Why Library-Size Scaling Can Fail

Why Total Counts Can Mislead

A library-size offset corrects for differences in the number of reads available across RNA-seq samples. This correction is useful when a larger library reflects greater sequencing depth and the libraries have broadly comparable RNA composition. But the total number of reads assigned to a sample is not a pure measure of sequencing depth: it can also change because a small number of transcripts occupy a larger share of the reads.

This distinction matters because sequencing counts describe the allocation of reads among transcripts. If a few genes become much more abundant, they can take up a larger fraction of a fixed number of reads. Other genes may then receive fewer reads even if their abundance has not changed. Conversely, if a library contains more reads overall because it was sequenced more deeply, counts may rise across genes without any biological expression change. Total-count scaling can fail when it treats these different situations as though they were the same.

In the log-linked count model introduced in the earlier material on library sizes as offsets, the offset is fixed rather than estimated as a gene-specific effect. A simplified expression is \(\log(\mu_{gj})=\log(L_j)+\eta_{gj}\), where \(\mu_{gj}\) is the expected count and \(\eta_{gj}\) contains the gene and sample effects of interest. The offset accounts for library size, but it does not itself determine whether \(L_j\) represents depth alone or depth entangled with a compositional shift.

The Compositional Mechanism

Let \(M_{gj}\) denote the amount of RNA from gene \(g\) in sample \(j\), and let \(M_{\cdot j}=\sum_g M_{gj}\) be the total RNA amount represented in the sample. Under a simple sampling model, a read from sample \(j\) comes from gene \(g\) with probability \(p_{gj}=M_{gj}/M_{\cdot j}\). If \(D_j\) reads are sampled, then the expected count is \(E(Y_{gj})=D_jp_{gj}\). The observed library total \(L_j\) is approximately the read depth \(D_j\), but the proportion of those reads assigned to a gene depends on the entire RNA composition.

After dividing by the library total, the expected normalized count is approximately \(p_{gj}\), not the absolute amount \(M_{gj}\). For two samples, the ratio of expected normalized counts is therefore approximately \(\frac{p_{gB}}{p_{gA}}=\frac{M_{gB}}{M_{gA}}\frac{M_{\cdot A}}{M_{\cdot B}}\). If a gene’s amount stays constant while total RNA doubles, its relative share is halved. A normalization that interprets that halving as a gene-specific decrease will report a misleading comparison if the scientific target is unchanged absolute abundance.

This relationship is a consequence of sampling proportions. Since \(E(Y_{gj})=D_jp_{gj}\) and \(L_j\) is approximately \(D_j\), dividing expected counts by library size leaves approximately \(p_{gj}\). Substituting \(p_{gj}=M_{gj}/M_{\cdot j}\) for each sample and taking their ratio gives the displayed expression. When \(M_{gB}=M_{gA}\) but \(M_{\cdot B}=2M_{\cdot A}\), the normalized-count ratio is approximately \(1/2\), even though the gene’s amount did not change.

Assumptions and Practical Checks

Total-count scaling is most defensible when differences in total counts primarily reflect sequencing depth and when composition is sufficiently stable that the library total provides a useful common scale. It does not require every gene to be unchanged. Rather, the normalization interpretation becomes unreliable when compositional changes are large enough to make the total a poor proxy for depth across samples. A few very abundant genes can have this effect because their counts contribute heavily to \(L_j\).

The following checks can reveal reasons to question a total-count offset. None proves, from the counts alone, that a particular normalization is correct; they help identify evidence that the composition assumption may be strained.

• Inspect the largest contributors. Check whether a small number of genes account for a very large or substantially different fraction of each library.
• Compare library totals with known technical information. Sequencing depth, read filtering, and the number of mapped reads help explain whether total-count differences are plausibly technical.
• Look for broad directional changes. If many genes appear to shift in the same direction after total-count scaling, a global compositional change is one possible explanation, alongside real widespread biological changes.
• Use reliable external information where available. Spike-in controls or well-justified reference genes can provide a comparison not based solely on the sample’s own total RNA composition. Their validity depends on how they were added or selected.

A warning sign is not a diagnosis. For example, one gene dominating a library may be biologically meaningful, an artifact, or a feature of the sample type. Also, RNA-seq counts alone identify relative allocation among sequenced molecules; they generally cannot establish absolute RNA molecules per cell without additional information about cell number, total RNA, or external controls.

Comparison, Limitations, and a Common Mistake

Total-count scaling is simple and transparent: it uses each library’s own total as the common measure of scale. It can be appropriate when sample compositions are comparable and library totals mainly represent sequencing depth. Other strategies estimate a scale using information across genes, with the aim of reducing sensitivity to a small number of extreme contributors; robust composition-aware approaches are examples. Such strategies still rely on assumptions about which genes provide a suitable reference. External spike-ins can address a different question by supplying an external scale, but only if their addition and behavior support that use. No scaling choice can recover absolute per-cell RNA abundance from relative counts without relevant additional information.

A common mistake is to reason, “Sample B has twice the total counts, so every gene in B must be divided by two; any gene whose scaled count is lower must therefore be downregulated.” The correction is that dividing by the total converts counts to relative shares. Those shares can change because other transcripts changed, even if the gene being examined did not. State what the offset corrects, inspect the composition, and qualify conclusions when the reference scale is uncertain.