Heavy-tailed prior distributions for sequence count data: removing the noise and preserving large differences

Heavy-tailed prior distributions for sequence count data: removing the noise and preserving large differences Anqi Zhu Joseph G. Ibrahim Michael I. Love

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Heavy-tailed prior distributions for sequence count data: removing the noise and preserving large differences 2018 Bioinformatics 10.1093/bioinformatics/bty895 zhu2018-heavy-tailed-prior-distributions-f zhu2018-heavy-tailed-prior-distributions-f.txt, the project's staged copy a367122991886500fbe7bb1eb93e3fe9189ecf2a cc-by-nc statistics

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them the logarithmic fold change between conditions in RNA-seq, and what to do when the estimate of it is dominated by noise Quotation withheld because this record is not cleared for redistribution. how to shrink unreliable effect-size estimates without losing the genes whose large effects are real Quotation withheld because this record is not cleared for redistribution. a heavy-tailed Cauchy prior that removes the need for filter thresholds and pseudocounts, with lower bias than earlier shrinkage estimators Quotation withheld because this record is not cleared for redistribution. method Quotation withheld because this record is not cleared for redistribution. maximum-likelihood effect sizes that blow up when counts are low, producing large estimates that are not differences Quotation withheld because this record is not cleared for redistribution. system-or-tool-building system-or-tool-building Quotation withheld because this record is not cleared for redistribution. the estimate is unreliable exactly where the counts are small, so the maximum likelihood LFC has high variance and produces `large estimates not representative of true differences` - the noise appears as a big effect, not as a small one Quotation withheld because this record is not cleared for redistribution. a heavy tail on the prior is what lets shrinkage be aggressive near zero and gentle far from it: the Cauchy pulls in the noise-driven estimates while leaving genuinely large fold changes where they are Quotation withheld because this record is not cleared for redistribution. swapping a Normal prior for a Cauchy gives heavy tails, so small effects are still shrunk while genuinely large ones survive - shrinkage without flattening Quotation withheld because this record is not cleared for redistribution. the prior's scale is fitted by subtracting each estimate's own error variance from its squared value, so the prior learns how much of the observed spread is real Quotation withheld because this record is not cleared for redistribution. the scale is set from a Normal assumption even though the prior itself is Cauchy - the two roles come apart and the authors say the mismatch works in practice Quotation withheld because this record is not cleared for redistribution. EVERY STANDARD CORRECTION TRADES ONE ERROR FOR THE OPPOSITE ONE: `filtering or application of Normal priors each can have drawbacks, either leading to loss of genes with sufficient signal, or overly aggressive shrinkage of true, large LFCs` Quotation withheld because this record is not cleared for redistribution. and the second-order cost is stated: filtering loses genes with real differences, and `pseudocounts provide a limited solution that must be adapted per dataset` - a correction re-tuned per dataset is a free parameter wearing a method's name Quotation withheld because this record is not cleared for redistribution. choosing the filter is named as an act of judgement rather than a setting: `Setting the threshold requires careful consideration of which genes may be lost` Quotation withheld because this record is not cleared for redistribution. if most genes move in the same direction the global normalisation breaks down - and the paper says this defeats EVERY method under comparison, not only theirs Quotation withheld because this record is not cleared for redistribution. that failure is detectable, and the paper names the diagnostics rather than leaving it as a caveat Quotation withheld because this record is not cleared for redistribution. where the maximum likelihood estimates are not supplied the prior scale falls back to a fixed value rather than being fitted Quotation withheld because this record is not cleared for redistribution. the method is compared against BOTH failure modes rather than against one baseline - filtering, which loses genes, and Normal priors, which over-shrink eliminates: a new estimator that beats the over-shrinking baseline by under-shrinking, or the reverse; the two-sided comparison is what makes 'lower bias while still reducing variance' a claim rather than a trade · outcome: held Quotation withheld because this record is not cleared for redistribution. whether the correction needs a per-dataset parameter eliminates: a method whose performance is really the analyst's tuning - the proposed prior 'avoids the use of filter thresholds or pseudocounts' entirely · outcome: held Quotation withheld because this record is not cleared for redistribution. whether the approach is tied to the negative-binomial likelihood it was developed on eliminates: a method that works because of one distributional assumption - apeglm 'accepts arbitrary likelihoods, as long as additional parameters are pre-specified' · outcome: held Quotation withheld because this record is not cleared for redistribution. testing robustness when the assumption of a unimodal symmetric distribution of effects is violated eliminates: the possibility that the method only works when its own prior assumption happens to hold · outcome: held Quotation withheld because this record is not cleared for redistribution. quantifying the effect of substituting estimated standard errors where the derivation requires known ones, specifically at very low counts eliminates: the possibility that the borrowed estimator breaks exactly where the data are weakest · outcome: held Quotation withheld because this record is not cleared for redistribution. trying an alternative posterior approximation by integrating over a fine grid instead of the Laplace method eliminates: the possibility that the chosen approximation was adopted without a competitor · outcome: failed Quotation withheld because this record is not cleared for redistribution. logarithmic fold change logarithmic fold change Quotation withheld because this record is not cleared for redistribution. pseudocounts pseudocounts Quotation withheld because this record is not cleared for redistribution. shrinkage estimator shrinkage estimator Quotation withheld because this record is not cleared for redistribution. Cauchy prior Cauchy prior Quotation withheld because this record is not cleared for redistribution. local false sign rate local false sign rate Quotation withheld because this record is not cleared for redistribution. Laplace approximation Laplace approximation Quotation withheld because this record is not cleared for redistribution. empirical Bayes empirical Bayes Quotation withheld because this record is not cleared for redistribution. maximum a posteriori maximum a posteriori Quotation withheld because this record is not cleared for redistribution. logarithmic fold change - AS ESTIMATED, NOT AS DEFINED. The definition is a ratio of average expression between conditions; the estimate at low counts is `large ... not representative of true differences`. THE SAME SYMBOL NAMES A QUANTITY AND A NUMBER THAT DOES NOT MEASURE IT Quotation withheld because this record is not cleared for redistribution. shrinkage - the family of corrections, and this paper's point is that the family members fail in OPPOSITE directions: a filter loses true signal, a Normal prior flattens true large effects. WHICH ERROR YOU GET IS A CHOICE, AND USUALLY AN UNEXAMINED ONE Quotation withheld because this record is not cleared for redistribution. pseudocount - a correction that `must be adapted per dataset`. The paper's remedy is to remove the parameter rather than to tune it, which is the same move a field makes when it replaces an inferred name with a measured one Quotation withheld because this record is not cleared for redistribution. critiques → count filtering as practised in edgeR and limma-voom, which removes genes before analysis and can lose those with sufficient signal Quotation withheld because this record is not cleared for redistribution. critiques → DESeq2's adaptive Normal prior, which shrinks true large fold changes too aggressively Quotation withheld because this record is not cleared for redistribution. extends → the empirical Bayes shrinkage tradition itself - the method is offered as a replacement for the prior, not for the framework Quotation withheld because this record is not cleared for redistribution. filtering loses genes with sufficient signal, while Normal priors over-shrink true large LFCs filtering loses genes with sufficient signal, while Normal priors over-shrink true large LFCs Quotation withheld because this record is not cleared for redistribution. pseudocounts provide only a limited solution that must be adapted to each dataset pseudocounts provide only a limited solution that must be adapted to each dataset Quotation withheld because this record is not cleared for redistribution. setting the filter threshold requires careful thought about which genes may be lost setting the filter threshold requires careful thought about which genes may be lost Quotation withheld because this record is not cleared for redistribution. at low or highly variable counts the maximum-likelihood LFC has high variance, giving large estimates not representative of true differences at low or highly variable counts the maximum-likelihood LFC has high variance, giving large estimates not representative of true differences Quotation withheld because this record is not cleared for redistribution. the proposed heavy-tailed Cauchy prior avoids filter thresholds and pseudocounts the proposed heavy-tailed Cauchy prior avoids filter thresholds and pseudocounts Quotation withheld because this record is not cleared for redistribution. the Laplace approximation was consistently more accurate than numerical integration over a grid Quotation withheld because this record is not cleared for redistribution. the resulting scale estimate is only slightly biased even at very low counts Quotation withheld because this record is not cleared for redistribution. shrinkage improves the ranking of genes by effect size relative to methods that do not shrink at all Quotation withheld because this record is not cleared for redistribution. the difference between conditions, defined as the log ratio of average expression levels logarithmic fold change Quotation withheld because this record is not cleared for redistribution. the local false sign rate given as a two-case posterior probability keyed on the sign of the MAP estimate local false sign rate Quotation withheld because this record is not cleared for redistribution. maximum likelihood maximum likelihood Quotation withheld because this record is not cleared for redistribution. variance variance Quotation withheld because this record is not cleared for redistribution. posterior SD posterior SD Quotation withheld because this record is not cleared for redistribution. library size library size Quotation withheld because this record is not cleared for redistribution. runtimes for the pipeline on a ten-thousand-gene simulation - dispersion and MLE fitting, Normal-prior shrinkage, Cauchy-prior shrinkage, and MAP-only Quotation withheld because this record is not cleared for redistribution.

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