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<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>Interpreting uncertainty in differential expression with DESeq2</title>
<meta charset="utf-8" />
<meta name="author" content="Martin Modrák Institute of Microbiology of the Czech Academy of Sciences" />
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<textarea id="source">
class: center, middle, inverse, title-slide
.title[
# Interpreting uncertainty in differential expression with DESeq2
]
.author[
### Martin Modrák
Institute of Microbiology of the Czech Academy of Sciences
]
---
class: center, middle, inverse
# Background - Biology
---
background-image: url("img-cc/Pair_of_mandarin_ducks.jpg")
background-position: center
background-size: cover
class: inverse
# Differential expression
.img_credit[
Image by By Francis C. Franklin, Wikimedia Commons CC-BY-SA 3.0
]
---
# Differential expression
.large_fig[
<img src="slides_uni_koeln_files/figure-html/diffexpexample-1.png" width="400px" />
]
---
# DESeq2
$$
`\begin{align}
y_{g,s} &\sim \mathrm{NegBinomial\_2}(\mu_{g,s} r_s, \frac{1}{\tau_g}) \\
\log(\mu_{g,s}) &= \alpha_g + X_s \beta_g \\
\log \tau_g &\sim \mathrm{N} \left(\frac{a}{\mu_{g}} + b, \sigma_\tau \right) \\
\end{align}`
$$
--
Primary output: p-values for interval hypotheses
???
Bunch of other methods to share dispersion
---
class: center, middle, inverse
# Background - Statistics
---
# Why confidence intervals?
DESeq2 does a good job with interval hypothesis
--
We might want to order genes by LFC
--
.mid_fig[
]
---
# Frequentist calibration of CIs
In x% of repetitions of the exact same experiment, x% confidence interval will contain the true value.
???
Assuming the model is correct. Needs to hold for any parameters! -> Worst case, asymptotic results, bounds
---
# The secret frequentists don't want you to know
1) Define likelihood
2) Maximize likelihood
3) ????
4) Profit!
---
# The secret frequentists don't want you to know
1) Define likelihood
2) Maximize likelihood
3) ~~????~~ Compute Hessian
4) ~~Profit!~~ Assume normality
--
5) Publish!
---
# Bayesian calibration
Averaged over the prior, x% credible interval will contain the true value x% of the time.
???
Assuming the model is correct. Can be exact.
---
# Simulation-based calibration
--
1. Simulate data _exactly_ according to the model
--
1. Fit the model to simulated data and draw `\(M\)` samples from the posterior.
--
2. Take the rank of the true value within the samples
- Rank: no. of samples < true value
--
3. Across many simulations, this rank should be uniformly distributed between `\(0\)` and `\(M\)`
---
class: center, middle, inverse
# What I did
---
# Bayesian interpretation of DESeq2
Frequentist models `\(\simeq\)` Bayesian models
--
- Flat priors
- Posterior is normal
???
DESeq2 was intended as Empirical Bayes
Note that this is the same assumption as before!
---
# Priors for the DESeq2 model
$$
`\begin{align}
y_{g,s} &\sim \mathrm{NegBinomial\_2}(\mu_{g,s} r_s, \frac{1}{\tau_g}) \\
\log(\mu_{g,s}) &= \alpha_g + X_s \beta_g \\
\log \tau_g &\sim \mathrm{N} \left(\frac{a}{\mu_{g}} + b, \sigma_\tau \right) \\
\end{align}`
$$
--
$$
\alpha \sim N(4,2);
\beta \sim \mathrm{N}(0,1)
$$
$$
\sigma_\tau \sim \mathrm{HalfN(0, 1)} ; a \sim \Gamma(3, 6) ; b \sim \Gamma(4, 2.3)
$$
???
Note that we are in between estimating dispersion and known dispersion
## Sampling from DESeq2
DESeq2 provides standard error (via Hessian)
1. Use normal approximation
2. Use T approximation with
---
class: center, middle, inverse
# Results
???
Only showing some settings, but results broadly consistent
---
# 3 replicates, default settings
- I.e. using the `apeglm` Student's T shrinkage
.large_fig[
]
---
# 3 replicates, default settings
Coverage of 95% CI: 91%
.large_fig[
]
---
# 3 replicates, no shrinkage
Coverage of 95% CI: 94%
.large_fig[
]
???
We are kind to the frequentist, because we are not testing all possible values.
---
# 3 replicates, T
Coverage of 95% CI: 98%
.large_fig[
]
---
# 20 replicates, default settings
Coverage of 95% CI: 93.5%
.large_fig[
]
---
# Multiple comparisons
Correction for multiple comparisons applies also to CIs!
--
E.g., for the 3 replicates without shrinkage:
95% CI coverage: 94%
95% CI coverage when p < 0.1: 67%
---
# DESeq - conclusions
- The CIs of DESeq2 can be slightly miscalibrated
--
- Especially with few replicates
--
- p-values still valid
--
- Bayesian interpretation of DESeq2 results is _somewhat_ possible
--
- Correct CIs for multiple comparisons
---
# Thank you - Questions?
https://github.com/cas-bioinf/SBCDESeq2
Talts et al. 2020 (http://www.stat.columbia.edu/~gelman/research/unpublished/sbc.pdf)
`SBC` R package
https://github.com/hyunjimoon/SBC/
This work was supported by ELIXIR CZ research infrastructure project (MEYS Grant No: LM2018131) including access to computing and storage facilities.
</textarea>
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