# Contents

The material in this course requires R version 3.2 and Bioconductor version 3.2

stopifnot(
getRversion() >= '3.2' && getRversion() < '3.3',
BiocInstaller::biocVersion() == "3.2"
)

# 1 Experimental design

Keep it simple

• Classical experimental designs
• Time series
• Without missing values, where possible
• Intended analysis must be feasbile – can the available samples and hypothesis of interest be combined to formulate a testable statistical hypothesis?

Replicate

• Extent of replication determines nuance of biological question.
• No replication (1 sample per treatment): qualitative description with limited statistical options.
• 3-5 replicates per treatment: designed experimental manipulation with cell lines or other well-defined entities; 2-fold (?) change in average expression between groups.
• 10-50 replicates per treatment: population studies, e.g., cancer cell lines.
• 1000’s of replicates: prospective studies, e.g., SNP discovery
• One resource: RNASeqPower

Avoid confounding experimental factors with other factors

• Common problems: samples from one treatment all on the same flow cell; samples from treatment 1 processed first, treatment 2 processed second, etc.

Record co-variates

Be aware of batch effects

• Known

• Phenotypic covariates, e.g., age, gender
• Experimental covariates, e.g., lab or date of processing
• Incorporate into linear model, at least approximately
• Unknown

• Or just unexpected / undetected
• Characterize using, e.g., sva.
• Surrogate variable analysis

• Leek et al., 2010, Nature Reviews Genetics 11 733-739, Leek & Story PLoS Genet 3(9): e161.
• Scientific finding: pervasive batch effects
• Statistical insights: surrogate variable analysis: identify and build surrogate variables; remove known batch effects
• Benefits: reduce dependence, stabilize error rate estimates, and improve reproducibility
• combat software / sva Bioconductor package

HapMap samples from one facility, ordered by date of processing.

# 2 Wet-lab

Confounding factors

• Record or avoid

• Sequence contaminants
• Enrichment bias, e.g., non-uniform transcript representation.
• PCR artifacts – adapter contaminants, sequence-specific amplification bias, …

# 3 Sequencing

Axes of variation

• Single- versus paired-end
• Length: 50-200nt
• Number of reads per sample

Application-specific, e.g.,

• ChIP-seq: short, single-end reads are usually sufficient
• RNA-seq, known genes: single- or paired-end reads
• RNA-seq, transcripts or novel variants: paired-end reads
• Copy number: single- or paired-end reads
• Variants: depth via longer, paired-end reads
• Microbiome: long paired-end reads (overlapping ends)

# 4 Alignment

Alignment strategies

• de novo
• No reference genome; considerable sequencing and computational resources
• Genome
• Established reference genome
• Splice-aware aligners
• Novel transcript discovery
• Transcriptome
• Established reference genome; reliable gene model
• Simple aligners
• Known gene / transcript expression

Splice-aware aligners (and Bioconductor wrappers)

# 5 Reduction to ‘count tables’

• Use known gene model to count aligned reads overlapping regions of interest / gene models
• Gene model can be public (e.g., UCSC, NCBI, ENSEMBL) or ad hoc (gff file)
• GenomicAlignments::summarizeOverlaps()
• Rsubread::featureCount()
• HTSeq, htseq-count

## 5.2 (kallisto / sailfish)

• ‘Next generation’ differential expression tools; transcriptome alignment
• E.g., kallisto takes a radically different approach: from FASTQ to count table without BAM files.
• Very fast, almost as accurate.

# 6 Analysis

Unique statistical aspects

• Large data, few samples
• Comparison of each gene, across samples; univariate measures
• Each gene is analyzed by the same experimental design, under the same null hypothesis

Summarization

• Counts per se, rather than a summary (RPKM, FRPKM, …), are relevant for analysis
• For a given gene, larger counts imply more information; RPKM etc., treat all estimates as equally informative.
• Comparison is across samples at each region of interest; all samples have the same region of interest, so modulo library size there is no need to correct for, e.g., gene length or mapability.

Normalization

• Libraries differ in size (total counted reads per sample) for un-interesting reasons; we need to account for differences in library size in statistical analysis.
• Total number of counted reads per sample is not a good estimate of library size. It is un-necessarily influenced by regions with large counts, and can introduce bias and correlation across genes. Instead, use a robust measure of library size that takes account of skew in the distribution of counts (simplest: trimmed geometric mean; more advanced / appropriate encountered in the lab).
• Library size (total number of counted reads) differs between samples, and should be included as a statistical offset in analysis of differential expression, rather than ‘dividing by’ the library size early in an analysis.

Appropriate error model

• Count data is not distributed normally or as a Poisson process, but rather as negative binomial.
• Result of a combination Poisson (shot’ noise, i.e., within-sample technical and sampling variation in read counts) with variation between biological samples.
• A negative binomial model requires estimation of an additional parameter (‘dispersion’), which is estimated poorly in small samples.
• Basic strategy is to moderate per-gene estimates with more robust local estimates derived from genes with similar expression values (a little more on borrowing information is provided below).

Pre-filtering

• Naively, a statistical test (e.g., t-test) could be applied to each row of a counts table. However, we have relatively few samples (10’s) and very many comparisons (10,000’s) so a naive approach is likely to be very underpowered, resulting in a very high false discovery rate
• A simple approach is perform fewer tests by removing regions that could not possibly result in statistical significance, regardless of hypothesis under consideration.
• Example: a region with 0 counts in all samples could not possibly be significant regradless of hypothesis, so exclude from further analysis.
• Basic approaches: ‘K over A’-style filter – require a minimum of A (normalized) read counts in at least K samples. Variance filter, e.g., IQR (inter-quartile range) provides a robust estimate of variability; can be used to rank and discard least-varying regions.
• More nuanced approaches: edgeR vignette; work flow today.

Borrowing information

• Why does low statistical power elevate false discovery rate?
• One way of developing intuition is to recognize a t-test (for example) as a ratio of variances. The numerator is treatment-specific, but the denominator is a measure of overall variability.
• Variances are measured with uncertainty; over- or under-estimating the denominator variance has an asymmetric effect on a t-statistic or similar ratio, with an underestimate inflating the statistic more dramatically than an overestimate deflates the statistic. Hence elevated false discovery rate.
• Under the typical null hypothesis used in microarray or RNA-seq experiments, each gene may respond differently to the treatment (numerator variance) but the overall variability of a gene is the same, at least for genes with similar average expression
• The strategy is to estimate the denominator variance as the between-group variance for the gene, moderated by the average between-group variance across all genes.
• This strategy exploits the fact that the same experimental design has been applied to all genes assayed, and is effective at moderating false discovery rate.

## 6.1 Statistical Issues In-depth

### 6.1.1 Normalization

DESeq2 estimateSizeFactors(), Anders and Huber, 2010

• For each gene: geometric mean of all samples.
• For each sample: median ratio of the sample gene over the geometric mean of all samples
• Functions other than the median can be used; control genes can be used instead

edgeR calcNormFactors() TMM method of Robinson and Oshlack, 2010

• Identify reference sample: library with upper quartile closest to the mean upper quartile of all libraries
• Calculate M-value of each gene (log-fold change relative to reference)
• Summarize library size as weighted trimmed mean of M-values.

### 6.1.2 Dispersion

DESeq2 estimateDispersions()

• Estimate per-gene dispersion
• Fit a smoothed relationship between dispersion and abundance

edgeR estimateDisp()`

• Common: single dispersion for all genes; appropriate for small experiments (<10? samples)
• Tagwise: different dispersion for all genes; appropriate for larger / well-behaved experiments
• Trended: bin based on abundance, estimate common dispersion within bin, fit a loess-smoothed relationship between binned dispersion and abundance

# 7 Comprehension

Placing differentially expressed regions in context

• Gene names associated with genomic ranges
• Gene set enrichment and similar analysis
• Proximity to regulatory marks
• Integrate with other analyses, e.g., methylation, copy number, variants, …

Correlation between genomic copy number and mRNA expression identified 38 mis-labeled samples in the TCGA ovarian cancer Affymetrix microarray dataset.