Unlocking RNA-seq tools for zero inflation and single cell applications using observation weights

Transcription

1 Unlocking RNA-seq tools for zero inflation and single cell applications using observation weights Koen Van den Berge, Ghent University Statistical Genomics,

2 The team Koen Van den Berge Fanny Perraudeau Jean-Philippe Vert Charlotte Soneson Mark Robinson Sandrine Dudoit Davide Risso Michael Love Lieven Clement 2

3 single-cell RNA-sequencing (scrna-seq) is noisier than bulk RNA-seq 3

4 Single-cell RNA-seq protocols I Full-length protocols (e.g., SMART-Seq2) I Cells must be isolated (manually, FACS,...). I Library prep is typically plate-based; one well contains one cell. I Droplet-based protocols (e.g., 10X, drop-seq) I Cells do not need to be isolated! I Cell-containing medium is mixed with bead-containing oil droplets. 4

5 single-cell RNA-sequencing (scrna-seq) is noisier than bulk RNA-seq data from [Pickrell et al. 2010, Fletcher et al. 2017, Zheng et al. 2017] 5

6 Bulk RNA-seq di erential expression (DE) analysis Popular methods (edger, DESeq2) adopt negative binomial (NB) models y gi NB(µ gi, g ) log(µ gi ) = gi gi = X i g + log(o i ) with y gi the expression count of gene g in sample i. 6

7 Bulk RNA-seq DE not worse than bespoke scrna-seq tools Jaakkoola et al. (2016), Bioinformatics: Our evaluations did not reveal systematic benefits of the currently available single-cell-specific methods. Soneson & Robinson (2018), Nat. Meth.: We found that bulk RNA-seq analysis methods do not generally perform worse than those developed specifically for scrna-seq. 7

8 Bulk RNA-seq methods still break down due to ZI Simulated (ZI-)bulk RNA-seq data using [Zhou et al. 2014] framework 8

9 Bulk RNA-seq methods still break down due to ZI Simulated (ZI-)bulk RNA-seq data using [Zhou et al. 2014] framework 8

10 Observation weights unlock bulk RNA-seq tools towards zero inflation Excess zeros observed! zero inflation We propose to model counts with a zero inflated negative binomial (ZINB) distribution f ZINB (y gi ; µ gi, g, gi )= gi +(1 gi )f NB (y gi ; µ gi, g ). (1) 9

11 Observation weights unlock bulk RNA-seq tools towards zero inflation Excess zeros observed! zero inflation We propose to model counts with a zero inflated negative binomial (ZINB) distribution f ZINB (y gi ; µ gi, g, gi )= gi +(1 gi )f NB (y gi ; µ gi, g ). (1) A ZINB model corresponds to a weighted NB where observation weights are posterior probabilities w gi = (1 gi)f NB (y gi ; µ gi, g ) f ZINB (y gi ; µ gi, g, gi ) (2) 9

12 Observation weights unlock bulk RNA-seq tools towards zero inflation Excess zeros observed! zero inflation We propose to model counts with a zero inflated negative binomial (ZINB) distribution f ZINB (y gi ; µ gi, g, gi )= gi +(1 gi )f NB (y gi ; µ gi, g ). (1) A ZINB model corresponds to a weighted NB where observation weights are posterior probabilities w gi = (1 gi)f NB (y gi ; µ gi, g ) f ZINB (y gi ; µ gi, g, gi ) (2) Weights are used to unlock RNA-seq NB models (edger, DESeq2) for zero inflation [Van den Berge,Perraudeau et al., 2018]. 9

13 10 zinbwave can be used to fit ZINB models in scrna-seq Estimation of the ZINB parameters using penalized likelihood implemented in the ZINB-WaVE model [Risso et al. 2018] Bioconductor: J genes log μ n samples } Known sample-level covariates Known gene-level covariates M J L J M β L VT + γ Τ = X + Unknown sample-level covariates K J α K W J genes n n n n samples logit π } Observed random variable } Unknown parameter } Unknown parameter } Observed random variable } Unobserved random variable } Unknown parameter X intercept acts as a gene-specific scaling factor V intercept acts as a sample-specific scaling factor

14 10 zinbwave can be used to fit ZINB models in scrna-seq Estimation of the ZINB parameters using penalized likelihood implemented in the ZINB-WaVE model [Risso et al. 2018] Bioconductor: J genes log μ n samples } Known sample-level covariates Known gene-level covariates M J L J M β L VT + γ Τ = X + Unknown sample-level covariates K J α K W J genes n n n n samples logit π } Observed random variable } Unknown parameter } Unknown parameter } Observed random variable } Unobserved random variable } Unknown parameter X intercept acts as a gene-specific scaling factor V intercept acts as a sample-specific scaling factor Alternatively: EM-algorithm (see last couple of slides)

15 Downweighting excess zeros recovers mean-variance trend, resulting in high power Simulated (ZI-)bulk RNA-seq data using [Zhou et al. 2014] framework 11

16 Downweighting excess zeros recovers mean-variance trend, resulting in high power Simulated (ZI-)bulk RNA-seq data using [Zhou et al. 2014] framework 11

17 12 High power, good FDR control in scrna-seq simulations Full-length protocols DESeq2 MAST ZINB-WaVE_DESeq2_common ZINB-WaVE_edgeR_common edger

18 High power, good FDR control in scrna-seq simulations Droplet-based protocols, e.g. 10X Genomics, Drop-seq 13

19 14 Mock comparisons on real data show good FPR control Non-UMI dataset on 622 neuronal cells from [Usoskin et al. 2015]. 45 vs. 45 mock comparisons.

20 15 Downweighting leads to biologically meaningful results 10X Genomics PBMC dataset, preprocessed using tutorial from Seurat.

21 16 Method is implemented in zinbwave Bioc package I computeobservationalweights for weights calculation I edger:glmweightedf for ZI-adjusted inference I DESeq2:nbinomWaldTest and nbinomlrt for ZI-adjusted inference I Tutorial available in zinbwave vignette

22 What follows are some slides on the EM algorithm used in the zinger method. 17

23 18 Azero-inflatednegativebinomialmodel Distribution of counts y for gene g over samples i y gi i +(1 i )f NB (µ gi, g ) i.e. mixture distribution between point-mass at zero and negative binomial Log-likelihood l(y gi )= X i log { i +(1 i )f NB (µ gi, g )} does not factorize! very di cult to maximize!

24 19 Fitting a mixture distribution with EM Estimate mixture using EM-algorithm: introduce latent variable Z gi B( gi ) to assign zeros to the zero-inflation or count component. The joint density becomes f (y gi, z gi )=f (y gi z gi )f (z gi ) =[ i ] z gi [(1 i )f NB (µ gi, g )] (1 z gi )

25 19 Fitting a mixture distribution with EM Estimate mixture using EM-algorithm: introduce latent variable Z gi B( gi ) to assign zeros to the zero-inflation or count component. The joint density becomes f (y gi, z gi )=f(y gi z gi )f (z gi ) =[ i ] z gi [(1 i )f NB (µ gi, g )] (1 z gi ) Maximization of expected log-likelihood given the data: Q = E(l(y gi, z gi ) y gi ) = E(z gi y gi )log i + E(z gi y gi )log +[1 E(z gi y gi )]log(1 i )+ [1 E(z gi y gi )]log[f NB (µ gi, g )] 1. E-step: Calculate expected likelihood 2. M-step: Maximize expected likelihood

26 20 E-step EM-algorithm I Calculate posterior probability that a zero belongs to zero-inflation component ˆ i I (y gi = 0) E(z gi y gi ) = ˆ i I (y gi = 0) + (1 ˆ i )f NB (y gi ;ˆµ gi, ˆg )

27 E-step EM-algorithm I Calculate posterior probability that a zero belongs to zero-inflation component M-step ˆ i I (y gi = 0) E(z gi y gi ) = ˆ i I (y gi = 0) + (1 ˆ i )f NB (y gi ;ˆµ gi, ˆg ) I Estimate NB component parameters µ gi and g using edger I Incorporate observation-level weights wgi =1 E y (z gi )for counts y gi I Because maximizing ZINB likelihood for NB model parameters is equivalent to maximizing a weighted NB likelihood. I Estimate i using logistic regression model i log = N i 1 i with N i log library size of sample i 20

28 Why we use logistic regression with library size in the EM 21

29 22 Case study: Islam et al. (2014) I Single-cell RNA-seq (scrna-seq) allowed the study of sparse cell populations. I One of the first datasets we worked with was from Islam et al. (2014). It demonstrates scrna-seq for 85 cells consisting of two cell populations in mouse: embryonic stem cells and fibroblasts. I This paper was one of the first scrna-seq studies and motivated our method development. I Link to paper: