The material in this course requires R version 3.2 and Bioconductor version 3.2
getRversion() >= '3.2' && getRversion() < '3.3',
BiocInstaller::biocVersion() == "3.2"
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?
- 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.
Be aware of batch effects
HapMap samples from one facility, ordered by date of processing.
Artifacts of your particular protocols
- Sequence contaminants
- Enrichment bias, e.g., non-uniform transcript representation.
- PCR artifacts – adapter contaminants, sequence-specific amplification bias, …
Axes of variation
- Single- versus paired-end
- Length: 50-200nt
- Number of reads per sample
- 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
- Structural variants: paired-end reads
- Variants: depth via longer, paired-end reads
- Microbiome: long paired-end reads (overlapping ends)
- de novo
- No reference genome; considerable sequencing and computational resources
- Established reference genome
- Splice-aware aligners
- Novel transcript discovery
- Established reference genome; reliable gene model
- Simple aligners
- Known gene / transcript expression
Splice-aware aligners (and Bioconductor wrappers)
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)
- HTSeq, htseq-count
(Bowtie2 / tophat / Cufflinks / Cuffdiff / etc)
- tophat uses Bowtie2 to perform basic single- and paired-end alignments, then uses algorithms to place difficult-to-align reads near to their well-aligned mates.
- Cufflinks (doi) takes tophat output and estimate existing and novel transcript abundance. How Cufflinks Works
- Cuffdiff assesses statistical significance of estimated abundances between experimental groups
- RSEM includes de novo assembly and quantification
(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.
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
- 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.
- 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).
- 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.
- 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.
Statistical Issues In-depth
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
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.
- Estimate per-gene dispersion
- Fit a smoothed relationship between dispersion and abundance
- 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
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.