In the context of differential expression analysis, limma is a popular R package that originally was designed for microarray data but has since been adapted for RNA-seq data (using voom transformation). One of the unique features of limma is its use of moderated statistics. Here’s a breakdown of the difference between ordinary p-values and moderated p-values in limma:

• Ordinary P-values:

  • These are the p-values you would get if you were to do standard hypothesis testing on each gene individually without borrowing information from other genes.
  • Calculated based on the ordinary standard errors.

• Moderated P-values:

  • Limma borrows information across genes to get more precise estimates of the variability for each gene. This is especially useful when the number of samples (replicates) is small.
  • The process involves “shrinking” the gene-wise sample variances towards a pooled estimate, resulting in moderated t-statistics, which are more stable than ordinary t-statistics.
  • Moderated p-values are calculated based on these moderated t-statistics.
  • As a result, these moderated p-values tend to be more reliable, especially in experiments with small sample sizes.

• Why is Moderation Necessary?:

  • In many genomics experiments, there’s a challenge: While there are thousands of genes (or more), there might be a relatively small number of replicates or samples. This can make estimates of variance for each gene unreliable.
  • By borrowing strength from the ensemble of genes, limma can stabilize these variance estimates, which, in turn, makes the resulting p-values more reliable.

• Empirical Bayes Method:

  • The moderation in limma is achieved through an empirical Bayes method. This doesn’t mean it’s a fully Bayesian approach but rather that it borrows some concepts from Bayesian statistics to stabilize variance estimates across genes.

In practice, when using limma, researchers often focus on the moderated p-values because of their enhanced reliability, especially in the context of multiple hypothesis testing in genomics. The moderated statistics help reduce the number of false positives that might arise from genes with unusually low variance estimates due to chance alone.