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| <math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study | | <math>U_{i,k} </math> is the score statistic for the <math>i^{th} </math> variant from the <math> k^{th} </math> study |
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| + | <math>\mathbf{U_k}</math> is the vector of score statistics of rare variants in a gene from the <math> k^{th} </math> study. |
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| <math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study | | <math>V_{ij,k} </math> is the covariance of the score statistics between the <math>i^{th} </math> and the <math>j^{th} </math> variant from the <math> k^{th} </math> study |
Revision as of 21:32, 8 April 2014
INTRODUCTION
The key idea behind meta-analysis with RAREMETAL is that various gene-level test statistics can be reconstructed from single variant score statistics and that, when the linkage disequilibrium relationships between variants are known, the distribution of these gene-level statistics can be derived and used to evaluate signifi-cance. Single variant statistics are calculated using the Cochran-Mantel-Haenszel method. The main formulae are tabulated in the following:
KEY FORMULAE
NOTATIONS
We denote the following to describe our methods:
is the score statistic for the variant from the study
is the vector of score statistics of rare variants in a gene from the study.
is the covariance of the score statistics between the and the variant from the study
is the number of studies
and are described in detail in RAREMETALWORKER method
SINGLE VARIANT META ANALYSIS
Single variant meta-analysis score statistic can be reconstructed from score statistics and their variances generate by each study, assuming that samples are unrelated across studies. Define meta-analysis score statistics as
and its variance
Then the score test statistics for the variant asymptotically follows standard normal distribution
BURDEN META ANALYSIS
VT META ANALYSIS
SKAT META ANALYSIS
Formulae for RAREMETAL
Test
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Statistics
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Null Distribution
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Notation
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Single Variant |
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un-weighted Burden |
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Weighted Burden |
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VT |
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SKAT |
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