experimental-design-sample-size

name	experimental-design-sample-size
description	Estimates the minimum biological replicates (or cells/events) for a target power at a target FDR in genomics experiments using ssizeRNA, PROPER, powsimR for scRNA-seq, and pilot-data dispersion estimation from DESeq2/edgeR. Covers the biological-versus-technical replication distinction (technical replicates do not add degrees of freedom for biological inference), replicate-number-versus-sequencing-depth budgeting, scRNA-seq sample-versus-cell allocation under a pseudobulk model, and the critique that "n=3" is a publication convention rather than a power calculation. Use when budgeting a sequencing experiment, writing the sample-size justification in a grant, estimating replicates from pilot data, allocating a fixed budget between samples and depth, or planning scRNA-seq cohort size. For clinical-trial sample size see clinical-biostatistics/power-and-sample-size; for the power-given-n direction see experimental-design/power-analysis.
tool_type	r
primary_tool	ssizeRNA

Version Compatibility

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

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: ssizeRNA provides ssizeRNA_single() (one mean/dispersion for all genes), ssizeRNA_vary() (genes vary), and check.power() (average power and true FDR for a given n); powsimR is GitHub-only with drifting signatures. Verify against the installed help before use.

Sample Size for Genomics Experiments

"How many samples do I need?" -> Find the smallest number of biological replicates per group that achieves a target marginal power at a target FDR, given the dispersion and effect-size distribution expected for the assay — counting biological units, not measurements.

• R: ssizeRNA::ssizeRNA_vary(), ssizeRNA::check.power() — FDR-aware NB sample size; pilot dispersions from DESeq2/edgeR

The Single Most Important Modern Insight -- The Biological Replicate Is the Unit, and n=3 Is a Convention

Sample size is a count of biological replicates — independent experimental units (animals, donors, cultures from independent passages), not measurements. Technical replicates (one library split across lanes, one RNA split into preps) reduce measurement noise but add no degrees of freedom for biological inference; averaging them into their biological unit is correct, and selling "n = 3 samples x 3 technical reps = 9" as biological power is a standard error (Blainey, Krzywinski & Altman 2014 Nat Methods 11:879). The ubiquitous "n=3" is a publication convention, not a calculation: in the 48-vs-48 yeast benchmark, >=6 biological replicates were needed to recover most true DE genes at realistic effect sizes, and below that the choice of DE tool mattered more than at higher n (Schurch 2016 RNA 22:839). Human and primary material, with higher dispersion, need more. For single-cell, the corollary is sharp: population-level DE power is set by the number of donors, not the number of cells, because cells are pseudoreplicates — pseudobulk per donor is the correct unit (Squair 2021 Nat Commun 12:5692; Murphy & Skene 2022 Nat Commun 13:7851).

Algorithmic Taxonomy

Approach	Model	Tool	Strength	Fails / costs when
FDR-aware NB sample size	NB, varying mean/dispersion	ssizeRNA::ssizeRNA_vary	controls average power at a true FDR	needs a dispersion/expression model
Pilot-dispersion simulation	empirical dispersions from pilot	PROPER, powsimR	most defensible; study-specific	requires a pilot dataset
Single-parameter NB	one mean/dispersion for all genes	ssizeRNA::ssizeRNA_single	quick; transparent	ignores the mean-dispersion trend
Verify a planned n	average power + true FDR at fixed n	ssizeRNA::check.power	sanity-checks a budget-driven n	not a search over n
scRNA-seq cohort sizing	pseudobulk over donors	powsimR	counts the right unit (donors)	cell-level sizing is wrong unit
Per-feature t-test n	Gaussian (Cohen's d)	pwr::pwr.t.test	proteomics/continuous after transform	wrong for raw counts

Decision Tree by Scenario

Scenario	Recommended approach	Why
Bulk RNA-seq, pilot available	estimate dispersions, then ssizeRNA_vary/PROPER	study-specific dispersion beats a guess
Bulk RNA-seq, no pilot	ssizeRNA_vary with a literature dispersion, stated as approximate	transparent starting point
Budget already fixed at some n	check.power to report achieved power and true FDR	answers "is this n adequate?"
scRNA-seq disease vs control	size the number of DONORS (pseudobulk; powsimR)	population power scales with donors
ChIP/ATAC/methylation	NB sample size per region; assay floor as minimum	overdispersed counts; detection floor
Proteomics (continuous)	pwr::pwr.t.test per protein, with missingness caveat	Gaussian after transform
Have technical replicates	collapse to biological units first	technical reps add no biological df
Clinical-trial endpoint	-> clinical-biostatistics/power-and-sample-size	regulated regime

FDR-Aware NB Sample Size -- ssizeRNA

Goal: Find the minimum biological replicates per group for a target power at a target FDR, accounting for the proportion of DE genes and the mean-dispersion structure.

Approach: Specify the number of genes, the proportion non-DE (pi0), the mean count and dispersion (ideally from pilot data), the fold change, the target FDR, and the target power; let ssizeRNA_vary search replicate numbers and return the smallest that reaches the target.

library(ssizeRNA)
res <- ssizeRNA_vary(nGenes = 20000, pi0 = 0.95,        # 5% DE
                     mu = 10, disp = 0.2,                # mean count + dispersion (from pilot ideally)
                     fc = 1.5, fdr = 0.05, power = 0.80,
                     maxN = 30)
res$ssize                                                # minimum n per group

# Verify a budget-fixed n: average power and TRUE realized FDR
check.power(nGenes = 20000, pi0 = 0.95, m = 6, mu = 10, disp = 0.2, fc = 1.5, fdr = 0.05, sims  

Pilot Dispersions Drive Honest Sample Size

Goal: Replace a guessed CV with a measured dispersion-mean trend from pilot data.

Approach: Fit dispersions on the pilot with DESeq2 or edgeR, summarize them, and feed them into the simulation-based estimator (PROPER or powsimR) rather than a single-CV closed form.

library(DESeq2)
dds <- DESeqDataSetFromMatrix(pilot_counts, pilot_coldata, ~ condition)
dds <- DESeq(dds)
disp <- dispersions(dds)                                 # per-gene dispersion estimates
summary(disp[is.finite(disp)])                           # feed median/trend to PROPER/powsimR
# A literature CV can be off by ~2x; a pilot dispersion is the defensible input.

Biological vs Technical Replication

Technical replicates estimate measurement variance; biological replicates estimate the variance that generalizes to the population, and only the latter supports inference about the biology. Average or sum technical replicates into their biological unit before any test. "n = 3 samples x 3 technical reps" is n = 3, not n = 9 (Blainey 2014). This is the sample-size face of the experimental-unit principle (see experimental-design/randomization-blocking).

Replicates vs Depth Under a Fixed Budget

Once depth is adequate (roughly >=10-20M mapped reads for bulk RNA-seq DE), additional biological replicates buy more power than additional depth (Liu 2014 Bioinformatics 30:301). Allocate a fixed budget toward more biological units first. scRNA-seq has an analogous rule at the donor level: more donors beat more cells per donor for population DE, with cells per cell type showing diminishing returns past a few hundred (Squair 2021; Murphy-Skene 2022).

Sample Size by Assay (floors under favorable conditions, not targets)

Assay	Practical minimum	For small effects	Source / note
Bulk RNA-seq	3 (convention)	6-12	Schurch 2016 RNA 22:839: >=6 recovers most true DE
scRNA-seq (population DE)	3 donors	6+ donors	Squair 2021; donors, not cells, drive power
ATAC-seq	2	4-6	library complexity + peak detection floor
ChIP-seq	2	3-4	IDR reproducibility framework (ENCODE)
Proteomics (DIA/TMT)	3	6-10	higher missingness; MNAR
Methylation (array/WGBS)	4	8-12	high per-CpG variance

The "minimum" columns are floors that assume low dispersion and large effects; treat them as the smallest defensible n only after a pilot or literature dispersion supports them.

Per-Method Failure Modes

Technical replicates counted as biological n

• Trigger: "n = 9: 3 samples x 3 technical reps."
• Mechanism: technical reps add no biological degrees of freedom (Blainey 2014).
• Symptom: over-stated power; results do not generalize.
• Fix: collapse technical reps to the biological unit; biological n = 3.

n=3 by convention

• Trigger: choosing 3 because "everyone uses 3."
• Mechanism: 3 is a habit, not a calculation; misses many true DE (Schurch 2016).
• Symptom: chronic underpowering, irreproducibility.
• Fix: size from dispersion + target FDR; expect >=6 for realistic effects, more for human material.

scRNA-seq sized on cells

• Trigger: "100k cells from 2 donors is plenty."
• Mechanism: population power scales with donors; cells are pseudoreplicates (Squair 2021).
• Symptom: false-discovery-laden DE that does not replicate.
• Fix: budget for more donors; size on a pseudobulk model.

Guessed CV instead of pilot dispersion

• Trigger: "human samples are ~0.4, so use 0.4."
• Mechanism: real dispersion is study-specific; the guess can be off ~2x.
• Symptom: the planned n is wrong by a large factor.
• Fix: estimate dispersion from any available pilot (DESeq2/edgeR).

Quantitative Thresholds

Threshold	Source	Rationale
>=6 biological replicates for bulk RNA-seq DE	Schurch 2016 RNA 22:839	recovers most true DE at realistic effects
n=3 is a convention, not a calculation	Schurch 2016	low power and tool-dependent below 6
Donors, not cells, set scRNA-seq DE power	Squair 2021 Nat Commun 12:5692	cells are pseudoreplicates
Technical reps add 0 biological df	Blainey 2014 Nat Methods 11:879	only biological reps generalize
Depth saturates ~10-20M reads; add replicates	Liu 2014 Bioinformatics 30:301	biological variance dominates
Add 10-20% extra units for failures	common practice	RNA degradation, failed libraries

Common Errors

Error / symptom	Cause	Solution
Over-stated power	technical reps counted as n	collapse to biological units
Underpowered at n=3	convention not calculation	size to >=6 (or pilot-driven)
scRNA-seq DE does not replicate	sized on cells	size on donors (pseudobulk)
Planned n off by a large factor	guessed CV	estimate dispersion from pilot
Study fails after sample loss	no failure margin	add 10-20% extra units

Anticipated Reviewer Pushback

Pushback	Response
"Why this n?"	smallest n reaching marginal power >= 0.8 at FDR 0.05 for the minimum meaningful FC; power curve provided
"Where did dispersion come from?"	estimated from pilot (DESeq2); literature value used only as a cross-check
"Is n=3 enough?"	no; sized to >=6 per Schurch 2016 for realistic effects
"Why so many donors for scRNA-seq?"	population DE power scales with donors, not cells (Squair 2021)
"Technical replicates?"	collapsed to biological units; they add no biological degrees of freedom

References

• Bi R, Liu P. 2016. Sample size calculation while controlling false discovery rate for differential expression analysis with RNA-sequencing experiments. BMC Bioinformatics 17:146.
• 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.
• Blainey P, Krzywinski M, Altman N. 2014. Points of significance: replication. Nat Methods 11:879-880.
• Liu Y, Zhou J, White KP. 2014. RNA-seq differential expression studies: more sequence or more replication? Bioinformatics 30:301-304.
• Squair JW, Gautier M, Kathe C, et al. 2021. Confronting false discoveries in single-cell differential expression. Nat Commun 12:5692.
• Murphy AE, Skene NG. 2022. A balanced measure shows superior performance of pseudobulk methods in single-cell RNA-sequencing analysis. Nat Commun 13:7851.
• 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.

Related Skills

• power-analysis - The power-given-n direction and simulation-based power
• randomization-blocking - The experimental unit defines what is counted as a replicate
• batch-design - Balanced designs assume equal n per group
• differential-expression/deseq2-basics - Estimating pilot dispersions for the sample-size model
• single-cell/preprocessing - Pseudobulk aggregation underlying scRNA-seq cohort sizing
• clinical-biostatistics/power-and-sample-size - Sample size for regulated clinical trials