Cited by 108Single-cell and spatial transcriptomicsGene expression and cancer classificationGenomics and Phylogenetic Studies

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scPower accelerates and optimizes the design of multi-sample single cell transcriptomic studies

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Published version of a preprint

Abstract

Single cell RNA-seq has revolutionized transcriptomics by providing cell type resolution for differential gene expression and expression quantitative trait loci (eQTL) analyses. However, efficient power analysis methods for single cell data and inter-individual comparisons are lacking. Here, we present scPower; a statistical framework for the design and power analysis of multi-sample single cell transcriptomic experiments. We modelled the relationship between sample size, the number of cells per individual, sequencing depth, and the power of detecting differentially expressed genes within cell types. We systematically evaluated these optimal parameter combinations for several single cell profiling platforms, and generated broad recommendations. In general, shallow sequencing of high numbers of cells leads to higher overall power than deep sequencing of fewer cells. The model, including priors, is implemented as an R package and is accessible as a web tool. scPower is a highly customizable tool that experimentalists can use to quickly compare a multitude of experimental designs and optimize for a limited budget.

Overview

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TL;DR

scPower is an analytic power-analysis framework for designing multi-sample single-cell transcriptomic experiments analyzed with pseudobulk, modeling sample size, cells per individual, and read depth to detect DEGs/eQTLs and rare cell types. It is implemented as an R package and web tool and is orders of magnitude faster than simulation-based methods.

Key findings

  • Shallow sequencing of high numbers of cells generally yields higher overall power than deep sequencing of fewer cells; the number of cells per individual is a major determinant of power.
  • Predicted and observed numbers of expressed genes were highly correlated (all r² > 0.9 in training and independent PBMC validation; r² = 0.995 for Drop-seq and r² = 0.991 for Smart-seq2).
  • Example maximum overall detection power was 74% for DE genes (iCLL vs mCLL priors; 3000 cells per cell type and individual, total balanced sample size 20, FDR-adjusted) and 64% for eQTL genes (200 individuals, 3000 cells per cell type and individual; Blueprint T cell priors).
  • Runtime and memory were much lower than simulations: Fig. 3c–e took 8 days for powsimR, 3 days for muscat, and less than a minute for scPower; 20 samples with 3000 cells per sample used 48 GB for powsimR and 35 GB for muscat versus few MB for scPower. Budget examples found optimal DE parameters of 1200 cells in 4 samples at 30,000 reads for 10,000€, and optimal eQTL parameters of 1500 cells in 242 samples at 10,000 reads for 30,000€.

Methods

  • Analytic framework for pseudobulk multi-sample comparisons: models expression probability using negative binomial and gamma-mixture priors, and DE/eQTL power using negative binomial regression and linear models/F-tests with FDR or FWER adjustment.
  • Priors were derived from single-cell atlases: 10X PBMC training data from 14 healthy individuals, an independent PBMC validation set, Drop-seq lung data, and Smart-seq2 pancreas data; effect sizes came from FACS-sorted bulk RNA-seq DEG and eQTL studies.
  • Benchmarked against powsimR and muscat simulations and a self-implemented eQTL simulation; cost optimization evaluated sample size, cells per sample, and read depth under fixed budgets.

Limitations

  • Stated: data-driven priors reliably assess power only for sample sizes smaller than or roughly equal to the pilot data; larger samples may identify new significant DEGs with lower effect sizes not included in the priors. Priors affect the optimal design and should be selected carefully.
  • Stated: the pseudobulk approach requires a discrete cell type definition, so continuous annotations such as pseudotime would need discretization. The default doublet rate is a lower bound, and actual experiments may have higher doublet rates and fewer usable cells; expression threshold choice also influences optimal parameters.
  • Stated: recommendations are optimized for differential expression between individuals; other applications such as co-expression analysis, rare cell type annotation, and variance QTL detection may have different optimal designs, and variance QTLs were not addressed due to lack of data-driven priors.

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Crossref · 10.1038/s41467-021-26779-7

Cites

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Figures

Fig. 1 Dependence of experimental design parameters. The cost determining factors (purple: number of samples, number of cells per sample and number of reads per cell) affect the overall detection power through the expression probability and the DE/eQTL power (blue). In addition, the power depends on prior knowledge or assumptions (green) as well as user-defined parameters such as the significance threshold and the expression cutoff (grey). Our model enables fast power calculation, independent of the chosen experimental parameters, and easy adaptation to different use-cases through reference priors.
Fig. 1 Dependence of experimental design parameters. The cost determining factors (purple: number of samples, number of cells per sample and number of reads per cell) affect the overall detection power through the expression probability and the DE/eQTL power (blue). In addition, the power depends on prior knowledge or assumptions (green) as well as user-defined parameters such as the significance threshold and the expression cutoff (grey). Our model enables fast power calculation, independent of the chosen experimental parameters, and easy adaptation to different use-cases through reference priors.CC BY · PubMed Central
Fig. 2 Expression probability model parameterized by UMI counts per cell. a The expression probabilities for genes in pseudobulk of a newly planned experiment are estimated based on the expression prior and the planned experimental parameters. For this, the expression prior is derived from the mean and dispersion parameters of gene-wise negative binomial distributions fitted from a matching pilot data set. b Using this approach, the number of expressed genes expected under our model (dashed line) closely matches the observed number of expressed genes (solid line) dependent on the number of cells per cell type (cell type indicated by point symbol) for one batch of the training PBMC data set (Supplementary Table S2). The data is subsampled to different read depths (indicated by colour). The r2 values between estimated and expressed genes were highly significant for both expression thresholds. c The model performed similarly well for the three batches of an independent validation PBMC data set47. Used expression threshold: count > 10 (right panels of b, c) or count > 0 (left panels of b, c) in more than 50% of the individuals.
Fig. 2 Expression probability model parameterized by UMI counts per cell. a The expression probabilities for genes in pseudobulk of a newly planned experiment are estimated based on the expression prior and the planned experimental parameters. For this, the expression prior is derived from the mean and dispersion parameters of gene-wise negative binomial distributions fitted from a matching pilot data set. b Using this approach, the number of expressed genes expected under our model (dashed line) closely matches the observed number of expressed genes (solid line) dependent on the number of cells per cell type (cell type indicated by point symbol) for one batch of the training PBMC data set (Supplementary Table S2). The data is subsampled to different read depths (indicated by colour). The r2 values between estimated and expressed genes were highly significant for both expression thresholds. c The model performed similarly well for the three batches of an independent validation PBMC data set47. Used expression threshold: count > 10 (right panels of b, c) or count > 0 (left panels of b, c) in more than 50% of the individuals.CC BY · PubMed Central
Fig. 3 Expression probability, DE/eQTL power and overall detection power and their validation in simulation studies. Power estimation using data driven priors for DE genes (a) and eQTL genes (b) dependent on the total sample size and the number of measured cells per cell type. The detection power is the product of the expression probability and the power to detect the genes as DE or eQTL genes, respectively. The fold change for DEGs and the R2 for eQTL genes were taken from published studies, together with the expression rank of the genes. For (a), the Blueprint CLL study with comparison iCLL vs mCLL was used, for (b), the Blueprint T cell study. The expression profile and expression probabilities in a single cell experiment with a specific number of samples and measured cells was estimated using our expression prior, setting the definition for expressed to > 10 counts in more than 50% of the individuals. Multiple testing correction was performed by using FDR adjusted p values for DE power and FWER adjusted p values for eQTL power. The probabilities calculated in (a) were verified by the simulation-based methods powsimR and muscat with each point representing one parameter combination. f The eQTL power of (b) could be replicated with a self-implemented simulation. Runtime (g) and memory requirements (h) were drastically higher in the simulations than for our tool scPower during the evaluations of (c–e), showing the strength of our analytic model.
Fig. 3 Expression probability, DE/eQTL power and overall detection power and their validation in simulation studies. Power estimation using data driven priors for DE genes (a) and eQTL genes (b) dependent on the total sample size and the number of measured cells per cell type. The detection power is the product of the expression probability and the power to detect the genes as DE or eQTL genes, respectively. The fold change for DEGs and the R2 for eQTL genes were taken from published studies, together with the expression rank of the genes. For (a), the Blueprint CLL study with comparison iCLL vs mCLL was used, for (b), the Blueprint T cell study. The expression profile and expression probabilities in a single cell experiment with a specific number of samples and measured cells was estimated using our expression prior, setting the definition for expressed to > 10 counts in more than 50% of the individuals. Multiple testing correction was performed by using FDR adjusted p values for DE power and FWER adjusted p values for eQTL power. The probabilities calculated in (a) were verified by the simulation-based methods powsimR and muscat with each point representing one parameter combination. f The eQTL power of (b) could be replicated with a self-implemented simulation. Runtime (g) and memory requirements (h) were drastically higher in the simulations than for our tool scPower during the evaluations of (c–e), showing the strength of our analytic model.CC BY · PubMed Central
Fig. 4 Parameter optimization for constant budget. Maximizing detection power by selecting the best combination of cells per individual and read depth for a DE study with a budget of 10,000€ (a) and an eQTL study with a budget of 30,000€ (b). Sample size is uniquely defined given the other two parameters due to the budget restriction and visualized using the point size. c–f Overall detection power dependent on cost determining factors. Influence of the cells per individual given the optimized read depth (c, e) and of the read depth given the optimized number of cells per individual (d, f). Corresponds to the DE study in (a), visualized in (a) by the red frame around the row with the optimal number of cells (corresponding to (c)) and the red frame around the column with the optimal read depth (corresponding to (d)). Same frames for (e, f) in the eQTL study (b). The optimal sample size values are shown in the upper x axes for (c–f). Vertical line in the subplots marks the optimal parameter combination. Effect sizes were chosen as in Fig. 3. Gene expression is defined as detected in >50% (DE analysis) or >9.5% (eQTL analysis) of individuals.
Fig. 4 Parameter optimization for constant budget. Maximizing detection power by selecting the best combination of cells per individual and read depth for a DE study with a budget of 10,000€ (a) and an eQTL study with a budget of 30,000€ (b). Sample size is uniquely defined given the other two parameters due to the budget restriction and visualized using the point size. c–f Overall detection power dependent on cost determining factors. Influence of the cells per individual given the optimized read depth (c, e) and of the read depth given the optimized number of cells per individual (d, f). Corresponds to the DE study in (a), visualized in (a) by the red frame around the row with the optimal number of cells (corresponding to (c)) and the red frame around the column with the optimal read depth (corresponding to (d)). Same frames for (e, f) in the eQTL study (b). The optimal sample size values are shown in the upper x axes for (c–f). Vertical line in the subplots marks the optimal parameter combination. Effect sizes were chosen as in Fig. 3. Gene expression is defined as detected in >50% (DE analysis) or >9.5% (eQTL analysis) of individuals.CC BY · PubMed Central
Fig. 5 Optimal parameters for varying budgets and 10X Genomics data. The maximal reachable detection power (column 1) and the corresponding optimal parameter combinations (columns 2–4) change depending on the given experimental budget (x-axis). The coloured lines indicate different effect sizes and gene expression rank distributions. Different simulated effect sizes and rank distributions for DEG studies (a) and eQTL studies (b) with models fitted on 10X PBMC data. highES = high effect sizes, lowES = low effect sizes, highRank = high expression ranks and unifRank = uniformly distributed expression ranks (always relative to effect sizes observed in published studies). Effect sizes and rank distributions observed in cell type sorted bulk RNA-seq DEG studies (c) and eQTL studies (d) with model fits analogously to (a, b). Expression thresholds were chosen as for Fig. 4.
Fig. 5 Optimal parameters for varying budgets and 10X Genomics data. The maximal reachable detection power (column 1) and the corresponding optimal parameter combinations (columns 2–4) change depending on the given experimental budget (x-axis). The coloured lines indicate different effect sizes and gene expression rank distributions. Different simulated effect sizes and rank distributions for DEG studies (a) and eQTL studies (b) with models fitted on 10X PBMC data. highES = high effect sizes, lowES = low effect sizes, highRank = high expression ranks and unifRank = uniformly distributed expression ranks (always relative to effect sizes observed in published studies). Effect sizes and rank distributions observed in cell type sorted bulk RNA-seq DEG studies (c) and eQTL studies (d) with model fits analogously to (a, b). Expression thresholds were chosen as for Fig. 4.CC BY · PubMed Central

Verification

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120 of 120
  • The authors state this as an assumption.

    An unconfounded experimental design with batches containing both controls and cases is assumed for batch effect correction.

    “under the assumptions of an unconfounded experimental design with batches containing both controls and cases, batch effects can be removed by adding a batch covariate to the regression model71.”
  • The authors state this as an assumption.

    The counts of each gene in each cell type follow a negative binomial distribution.

    “We assume a negative binomial distribution () for the counts of each gene in each cell type with and .”
  • The authors state this as an assumption.

    The sum of gene counts follows a negative binomial distribution with parameters altered by the number of cells per cell type and donor.

    “The sum of gene counts follows a negative binomial distribution where the parameters are altered by the number of cells per cell type and donor to and .”
  • The authors state this as an assumption.

    The distribution of mean values over all genes in a cell type is a mixture of a zero component and two left-censored gamma distributions.

    “To generalize the expression probability model also for unseen data sets, the distribution of the mean values over all genes in a cell type is modelled as a mixture distribution with three components, a zero component and two left-censored gamma distributions 7”
  • The authors state this as an assumption.

    The relationship between mean UMI counts per cell and the gamma parameters is linear.

    “The relationship between the mean UMI counts per cell and the gamma parameters (mean and standard deviation of the two gamma distributions) is linear and values are estimated by linear regression, fitted over the gamma distribution for each run and all subsampled runs.”
  • The authors state this as an assumption.

    The number of transcriptome mapped reads is linearly related to the logarithm of the mean UMI counts per cell, with increasing read depth leading to saturation of UMIs.

    “The number of transcriptome mapped reads is linearly related to the logarithm of the mean UMI counts per cell, with an increasing read depth leading to a saturation of UMIs.”
  • The authors state this as an assumption.

    The residuals in the eQTL power calculation are i.i.d. normally distributed.

    “This power calculation assumes that the residuals are i.i.d. normally distributed.”
  • The authors state this as an assumption.

    Genotypes are generated according to Hardy-Weinberg equilibrium.

    “A random genotype vector with of length is generated with the expected number of each genotype according to Hardy Weinberg equilibrium.”
  • The authors state this as an assumption.

    Gene expression counts are sampled from a negative binomial distribution parameterized for each genotype.

    “The associated gene expression count vector is sampled from a negative binomial distribution parameterized for each genotype with mean and dispersion .”
  • The authors state this as an assumption.

    Overall detection power is the product of expression probability and power to detect DEGs/eQTLs, as both are conditionally independent given expression mean.

    “The overall detection power for DEGs/eQTLs is the product of the expression probability and power to detect DEGs/eQTLs, as both probabilities are conditionally independent given the expression mean of the gene.”
  • The authors state this as an assumption.

    Nearly all doublets are detectable using Demuxlet and Scrublet and discarded during preprocessing of the data set.

    “We assume that nearly all doublets are detectable using Demuxlet and Scrublet and discarded during the preprocessing of the data set.”
  • The authors state this as an assumption.

    Doublets contain 80% more reads than singlets.

    “Again following the approach of37, we assume that doublets contain 80% more reads than singlets.”
  • The paper relies on this without support.

    No simulation-based power analysis for eQTLs exists (and also no other method).

    “As no simulation-based power analysis for eQTLs exists (and also no other method), we benchmarked the eQTL power with our own simulation tool (described in the methods section Power analysis for expression quantitative trait loci).”
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Metadata

Authors
Schmid, K. T., Höllbacher, B., Cruceanu, C., Böttcher, A., Lickert, H., Binder, E. B., Theis, F. J., & Heinig, M.
Affiliations
  • Helmholtz Munich (DE)
  • Max Planck Institute of Psychiatry (DE)
  • Emory University (US)
Corresponding author
Heinig, Matthias
Venue
Nature Communications
Published
2021-11-16
Volume
12
Issue
1
Pages
6625-6625
ISSN
2041-1723 (ISSN-L)
OpenAlex
W3211534834
Cited by
108
References
110
Citations by year
2026: 19 · 2025: 24 · 2024: 26 · 2023: 13 · 2022: 19 · 2021: 6
FWCI
5.02
Type
journal article
Language
en
Open access
Locations
  • Nature Communications (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
  • Research Square (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
  • PuSH - Publication Server of Helmholtz Zentrum München (submittedVersion, cc-by)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • mediaTUM (Technical University of Munich) (submittedVersion, other-oa)
  • Site cant be reached (submittedVersion, cc-by)
Funders
  • Silicon Valley Community Foundation (182835)
  • Chan Zuckerberg Initiative (182835)
  • Bundesministerium für Bildung und Forschung (01IS18053A, 01IS18036A)
  • Helmholtz Zentrum München
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Single-cell and spatial transcriptomics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Genomics and Phylogenetic Studies
Keywords
single-cell RNA sequencing, statistical power analysis, sample size optimization, sequencing depth, expression quantitative trait loci, R package, web-based tool
MeSH terms
Exome Sequencing, Humans, Research Design, Gene Expression, Sequence Analysis, RNA, Sample Size, Gene Expression Profiling, Quantitative Trait Loci, Single-Cell Analysis, Transcriptome

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