Table 1 Statistical models of mTADA.

From: mTADA is a framework for identifying risk genes from de novo mutations in multiple traits

Hypothesis

Proportion

First trait

Second trait

H0

Ď€0

\(x_{i1}\sim Poisson\left( {2N_1\mu _i} \right)\)

\(x_{i2}\sim Poisson(2N_2\mu _i)\)

H1

Ď€1

\(x_{i1}\sim Poisson(2N_1\mu _i\gamma _{i1})\)

\(\gamma _{i1}\sim Gamma(\bar \gamma _1\beta _1,\beta _1)\)

\(x_{i2}\sim Poisson(2N_2\mu _i)\)

H2

Ď€2

\(x_{i1}\sim Poisson(2N_1\mu _i)\)

\(x_{i2}\sim Poisson(2N_2\mu _i\gamma _{i2})\)

\(\gamma _{i2}\sim Gamma(\bar \gamma _2\beta _2,\beta _2)\)

H3

Ď€3

\(x_{i1}\sim Poisson(2N_1\mu _i\gamma _{i1})\)

\(\gamma _{i1}\sim Gamma(\bar \gamma _1\beta _1,\beta _1)\)

\(x_{i2}\sim Poisson(2N_2\mu _i\gamma _{i2})\)

\(\gamma _{i2}\sim Gamma\left( {\bar \gamma _2\beta _2,\beta _2} \right)\)

  1. Statistical models for four hypotheses in mTADA for one category of variants in each trait at the ith gene. mTADA assumes that the gene can be in one of four models M0..M3. πj (j = 0..3) is the prior probability of the jth model. xk and Nk (k = 1, 2) are the data and the sample size of the kth trait. μi is the mutation rate of the gene. For each trait, the relative risks of shared and specific genes (γk) are from a Gamma distribution with two parameters: \(\bar \gamma _k\) (mean relative risk) and βk (to control the variance of relative risks).
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