calc_weight: Calculate Weight for ASM Score

In DAMEfinder: Finds DAMEs - Differential Allelicly MEthylated regions

Description

This function calculates a weight which reflects MM to UU balance, where M stands for methylated and U for unmethylated. Given the MM and UU counts for a particular tuple, the weight is obtained using the link{pbeta} function.

Usage

calc_weight(MM, UU, beta = 0.5, a = 0.2)

Arguments

MM	The read counts for where pos1 and pos2 of the tuple were both methylated.
UU	The read counts for where pos1 and pos2 of the tuple were both unmethylated.
beta	parameter for the beta distribution. In B(alpha,beta), we set alpha=beta=0.5 by default.
a	parameter for how far from 0.5 we go as a measure of allele-specific methylation. The weight is the probability that the MM:(MM+UU) ratio is between 0.5-a and 0.5+a. The default is set to 0.2.

Details

For a given tuple with MM and UU counts, the weight that reflects allele-scpecificity is calculated as follows:

• Prior:

  p(θ|α,β) \sim Beta(α,β),

  where θ = \frac{MM}{MM+UU} and α = β = 0.5. p(θ|α,β) represents our prior belief which is that tuples are either fully methylated or fully unmethylated, rather than allele-specifically methylated which is a much rarer event.

• Likelihood:

  p(x|α,β) \propto θ^{MM}(1-θ)^{UU},

  where x is our observation (the MM and UU counts).

• Posterior:

  p(θ|x) \propto p(x|θ)*p(θ|α,β)

  p(θ|x) \propto θ^{MM-0.5}(1-θ)^{UU-0.5},

  where α = β = 0.5. This posterior also follows a beta distribution \sim Beta(α'=MM+0.5, β'=UU+0.5)

Value

A number that reflects allele-specificity given MM and UU counts for a CpG pair. This is used as a weight that is multiplied by the log odds ratio to give the final ASM score of that tuple.

#calc_weight(MM=50, UU=50) #0.9999716

#calc_weight(MM=20, UU=60) #0.1646916

DAMEfinder documentation built on Nov. 8, 2020, 11:10 p.m.