overdispersion_shrinkage: Shrink the overdispersion estimates

In glmGamPoi: Fit a Gamma-Poisson Generalized Linear Model

Description

Low-level function to shrink a set of overdispersion estimates following the quasi-likelihood and Empirical Bayesian framework.

Usage

overdispersion_shrinkage(
  disp_est,
  gene_means,
  df,
  disp_trend = TRUE,
  ql_disp_trend = NULL,
  ...,
  verbose = FALSE
)

Arguments

disp_est	vector of overdispersion estimates
gene_means	vector of average gene expression values. Used to fit disp_trend if that is NULL.
df	degrees of freedom for estimating the Empirical Bayesian variance prior. Can be length 1 or same length as disp_est and gene_means.
disp_trend	vector with the dispersion trend. If NULL or TRUE the dispersion trend is fitted using a (weighted) local median fit. Default: TRUE.
ql_disp_trend	a logical to indicate if a second abundance trend using splines is fitted for the quasi-likelihood dispersions. Default: NULL which means that the extra fit is only done if enough observations are present.
...	additional parameters for the loc_median_fit() function
verbose	a boolean that indicates if information about the individual steps are printed while fitting the GLM. Default: FALSE.

Details

The function goes through the following steps

1. Fit trend between overdispersion MLE's and the average gene expression. Per default it uses the loc_median_fit() function.

2. Convert the overdispersion MLE's to quasi-likelihood dispersion estimates by fixing the trended dispersion as the "true" dispersion value: disp_ql = (1 + mu * disp_mle) / (1 + mu * disp_trend)

3. Shrink the quasi-likelihood dispersion estimates using Empirical Bayesian variance shrinkage (see Smyth 2004).

Value

the function returns a list with the following elements

dispersion_trend

the dispersion trend provided by disp_trend or the local median fit.

ql_disp_estimate

the quasi-likelihood dispersion estimates based on the dispersion trend, disp_est, and gene_means

ql_disp_trend

the ql_disp_estimate still might show a trend with respect to gene_means. If ql_disp_trend = TRUE a spline is used to remove this secondary trend. If ql_disp_trend = TRUE it corresponds directly to the dispersion prior

ql_disp_shrunken

the shrunken quasi-likelihood dispersion estimates. They are shrunken towards ql_disp_trend.

ql_df0

the degrees of freedom of the empirical Bayesian shrinkage. They correspond to spread of the ql_disp_estimate's

References

• Lund, S. P., Nettleton, D., McCarthy, D. J., & Smyth, G. K. (2012). Detecting differential expression in RNA-sequence data using quasi-likelihood with shrunken dispersion estimates. Statistical Applications in Genetics and Molecular Biology, 11(5). https://doi.org/10.1515/1544-6115.1826.

• Smyth, G. K. (2004). Linear models and empirical bayes methods for assessing differential expression in microarray experiments. Statistical Applications in Genetics and Molecular Biology, 3(1). https://doi.org/10.2202/1544-6115.1027

See Also

limma::squeezeVar()

Examples

 Y <- matrix(rnbinom(n = 300 * 4, mu = 6, size = 1/4.2), nrow = 30, ncol = 4)
 disps <- sapply(seq_len(nrow(Y)), function(idx){
   overdispersion_mle(Y[idx, ])$estimate
 })
 shrink_list <- overdispersion_shrinkage(disps, rowMeans(Y), df = ncol(Y) - 1,
                                         disp_trend = FALSE, ql_disp_trend = FALSE)

 plot(rowMeans(Y), shrink_list$ql_disp_estimate)
 lines(sort(rowMeans(Y)), shrink_list$ql_disp_trend[order(rowMeans(Y))], col = "red")
 points(rowMeans(Y), shrink_list$ql_disp_shrunken, col = "blue", pch = 16, cex = 0.5)

glmGamPoi documentation built on Nov. 8, 2020, 7:14 p.m.