adjustScvForBias: Adjust an SCV value for the bias arising when it is...

In DESeq: Differential gene expression analysis based on the negative binomial distribution

Description

Assume that a small sample of i.i.d. random variables from a negative binomial distribution is given, and you have obtained unbiased estimates of mean and raw variance. Then, a new bias is introduced when the squared coefficient of variation (SCV, a.k.a. dispersion) is calculated from these unbiased estimates by dividing the raw variance by the square of the mean. This bias can be calculated by numerical simulation and a pre-calculated adjustment table (or rather a fit through tabulated values) is supplied with the package. The present function uses this to remove the bias from a raw SCV estimate.

This function is used internally in nbinomTest. You will rarely need to call it directly.

Usage

adjustScvForBias(scv, nsamples)

Arguments

scv	An estimate for the raw squared coefficient of variation (SCV) for negative binomially distributed data, which has been obtained by dividing an unbiased estimate of the raw variance by the square of an unbiased estimate of the mean.
nsamples	The size of the sample used in the estimation.

Value

an unbiased estimate of the raw SCV

Author(s)

Simon Anders

Examples

   true_mean <- 100
   true_scv <- .1
   nsamples <- 3
   res <- replicate( 1000, {
      mySample <- rnbinom( nsamples, mu=true_mean, size=1/true_scv )
      mu_est <- mean( mySample )
      raw_var_est <- var( mySample ) - mean( mySample )
      raw_scv_est <- raw_var_est / mu_est^2
      unbiased_raw_scv_est <- adjustScvForBias( raw_scv_est, 4 )
      c( raw_scv_est = raw_scv_est, unbiased_raw_scv_est = unbiased_raw_scv_est ) } )
   rowMeans( res )

DESeq documentation built on April 28, 2020, 6:37 p.m.