the likelihood ratio (LR), is central to linkage analysis. Users interpret lods by translating them into standard statistical concepts such as p values, alpha levels and power. An alternative statistical paradigm, the Evidential Framework, in contrast, works directly with the LR. A key feature of this paradigm is that it decouples error probabilities from measures of evidence. We describe the philosophy behind and the operating characteristics of this paradigm--based on new, alternatively-defined error probabilities. We then apply this approach to linkage studies of a genetic trait for: I. fully informative gametes, II. double backcross sibling pairs, and III. nuclear families. We consider complete and incomplete penetrance for the disease model, as well as using an incorrect penetrance. We calculate the error probabilities (exactly for situations I and II, via simulation for III), over a range of recombination fractions, sample sizes, and linkage criteria. We show how to choose linkage criteria and plan linkage studies, such that the probabilities of being misled by the data (i.e. concluding either that there is strong evidence favouring linkage when there is no linkage, or that there is strong evidence against linkage when there is linkage) are low, and the probability of observing strong evidence in favour of the truth is high. We lay the groundwork for applying this paradigm in genetic studies and for understanding its implications for multiple tests.