Power analysis

Version Compatibility

Reference examples tested with: RNASeqPower 1.42+, PROPER 1.34+, powsimR 1.2+ (GitHub), DESeq2 1.42+, edgeR 4.0+, pwr 1.3+.

Before using code patterns, verify installed versions match. If versions differ:

• R: packageVersion('<pkg>') then ?function_name to verify parameters

If code throws an error, introspect the installed package and adapt to the actual API. Notes: RNASeqPower::rnapower() solves for whichever of n or power is omitted; PROPER is a multi-step pipeline (RNAseq.SimOptions.2grp -> simRNAseq -> runSims -> comparePower); powsimR is GitHub-only and its estimateParam/Setup/simulateDE signatures drift — pin a commit SHA for reproducible work. Verify each against the installed help before relying on argument names.

Power Analysis for Genomics Experiments

"How many replicates does my sequencing experiment need?" -> Compute the probability of detecting a biologically meaningful effect given replicate number, sequencing depth, and biological variability — modeling counts as negative-binomial and recognizing that power is a per-gene quantity, not one number for the whole transcriptome.

• R: RNASeqPower::rnapower() — closed-form NB power/sample size; PROPER, powsimR — simulation from the mean-dispersion trend

The Single Most Important Modern Insight -- Genomics Power Is Per-Gene; Simulate, and Never Report Observed Power

Power in a sequencing experiment is not a single number. It is a per-gene quantity that depends on that gene's mean expression and dispersion, so the honest summary is the marginal (average) power across the expression distribution at a target FDR — the expected discovery rate. A single coefficient of variation plugged into a closed-form formula mis-states power for low- and high-expressed genes alike, because dispersion varies systematically with the mean; the defensible default for count data is simulation from the empirical mean-dispersion trend (PROPER, Wu 2015 Bioinformatics 31:233; powsimR, Vieth 2017 Bioinformatics 33:3486). The second rule is negative: observed (post-hoc) power is information-free. Computed from the effect a study actually estimated, it is a one-to-one function of the p-value and cannot explain a null result (Hoenig & Heisey 2001 Am Stat 55:19). Power is a design-stage quantity, computed for hypothesized effects before data exist. Underpowering does not merely miss true effects — it makes the significant ones overstate magnitude (Type-M) and sometimes reverse sign (Type-S), lowering the chance a significant call is real (Button 2013 Nat Rev Neurosci 14:365; Gelman & Carlin 2014 Perspect Psychol Sci 9:641).

Algorithmic Taxonomy

Approach	Model	Tool	Strength	Fails / costs when
NB closed-form	negative-binomial, single CV/dispersion	RNASeqPower::rnapower	fast; transparent; grant-ready	one CV cannot represent the mean-dispersion trend
Simulation, parametric	NB with mean-dispersion relationship	PROPER	honest marginal power + EDR at target FDR	needs a dispersion model / pilot
Simulation, empirical	resampled from pilot (incl. dropout)	powsimR	bulk AND scRNA-seq; realistic	GitHub-only; heavier; version drift
Gaussian closed-form	t-test / Cohen's d	pwr::pwr.t.test	per-feature ATAC/proteomics after transform	wrong for raw counts; ignores overdispersion
Effect-inflation design analysis	retrodesign for Type-S/Type-M	retrodesign (Gelman)	exposes exaggeration in noisy small-n	needs a plausible true effect

Decision Tree by Scenario

Scenario	Recommended approach	Why
Bulk RNA-seq, pilot data available	PROPER/powsimR simulation from pilot dispersions	matches the real mean-dispersion trend
Bulk RNA-seq, no pilot, quick grant number	rnapower() with a literature CV, stated as approximate	transparent; flag as conservative-to-rough
scRNA-seq cross-condition DE	powsimR on a pseudobulk model; power scales with samples	population power is set by donors, not cells
ATAC/ChIP/methylation per-region	NB simulation (PROPER-style) or pwr after variance-stabilizing	overdispersed counts; per-region power
Proteomics (continuous, log-abundance)	pwr::pwr.t.test per protein with missingness caveat	Gaussian after transform; MNAR matters
Justifying a null result post-hoc	report CI / effect size, NOT observed power	post-hoc power is uninformative (Hoenig-Heisey)
Fixed budget: depth vs replicates	favor replicates past ~10-20M mapped reads	biological variance dominates (Liu 2014)
Clinical-trial endpoint	-> clinical-biostatistics/power-and-sample-size	regulated regime, different machinery

Closed-Form NB Power -- RNASeqPower

Goal: Get a fast, transparent power or replicate number for bulk RNA-seq from depth, biological CV, and fold change.

Approach: Supply per-gene depth, biological coefficient of variation, the fold change to detect, and alpha; supply n to get power, or power to get the required n. Treat the result as a single-gene approximation and sanity-check against simulation.

library(RNASeqPower)
# depth = reads/gene; cv = biological coefficient of variation; effect = fold change
rnapower(depth = 20, n = 5, cv = 0.4, effect = 2, alpha = 0.05)          # solves for POWER
rnapower(depth = 20, cv = 0.4, effect = 2, alpha = 0.05, power = 0.80)   # solves for n per group

Simulation-Based Power -- the Honest Default for Counts

Goal: Estimate marginal power and the true realized FDR across the whole expression distribution, accounting for the mean-dispersion trend.

Approach: Build (or fit from pilot) a simulation model of counts with a realistic dispersion-mean relationship and DE-effect distribution, simulate many datasets at each candidate sample size, run the intended DE test, and read the average power at the target FDR.

library(PROPER)
sim_opts <- RNAseq.SimOptions.2grp(ngenes = 20000, p.DE = 0.05,
                                   lOD = 'cheung', lBaselineExpr = 'cheung')  # empirical dispersion/expr priors
sims <- runSims(Nreps = c(3, 5, 8, 12), sim.opts = sim_opts, nsims = 50,
                DEmethod = 'edgeR')
powr <- comparePower(sims, alpha.type = 'fdr', alpha.nominal = 0.05,
                     stratify.by = 'expr', delta = log(1.5))          # delta is NATURAL-log lfc in PROPER; marginal power by expression stratum
summaryPower(powr)

Depth vs Replicates -- the Budget Question

For bulk RNA-seq differential expression, sequencing depth shows diminishing returns once it is adequate — Liu, Zhou & White 2014 (Bioinformatics 30:301) found the inflection near ~10 million mapped reads in MCF7 (commonly generalized to a 10-20M band) — whereas adding biological replicates improves power across the whole range. Under a fixed budget, allocate to more biological units before more depth. ATAC/ChIP have their own depth floors (library complexity, peak detection), but the principle holds: biological variance, not read count, limits discovery once depth is adequate.

CV / Dispersion Guidelines (estimate from pilot when possible)

Material	Typical biological CV	Source / note
Cell lines (technical replicates)	0.1-0.2	low biological variability
Inbred mice	0.2-0.3	moderate
Primary cells / donor-derived	0.3-0.4	donor-dependent
Human population samples	0.3-0.5	high; Hart 2013 J Comput Biol 20:970 default examples

These are starting points, not substitutes for a pilot estimate; real dispersion is study-specific and a literature CV can be off by a factor of two (estimate via DESeq2/edgeR estimateDispersions — see experimental-design/sample-size).

Per-Method Failure Modes

Single CV for the whole transcriptome

• Trigger: one cv plugged into rnapower() for all genes.
• Mechanism: dispersion varies with mean expression; a single CV mis-states low/high-expressed genes.
• Symptom: simulation gives materially different power than the closed form.
• Fix: simulation-based power (PROPER/powsimR) from the mean-dispersion trend.

Observed (post-hoc) power

• Trigger: "non-significant, but observed power was 0.3, so add samples."
• Mechanism: observed power is a monotone function of the p-value (Hoenig-Heisey 2001).
• Symptom: circular reasoning that adds nothing to the CI.
• Fix: report effect size + CI; do prospective power for the next study.

Powering to the expected (or pilot-observed) effect

• Trigger: setting the effect to the hoped-for or pilot point estimate.
• Mechanism: the pilot estimate is itself noisy; building it in bakes in the winner's curse.
• Symptom: chronic underpowering; inflated significant effects (Type-M).
• Fix: power to the minimum biologically meaningful effect; propagate pilot variance, not its mean.

Depth instead of replicates

• Trigger: "we will sequence deeper rather than add samples."
• Mechanism: past ~10-20M reads, biological variance dominates technical (Liu 2014).
• Symptom: deep libraries, still underpowered.
• Fix: add biological replicates.

scRNA-seq power computed on cells

• Trigger: "100k cells from 2 patients gives huge power."
• Mechanism: population DE power is set by the number of biological samples; cells are pseudoreplicates.
• Symptom: power estimate wildly optimistic; results do not replicate.
• Fix: power on a pseudobulk model over donors (powsimR); see randomization-blocking.

Quantitative Thresholds

Threshold	Source	Rationale
Power >= 0.80 standard; >= 0.90 for pivotal	convention	tolerable Type-II risk
Depth saturates ~10-20M mapped reads for DE	Liu 2014 Bioinformatics 30:301	biological variance then dominates
>=6 biological replicates recover most true DE	Schurch 2016 RNA 22:839	n=3 misses many true DE at realistic effects
Observed power is a function of the p-value	Hoenig-Heisey 2001 Am Stat 55:19	never use it to interpret a null
Type-M exaggeration large in noisy small-n	Gelman-Carlin 2014 Perspect Psychol Sci 9:641	significant effects overstated

Common Errors

Error / symptom	Cause	Solution
Closed-form and simulation power disagree	single CV vs mean-dispersion trend	use simulation for the reported number
"Underpowered (observed power 0.3)" to excuse a null	post-hoc power fallacy	report CI; prospective power only
Deep libraries still underpowered	depth over replicates	add biological replicates
scRNA-seq power absurdly high	power computed on cells	pseudobulk power over donors
Significant effect far larger than literature	winner's curse from underpowering	design analysis (Type-S/Type-M); replicate

Anticipated Reviewer Pushback

Pushback	Response
"Where did the CV come from?"	estimated from pilot dispersions (DESeq2); literature value used only as a conservative cross-check
"Why simulation rather than a formula?"	count power is per-gene; simulation captures the mean-dispersion trend and reports marginal power at the target FDR
"Is the study powered?"	marginal power >= 0.8 at FDR 0.05 for the minimum meaningful fold change; power curve provided
"Why not just sequence deeper?"	depth saturates ~10-20M reads (Liu 2014); replicates added instead
"Observed power of the null?"	observed power is uninformative (Hoenig-Heisey); CI on the effect reported instead

References

• Hart SN, Therneau TM, Zhang Y, Poland GA, Kocher JP. 2013. Calculating sample size estimates for RNA sequencing data. J Comput Biol 20:970-978.
• Wu H, Wang C, Wu Z. 2015. PROPER: comprehensive power evaluation for differential expression using RNA-seq. Bioinformatics 31:233-241.
• Vieth B, Ziegenhain C, Parekh S, Enard W, Hellmann I. 2017. powsimR: power analysis for bulk and single cell RNA-seq experiments. Bioinformatics 33:3486-3488.
• Liu Y, Zhou J, White KP. 2014. RNA-seq differential expression studies: more sequence or more replication? Bioinformatics 30:301-304.
• Schurch NJ, Schofield P, Gierliński M, et al. 2016. How many biological replicates are needed in an RNA-seq experiment and which differential expression tool should you use? RNA 22:839-851.
• Hoenig JM, Heisey DM. 2001. The abuse of power: the pervasive fallacy of power calculations for data analysis. Am Stat 55:19-24.
• Button KS, Ioannidis JPA, Mokrysz C, Nosek BA, Flint J, Robinson ESJ, Munafò MR. 2013. Power failure: why small sample size undermines the reliability of neuroscience. Nat Rev Neurosci 14:365-376.
• Gelman A, Carlin J. 2014. Beyond power calculations: assessing Type S (sign) and Type M (magnitude) errors. Perspect Psychol Sci 9:641-651.
• Ioannidis JPA. 2005. Why most published research findings are false. PLoS Med 2:e124.

Related Skills

• sample-size - The inverse problem: minimum replicates for a target power at a target FDR
• randomization-blocking - The experimental unit defines what is replicated; blocking changes error variance
• batch-design - Account for batch/blocking factors in the power model
• differential-expression/deseq2-basics - Estimating dispersions from pilot data for the power model
• single-cell/preprocessing - Pseudobulk model underlying scRNA-seq power
• clinical-biostatistics/power-and-sample-size - Power for regulated clinical-trial endpoints