666.15 - Replacing IBS with IBD: The MLS Method...

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Replacing IBS with IBD: The MLS Method Biostatistics 666 Lecture 15
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Previous Lecture z Analysis of Affected Relative Pairs z Test for Increased Sharing at Marker z Expected Amount of IBS Sharing
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Previous Lecture: Expected IBS Sharing z Calculated probability of IBS for each IBD state z Probability of IBD state depends on relationship Under the null hypothesis of no linkage = = = = = = 2 0 ) | ( ) | ( ) | ( j R j IBD P j IBD i IBS P R i IBS P
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Shortcomings of IBS Method z All sharing is weighted equally Sharing a rare allele Sharing a common allele Sharing homozygous genotype Sharing heterozygous genotype z Inefficient. Data contains additional information that is being ignored.
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Today z A likelihood based approach z Evaluate linkage in fully informative pairs z An E-M algorithm for practical settings z MLS method, Risch (1990)
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Simple Case z If IBD could be observed z Each pair of individuals scored as IBD=0 IBD=1 IBD=2 z Evaluate likelihood for null and alternative hypothesis
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The Model z Depends on three parameters z 0 , z 1 , z 2 Probability of sharing 0, 1 and 2 alleles IBD z Under the null, determined by relationship z Under the alternative, determined by genetic model
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Sib Pair Likelihood (Fully Informative Data) () ( ) 2 1 0 2 1 0 2 1 0 4 1 2 1 4 1 ˆ ˆ ˆ hypothesis e alternativ Under the ) ( ) ( ) ( : hypothesis null Under the IBD IBD IBD IBD IBD IBD n n n n n n z z z L L = =
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Testing for Linkage z Evaluate likelihood at null hypothesis z Evaluate likelihood at MLE z Compare alternatives using likelihood ratio test
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Commonly Used Test Statistics ) , , ( ln 2 ) ˆ , ˆ , ˆ ( ln 2 ) , , ( ) ˆ , ˆ , ˆ ( ln 2 ) , , ( ) ˆ , ˆ , ˆ ( log 4 1 2 2 1 1 4 1 0 2 1 0 4 1 2 2 1 1 4 1 0 2 1 0 2 4 1 2 2 1 1 4 1 0
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666.15 - Replacing IBS with IBD: The MLS Method...

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