name: bio-experimental-design-power-analysis description: Calculates statistical power for high-dimensional genomics experiments (bulk RNA-seq, scRNA-seq, ATAC-seq, ChIP-seq, methylation, proteomics) under negative-binomial count models using RNASeqPower, PROPER, and simulation via powsimR, distinguishing per-gene from marginal (transcriptome-wide) power, the role of mean expression and dispersion, and the sequencing-depth-versus-replicate tradeoff. Covers simulation as the honest default for overdispersed counts, FDR-aware average power versus single-test power, observed/post-hoc power as an anti-pattern, and the winner's-curse / Type-S / Type-M consequences of underpowering. Use when planning replicate number for a sequencing experiment, deciding whether to add depth or samples, choosing closed-form versus simulation power, estimating power from pilot dispersions, or justifying replication in a grant. For clinical-trial power see clinical-biostatistics/power-and-sample-size; for the inverse sample-size question see experimental-design/sample-size. origin: openai4s category: bioskills/experimental-design metadata: tool_type: r primary_tool: RNASeqPower third_party: name: GPTomics/bioSkills repository: https://github.com/GPTomics/bioSkills commit: d91ed3d563019e649dc854c56ccd62551359488a license: MIT
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.
"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
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).
| 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 |
| 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 |
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
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)
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.
| 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).
cv plugged into rnapower() for all genes.| 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 |
| 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 |
| 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 |