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Here we describe the improvements to limma’s diffSplice method. diffSplice works on the bin-wise coefficient of the linear model which corresponds to the log2 fold changes between conditions. It compares the log2(fold change) ˆβk,g of a bin k belonging to gene g, to a weighted average of log2(fold change) of all the other bins of the same gene combined ˆBk,g (the subscript g will be henceforth omitted for ease of reading). The weighted average of all the other bins in the same gene is calculated by ˆBk=Ni,ikwiˆβiNi,ikwi where wi=1u2i and ui refers to the diagonal elements of the unscaled covariance matrix (XTVX)1. X is the design matrix and V corresponds to the weight matrix estimated by voom. The difference of log2 fold changes, which is also the coefficient returned by diffSplice() is then calculated by ˆCk=ˆβkˆBk. Instead of calculating the t-statistic with ˆCk, this value is scaled again in the original code:

ˆDk=ˆCk1wkNiwi

and the t-statistic is calculated as:

tk=ˆDkuksg

s2g refers to the posterior residual variance of gene g, which is calculated by averaging the sample values of the residual variances of all the bins in the gene, and then squeezing these residual variances of all genes using empirical Bayes method. This assumes that the residual variance is constant across all bins of the same gene.

In , we applied three changes to the above method. First, the residual variances are not assumed to be constant across all bins of the same gene. This results in the sample values of the residual variances of every bin now being squeezed using empirical Bayes method, resulting in posterior variances s2i for every individual bin i. Second, the weights wi, used to calculate ˆBk, now incorporate the individual variances by wi=1s2iu2i. Third, the ˆCk value is directly used to calculate the t-statistic, which after all these changes now corresponds to

tk=ˆCkuksi.






Using a simulation from a previous DEU benchmark Soneson et al. 2016, we show that our modifications improve the accuracy of the original limma method:

diffSplice2 improves upon the original method in a DEU simulation.

Figure 1: diffSplice2 improves upon the original method in a DEU simulation

Of note, however, in most settings the accuracy of diffSplice2 is still inferior to that of DEXSeq, which therefore remains the method of choice for DEU. However, as the computationally-heavy DEXSeq does not scale well and is not applicable in all situations, we recommend diffSplice2 as the next best method.