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, 13:40, 4 June 2013
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| − | === Formulation ===
| + | #REDIRECT [[Genotype Likelihood based Hardy-Weinberg Test]] |
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| − | Hardy Weinberg equilibrium is expected in a panmictic population. The following formulation is a likelihood ratio test statistic that incorporates genotype uncertainty via genotype likelihoods. | |
| − | <math>P(R_{k}|\textbf{p})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus observes HWE.
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| − | <math>P(R_{k}|\textbf{g})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus does not observe HWE.
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| − | <math>G_{i,j}</math> denotes the genotype composed of alleles <math>i</math> and <math>j</math> . <math>k</math> indexes the individuals from <math>1</math> to <math> N</math> .
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| − | <math>P(R_{k} |G_{i,j})</math> is the genotype likelihood.
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| − | <math>P(G_{i,j}|\textbf{p})</math> and <math>P(G_{i,j}|\textbf{g})</math> are the [[AF|genotype frequencies estimated with and without HWE assumption]] respectively.
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| − | <math>
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| − | \begin{align}
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| − | L(R|g) & = \frac{\prod_{k}{P(R_{k}|\textbf{p})}}
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| − | {\prod_{k}{P(R_{k}|\textbf{g})}} \\
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| − | & = \frac{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}|\textbf{p})}}}
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| − | {\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}|\textbf{g})}}} \\
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| − | & = \frac{\prod_{k}{\sum_{i,j}{P(R_{k} |G_{i,j} )P(G_{i,j}|\textbf{p})}}}
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| − | {\prod_{k}{\sum_{i,j}{P(R_{k} |G_{i,j})P(G_{i,j}|\textbf{g})}}} \\
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| − | \end{align}
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| − | </math>
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| − | The likelihood ratio test statistic is as follows with <math>v</math> degrees of freedom where <math>n</math> is the number of alleles.
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| − | <math>
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| − | \begin{align}
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| − | -2logL(R|g) \sim X^2_v, v = \frac{n(n-1)}{2}
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| − | \end{align}
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| − | </math>
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| − | === Derivation ===
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| − | Hyun.
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| − | === Maintained by ===
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| − | This page is maintained by [mailto:atks@umich.edu Adrian]
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