In comparative RNA sequencing (RNA-seq) experiments, selecting the appropriate sample size is an important optimization step [1]. Empirical RNA-seq Sample Size Analysis (ERSSA) is a R software package designed to test whether an existing RNA-seq dataset has sufficient biological replicates to detect a majority of the differentially expressed genes (DEGs) between two conditions. In contrast to existing RNA-seq sample size analysis algorithms, ERSSA does not rely on any a priori assumptions about the data [2]. Rather, ERSSA takes a user-supplied RNA-seq sample set and evaluates the incremental improvement in identification of DEGs with each increase in sample size up to the total samples provided, enabling the user to determine whether sufficient biological replicates have been included.

Based on the number of replicates available (N for each of the two conditions), the algorithm subsamples at each step-wise replicate levels (n= 2, 3, 4, â€¦, N-1) and uses existing differential expression (DE) analysis software (e.g., edgeR [8] and DESeq2 [9]) to measure the number of DEGs. As N increases, the set of all distinct subsamples for a particular n can be very large and experience with ERSSA shows that it is not necessary to evaluate the entire set. Instead, 30-50 subsamples at each replicate level typically provide sufficient evidence to evaluate the marginal return for each increase in sample size. If the number of DEGs identified is similar for n = N-2, N-1 and N, there may be little to be gained by analyzing further replicates. Conversely, if the number of DEGs identified is still increasing strongly as n approaches N, the user can expect to identify significantly more DEGs if they acquire additional samples.

When applied to a diverse set of RNA-seq experimental settings (human tissue, human population study and in vitro cell culture), ERSSA demonstrated proficiency in determining whether sufficient biological replicates have been included. Overall, ERSSA can be used as a flexible and easy-to-use tool that offers an alternative approach to identify the appropriate sample size in comparative RNA-seq studies.

Install the latest stable version of ERSSA by entering the following commands in R console:

```
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("ERSSA")
```

In this vignette, we demonstrate ERSSAâ€™s analytical approach using an RNA-seq dataset containing 10 human heart samples and 10 skeletal muscle samples from GTEx [3] and ask whether 10 replicates are sufficient to identify a majority of DE genes (adjusted p-value < 0.05 and |log2(fold-change)| > 1). At the end of the ERSSA run, four plots are generated to summarize the results. For now, letâ€™s briefly focus on the most important of these, the number of DEGs identified as a function of the number of replicates included in the analysis. In the present example, the average number of DEGs discovered increases approximately 3% from n=6 to n=7 and little to no improvement as n increases to 8 and beyond. This suggests that our example dataset with N=10 replicates is sufficient to identify the vast majority of DEGs. To verify this conclusion, an additional 15 human heart and 15 skeletal muscle samples from GTEx were added and the analysis was repeated with N=25. The results for n<10 obtained with N=25 gave similar mean and distribution of the number of DEGs identified as those obtained with N=10, validating the utility of the statistical subsampling approach. The rest of this vignette will further explore ERSSAâ€™s functionalities using the 10-replicate GTEx heart vs.Â muscle dataset. We will also briefly go through two additional examples that help to illustrate the variety of experimental settings where ERSSA can be applied.