1. A Correlated Random Effects Hurdle Model for Detecting Differentially Expressed Genes in Discrete Single Cell RNA Sequencing Data
Michael Sekula
Department of Bioinformatics and Biostatistics
University of Louisville
JSM: July 30th, 2018
Advisors: Dr. Susmita Datta and Dr. Jeremy Gaskins

2. Overview Motivation Proposed Method
Hurdle Model with Correlated Random Effects
Detecting Differentially Expressed (DE) Genes
Results
Conclusions

3. Motivation

4. Differential Expression
Old question on new data
Bulk RNA-sequencing (RNA-seq)
Averaged gene expression levels
Single cell RNA-sequencing (scRNA-seq)
Expressions from individual cells
Abundance of zeros
Cell-to-cell variability

5. Proposed Method
Hurdle model with correlated random effects

6. Logistic Regression Truncated Negative Binomial Regression
Hurdle Model
𝑌 𝑔𝑖 = expression count for gene 𝑔 in cell 𝑖
𝑍 𝑔𝑖 = indicator of expression for gene 𝑔 in cell 𝑖
( 𝑍 𝑔𝑖 =1 when 𝑌 𝑔𝑖 >0)
Logistic Regression Truncated Negative Binomial Regression
𝑙𝑜𝑔𝑖𝑡 𝜃 𝑔𝑖 = 𝛽 0𝑔 𝐿 +𝑋 𝑖 𝜷 𝒈 𝑳 + 𝜔 𝑖 𝜁 𝑔 𝐿
𝜃 𝑔𝑖 =𝑃( 𝑍 𝑔𝑖 = 1)
𝑙𝑜𝑔 𝜇 𝑔𝑖 = 𝛽 0𝑔 𝐶 +𝑋 𝑖 𝜷 𝒈 𝑪 + 𝜔 𝑖 𝜁 𝑔 𝐶

7. Correlated Random Effects

8. Correlated Random Effects
Create initial rough clustering of cells
𝐾 0 subpopulations in control group
𝐾 1 subpopulations in treatment group

9. Correlated Random Effects
𝜔 𝑖 = 𝛾 𝑡, 𝑘 𝑡 (𝑖) + 𝜔 𝑖 ∗ 𝛾 𝑡,𝑘 ~ 𝑖.𝑖.𝑑. 𝑁𝑜𝑟𝑚𝑎𝑙(0, 𝜎 𝑡 2 ) 𝜔 𝑖 ∗ ~ 𝑖.𝑖.𝑑. 𝑁𝑜𝑟𝑚𝑎𝑙(0, 𝜎 ∗ 2 ) Correlation between cells within same subpopulation of treatment t
𝜌 𝑡 = 𝜎 𝑡 2 𝜎 𝑡 2 + 𝜎 ∗ 2

10. Proposed Method
Detecting differentially expressed (DE) genes

11. Parameter Estimation Bayesian approach
Markov Chain Monte Carlo (MCMC) sampling
Natural choice
SLOW!

12. Parameter Estimation Bayesian approach
Markov Chain Monte Carlo (MCMC) sampling
Natural choice
SLOW!
Automatic differentiation variational inference* (ADVI)
Variational Bayes method implemented in STAN
Faster alternative
Obtain samples from the approximate posterior distribution
* Kucukelbir et al., 2015

13. DE Method 𝑊 𝑔 = 𝑩 𝒈 𝑻 𝑽 𝒈 −𝟏 𝑩 𝒈 → 𝜒 2 (2)
Evaluate posterior estimates of 𝛽 1𝑔 𝐿 and 𝛽 1𝑔 𝐶
Coefficients of treatment indicator (treatment vs. control)
Under frequentist null hypothesis: 𝛽 1𝑔 𝐿 =0 and 𝛽 1𝑔 𝐶 =0
𝑊 𝑔 = 𝑩 𝒈 𝑻 𝑽 𝒈 −𝟏 𝑩 𝒈 → 𝜒 2 (2)

14. Data Analysis Results

15. Hurdle model simulation
TPR
FPR
FDR
AUC
DE Genes
CRE, SC3
0.682
0.010
0.046
0.958
1548
CRE, SNN-Cliq
0.009
0.045
0.959
1547
CRE, TRUE
0.047
1551
IRE
0.686
0.011
0.050
1564
NRE
0.669
0.019
0.086
0.947
1591
MAST
0.594
0.007
0.038
0.948
1337
SCDE
0.126
0.094
0.200
0.646
974
DESeq2
0.402
0.058
0.321
0.777
1304
edgeR
0.396
0.073
0.377
0.764
1400
Splat* simulation
0.475
0.006
0.051
0.924
576
0.052
0.923
0.501
0.008
0.063
615
0.404
0.910
497
0.220
0.002
0.032
0.879
264
0.238
0.030
0.905
274
0.601
0.042
0.215
0.887
892
0.740
0.076
0.297
0.911
1219
* Zappia et al., Genome Biology, 2017

16. Islam et al., Genome Research, 2011

17. Top 500 DE genes from MEC dataset
CRE
MAST
SCDE
DESeq2
edgeR
Key
FC(+)
PZ (-)
FC(+)
PZ (+)
FC(-)
PZ (-)
FC(-)
PZ (-)
Top 500 DE genes from MEC dataset

18. Conclusions

19. Final Thoughts Identify high number of DE genes
Outperform current methods across most performance measures (simulation studies)
Identify high number of DE genes
More DE genes than other scRNA-seq methods
Maintain FDR

20. THANK YOU!

21. References
Islam, S., Kjällquist, U., Moliner, A., Zajac, P., Fan, J. B., Lönnerberg, P., & Linnarsson, S. (2011). Characterization of the single-cell transcriptional landscape by highly multiplex RNA-seq. Genome research, 21(7),
Kucukelbir, A., Ranganath, R., Gelman, A., & Blei, D. (2015). Automatic variational inference in Stan. In Advances in neural information processing systems (pp ).
Zappia, L., Phipson, B., and Oshlack, A. (2017). Splatter: Simulation of Single-Cell RNA Sequencing Data. Genome biology, 18(1), 174.