Recent advancements in deep sequencing technique enable the ultra-high-throughput sequencing (called the second- or next- generation sequencing) approaches, to be used for transcriptome, including gene expression, analyses [1–4]. RNA-seq produces a count (the total number of short reads which are annotated to positions within a gene or transcript) for each gene expression level. Some researchers have shown that the count data can be quite reasonably modelled as Poisson distribution [1, 3]. To detect differentially expressed genes (DEGs) under two conditions (e.g., disease vs. healthy status), some statistical methods have been used. For example, Marioni et al [3] have proposed to use likelihood ratio test (LRT) based on a generalized linear model (GLM) with dependent variable (count) having Poisson distribution to detect DEGs under two conditions without biological replicates. Fisher exact test has also been proposed to detect DEGs for RNA-seq data [5, 6]. Some researchers modelled the count data as binomial distribution bin(n,p), where n is the total counts on the same lane, which usually ranges from several millions to tens of millions [7]. However, it is well known that for a binomial distribution bin(n,p) with large n and small p, it can be approximated by Poisson distribution. It is expected that for RNA-seq data methods based on binomial distribution should have similar performance as those methods based on Poisson distribution and therefore are not considered in this paper.

If there are biological replicates, the count data may have larger variances than expected from the Poisson distribution as biological replicates bring extra variances. Under this kind of situations, Poisson distribution with over-dispersed variances or negative binomial distributions are thought to be more appropriate [8, 9]. However, due to the high cost, recent studies rarely used biological replicates; we therefore focus on the situations where at most technical replicates are used and Poisson distribution is assumed to be appropriate.

Besides Fisher exact test and LRT from GLM, several other test approaches in statistical literature have been proposed to detect the difference of two Poisson means. For example, under the null hypothesis that X_{1} and X_{2} are both from Poi(*λ*), then given k = X_{1}+X_{2}, X_{1} has a binomial distribution Bin(k,p), where p = X_{1}/k. Therefore the conditional exact test can be used to detect the difference of the two Poisson means. One of the advantages of the GLM is that it can incorporate some covariates that we are interested in. If no covariates are considered due to the small sample size and large number of genes, the LRT can be constructed directly. Similar to LRT, Wald test also has an asymptotical Chi-square distribution with df = 1 [10–12]. A modified Wald test (Wald-Log) with data being first log-transformed has also been proposed for detecting the difference between two Poisson means [11]. Another method called variance stabilizing transformation (VST) was proposed by Huffman [10, 13].

In this paper, we first compare the above mentioned methods by using simulations. Since for those methods having the same asymptotic distribution, they are expected to have similar performances for large sample sizes (e.g., Poisson distributions with large means), we focus on simulating Poisson distributions with small or moderate means. We then use a real RNA-seq data to show the performances of those methods.