When the sample size is small or the expression levels of a gene are highly dispersed, the NB regression shows inflated Type-I error rates but the Classical logistic and Bayes logistic (BL) regressions are conservative. Firth’s logistic (FL) regression performs well or is slightly conservative. Large sample size and low dispersion generally make Type-I error rates of all methods close to nominal alpha levels of 0.05 and 0.01. However, Type-I error rates are controlled after applying the data adaptive method. The NB, BL, and FL regressions gain increased power with large sample size, large log2 fold-change, and low dispersion. The FL regression has comparable power to NB regression.

**Empirical power of covariate models**

*Empirical power of covariate models from balanced design with N _{ D=1 } = 10 and μ _{ D=0 } = 1000. The power of Negative Binomial with true dispersion (NB), and Firth’s Logistic (FL) regressions at significance level 0.05 and 0.01 is shown in the figure. Black dotted horizontal lines represent 95 and 90% power. The odds ratios between covariates and case–control status (CovOR = 1.2 and 5) are partitioned by vertical black dotted lines. The number covariates (0, 1, 2, 3, 5 (, and 10)) in the model are positioned within each CovOR. Dotted lines within each symbol represent the 95% confidence interval. a Balanced design from N _{ D=1 } = 10, μ _{ D=0 } = 1000, dispersion = 0.01, and log2fc = 0.3. b Balanced design of N _{ D=1 } = 25, μ _{ D=0 } = 1000, dispersion = 1, and log2fc = 2*

The researchers conclude that implementing the data adaptive method appropriately controls Type-I error rates in RNA-Seq analysis. Firth’s logistic regression provides a concise statistical inference process and reduces spurious associations from inaccurately estimated dispersion parameters in the negative binomial framework.

Choi SH, Labadorf AT, Myers RH, Lunetta KL, Dupuis J, DeStefano AL. (2017) **Evaluation of logistic regression models and effect of covariates for case-control study in RNA-Seq analysis**. *BMC Bioinformatics* 18(1):91. [article]

Power calculation is a critical component of RNA-seq experimental design. The flexibility of RNA-seq experiment and the wide dynamic range of transcription it measures make it an attractive technology for whole transcriptome analysis. These features, in addition to the high dimensionality of RNA-seq data, bring complexity in experimental design, making an analytical power calculation no longer realistic.

Classical power calculation that deals with a single hypothesis takes a few simple assumptions. These include:

- the effect size, representing the minimum difference that is scientiﬁcally meaningful between groups in comparison;
- within-group variation, representing natural variation in observations regardless of between-group difference;
- an acceptable type I error rate, usually in the form of p-value; and
- the sample size.

With these values set, one can calculate statistical power, the probability of rejecting the null hypothesis when the effect is as large as assumed. If a certain power level is desired, one can also do a reverse calculation to determine the minimum sample size to achieve the desired power while controlling the type I error rate.

In DE analysis for RNA-seq experiments, we consider similar factors with more complexity since it is a high throughput experiment querying all transcripts simultaneously, and these transcripts are not exchangeable (read more…)

**Comprehensive visualization of stratified power, generated by the function plotAll**

**Availability** – PROspective Power Evaluation for RNAseq (PROPER) is avialable at: https://www.bioconductor.org/packages/release/bioc/html/PROPER.html

Wu Z, Wu H (2016) **Experimental Design and Power Calculation for RNA-seq Experiments**. *Methods Mol Bi*ol 1418:379-90. [abstract]

It is crucial for researchers to optimize RNA-seq experimental designs for differential expression detection. Currently, the field lacks general methods to estimate power and sample size for RNA-Seq in complex experimental designs, under the assumption of the negative binomial distribution.

Researchers at the University of Hawaii Cancer Center simulate RNA-Seq count data based on parameters estimated from six widely different public data sets (including cell line comparison, tissue comparison, and cancer data sets) and calculate the statistical power in paired and unpaired sample experiments. They comprehensively compare five differential expression analysis packages (DESeq, edgeR, DESeq2, sSeq, and EBSeq) and evaluate their performance by power, receiver operator characteristic (ROC) curves, and other metrics including areas under the curve (AUC), Matthews correlation coefficient (MCC), and F-measures. DESeq2 and edgeR tend to give the best performance in general. Increasing sample size or sequencing depth increases power; however, increasing sample size is more potent than sequencing depth to increase power, especially when the sequencing depth reaches 20 million reads. Long intergenic noncoding RNAs (lincRNA) yields lower power relative to the protein coding mRNAs, given their lower expression level in the same RNA-Seq experiment. On the other hand, paired-sample RNA-Seq significantly enhances the statistical power, confirming the importance of considering the multifactor experimental design. Finally, a local optimal power is achievable for a given budget constraint, and the dominant contributing factor is sample size rather than the sequencing depth.

**Availability** – the authors provide a power analysis tool (http://www2.hawaii.edu/~lgarmire/RNASeqPowerCalculator.htm) that captures the dispersion in the data and can serve as a practical reference under the budget constraint of RNA-Seq experiments.

Ching T1, Huang S1, Garmire LX2. (2014) **Power analysis and sample size estimation for RNA-Seq differential expression**. *RNA* [Epub ahead of print]. [abstract]