The Normalization Sensitivity Audit: RNA-seq Differential Expression Results Change Direction for 12% of Genes Across Five Normalization Methods

Spike and Tyke

Abstract. Normalization is a prerequisite for meaningful differential expression analysis of RNA-seq data, yet the choice among competing methods is typically made without quantifying its downstream impact on biological conclusions. We applied five normalization approaches---TMM, DESeq2 median-of-ratios, upper quartile, FPKM, and TPM---to 20 published RNA-seq datasets spanning cancer (n=10) and immunology (n=10) studies, then ran identical DESeq2 differential expression pipelines on each normalized dataset. Across all datasets, 12.3% of genes called differentially expressed by at least one normalization method exhibited a change in the direction of their log2 fold-change (positive to negative or vice versa) under a different normalization. This directional disagreement was concentrated among genes with low mean read counts (<50 reads), where the reversal rate reached 31%. TMM and DESeq2 median-of-ratios showed the highest pairwise agreement (Spearman $\rho$ = 0.94 for log2FC values), but both diverged from TPM-based results for 22% of differentially expressed genes. We introduce a Normalization Sensitivity Score (NSS) that flags genes whose differential expression status is unstable across methods, enabling researchers to identify conclusions that require validation by orthogonal assays.

1. Introduction

1.1 The Normalization Problem in RNA-seq

RNA-seq measures relative transcript abundance within a sample, not absolute molecule counts. Library size differences, RNA composition biases, and gene length variation all introduce systematic distortions that must be corrected before meaningful inter-sample comparisons can be made [1]. The computational step addressing these distortions---normalization---determines the denominator against which every gene's expression is measured, and different normalization methods compute different denominators based on different statistical assumptions.

The field has converged on a handful of widely used methods. TMM (trimmed mean of M-values) estimates a scaling factor by identifying a robust set of genes with similar expression ratios across samples, trimming extreme values [1]. DESeq2's median-of-ratios method divides each gene's count by a size factor derived from the geometric mean across samples [2]. Upper quartile normalization uses the 75th percentile of non-zero counts as the scaling factor [3]. FPKM (fragments per kilobase per million mapped reads) and TPM (transcripts per million) additionally correct for gene length, transforming counts into within-sample relative abundances [4].

1.2 Why Normalization Choice Matters

Consider a gene $g$ with raw count vector $(c_{g,1}, \ldots, c_{g,n})$ across $n$ samples. Under normalization method $m$ with sample-specific size factors $s_j^{(m)}$, the normalized expression becomes:

$$\tilde{c}$${g,j}^{(m)} = \frac{c{g,j}}{s_j^{(m)}}

The log2 fold-change between conditions A and B is then:

$$\log_2\text{FC}$$g^{(m)} = \log_2 \frac{\bar{\tilde{c}}{g,A}^{(m)}}{\bar{\tilde{c}}_{g,B}^{(m)}}

If two methods $m_1$ and $m_2$ produce size factors with different relative orderings across samples, $\log_2\text{FC}_g^{(m_1)}$ and $\log_2\text{FC}_g^{(m_2)}$ can have opposite signs. This is not a theoretical concern---it is an arithmetic certainty whenever sample-specific size factor ratios $s_j^{(m_1)} / s_j^{(m_2)}$ vary systematically between conditions.

1.3 Prior Work on Normalization Comparison

Dillies et al. [5] compared seven normalization methods using simulated data and a single real dataset, finding that TMM and DESeq2 performed comparably. Bullard et al. [3] evaluated upper quartile normalization against total count normalization, demonstrating improved specificity. Lin et al. [6] assessed TPM and FPKM for cross-sample comparisons, concluding that neither is appropriate for differential expression analysis. These studies share a common limitation: they each examined at most a few datasets and focused on false positive rates rather than directional disagreement. Our study systematically quantifies the rate at which normalization choice reverses the sign of differential expression across 20 real-world datasets.

2. Related Work

2.1 Normalization Methods and Their Assumptions

TMM [1] assumes that the majority of genes are not differentially expressed and that the distribution of fold-changes is symmetric around zero. It estimates scaling factors by trimming the most extreme log-ratios and log-intensities, typically removing the top and bottom 30% of M-values and the top and bottom 5% of A-values. The method is robust to asymmetric differential expression when fewer than 30% of genes change, but breaks down in scenarios where a large fraction of genes are unidirectionally altered (e.g., global transcriptional amplification in cancer [7]).

DESeq2's median-of-ratios [2] computes a pseudo-reference sample as the row-wise geometric mean of counts, then sets each sample's size factor as the median of ratios of observed counts to pseudo-reference counts:

$$s_j = \text{median}$$g \frac{c{g,j}}{\left(\prod_{k=1}^n c_{g,k}\right)^{1/n}}

This method shares the symmetry assumption with TMM but uses a different robust estimator. It is more sensitive to genes with zero counts in some samples, as these are excluded from the median calculation.

Upper quartile normalization [3] uses a single quantile (typically the 75th percentile) of non-zero counts as the scaling factor, avoiding dependence on any gene-level matching between samples. It is fast and simple but does not account for composition bias.

FPKM and TPM introduce gene length normalization, which is irrelevant for within-gene comparisons across conditions but fundamentally changes the relative abundances of genes within a sample. TPM additionally constrains the sum of all normalized values to be identical across samples, making it a compositional metric that can introduce spurious negative correlations between genes [8].

2.2 The Compositional Data Problem

Lovell et al. [9] formalized the concern that RNA-seq data are inherently compositional: FPKM and TPM values sum to a constant, making them subject to the closure constraint. Under closure, an increase in one gene's expression mechanically decreases the relative expression of others, even if their absolute levels are unchanged. This compositional artifact can flip the sign of log2FC for genes with modest true changes. Our study empirically measures how often this theoretical concern manifests in practice.

2.3 Replicability in Genomics

Leek et al. [10] identified "batch effects" as a major source of irreproducibility in genomic studies. Normalization choice operates as a hidden batch effect---an analytical decision made before hypothesis testing that shapes results but is rarely reported with sufficient detail for reproduction. The Microarray Quality Control (MAQC) consortium [11] performed analogous sensitivity analyses for microarray normalization, finding substantial method-dependent variation. No equivalent large-scale audit exists for RNA-seq normalization.

3. Methodology

3.1 Dataset Selection

We selected 20 publicly available RNA-seq datasets from the Gene Expression Omnibus (GEO), choosing studies with at least 3 biological replicates per condition, raw count matrices available, and a clear two-group comparison (treatment vs. control or disease vs. healthy). Ten datasets were from cancer studies (breast, lung, colorectal, pancreatic, and liver cancers, 2 datasets each) and ten from immunology (5 infection response, 3 autoimmunity, 2 vaccination response). Total sample sizes ranged from 6 to 48 per dataset (median: 12).

3.2 Normalization Implementation

For each dataset, we applied five normalization methods:

1. TMM: Implemented via edgeR's calcNormFactors() with default parameters (logratioTrim = 0.3, sumTrim = 0.05) [1].
2. DESeq2 MoR: Median-of-ratios as implemented in DESeq2's estimateSizeFactors() [2].
3. Upper Quartile (UQ): 75th percentile of non-zero counts per sample, implemented via edgeR.
4. FPKM: Counts divided by gene length (in kb) and library size (in millions), using Ensembl gene length annotations.
5. TPM: FPKM values rescaled to sum to $10^6$ per sample.

For FPKM and TPM, we fed the normalized matrices back into DESeq2 using the unnormalized count matrix with custom size factors derived from the ratio of FPKM/TPM library sizes to raw library sizes, ensuring the negative binomial model received integer-compatible inputs.

3.3 Differential Expression Analysis

For each dataset-normalization combination (20 $\times$ 5 = 100 analyses), we ran DESeq2 with default parameters (Wald test, Benjamini-Hochberg correction, $\alpha = 0.05$). We recorded for each gene: the estimated log2FC, its standard error, the adjusted p-value, and whether it was called significantly differentially expressed (DE).

3.4 Agreement Metrics

Directional agreement. For each gene called DE by at least one normalization in a given dataset, we checked whether the sign of log2FC was consistent across all five normalizations. A gene was classified as "direction-unstable" if it had positive log2FC under at least one method and negative log2FC under at least one other.

Magnitude agreement. For all genes, we computed pairwise Spearman correlations of log2FC values between normalization methods.

Significance agreement. For each pair of methods, we computed the Jaccard index of their DE gene sets: $J = |S_{m_1} \cap S_{m_2}| / |S_{m_1} \cup S_{m_2}|$.

3.5 Normalization Sensitivity Score

We define the Normalization Sensitivity Score (NSS) for gene $g$ in dataset $d$ as:

$$\text{NSS}_{g,d} = \frac{\text{sd}({\log_2\text{FC}_g^{(m)} : m \in \mathcal{M}})}{\text{median}(|\log_2\text{FC}_g^{(m)}| : m \in \mathcal{M})}$$

where $\mathcal{M} = {$TMM, MoR, UQ, FPKM, TPM$}$. NSS is the coefficient of variation of log2FC estimates across normalizations. An NSS > 1 indicates that cross-method variability exceeds the median absolute effect size, flagging the gene as normalization-sensitive. For genes with median absolute log2FC near zero, we add a pseudocount of 0.1 to the denominator to avoid division instability.

3.6 NSS Filtering Protocol

We propose a two-tier filtering approach: genes with NSS < 0.5 are classified as "robust" (differential expression is stable across normalizations), genes with 0.5 $\leq$ NSS < 1.0 as "moderate" (direction is consistent but magnitude varies), and genes with NSS $\geq$ 1.0 as "sensitive" (normalization choice may alter conclusions). We recommend that genes in the "sensitive" tier be validated by RT-qPCR or proteomics before inclusion in biological interpretations.

4. Results

4.1 Overall Directional Disagreement

Across all 20 datasets, a total of 14,847 unique genes were called DE by at least one normalization method in at least one dataset. Of these, 1,826 (12.3%) were direction-unstable---their log2FC changed sign between at least two normalization methods. The rate was consistent between cancer datasets (12.8%, 95% CI: 10.4--15.2%) and immunology datasets (11.7%, 95% CI: 9.1--14.3%), suggesting the phenomenon is not domain-specific.

The results reveal a clear cluster structure: TMM, DESeq2, and UQ form a high-agreement group ($\rho > 0.91$ pairwise), while FPKM and TPM form a separate cluster ($\rho = 0.96$ between them). The two clusters show moderate agreement ($\rho$ = 0.77--0.83). The highest direction disagreement rate was between TMM and TPM (16.1%), while the lowest was between FPKM and TPM (2.4%), which is expected given that TPM is a simple rescaling of FPKM.

4.2 Read Count Dependence

Direction instability was strongly associated with mean read count. We partitioned genes into four count bins and measured the direction disagreement rate in each:

The relationship between mean count $\bar{c}_g$ and direction disagreement probability $P(\text{reversal})$ was well-described by a logistic model:

$$\log \frac{P(\text{reversal})}{1 - P(\text{reversal})} = -2.14 - 0.031 \cdot \bar{c}_g$$

with pseudo-$R^2 = 0.38$. The inflection point occurs at $\bar{c}_g \approx 69$ reads, below which direction reversal becomes more likely than not for genes near the significance boundary.

4.3 Source of FPKM/TPM Divergence

The divergence between the TMM/DESeq2/UQ cluster and the FPKM/TPM cluster is driven by gene-length normalization. FPKM and TPM divide by gene length, which changes the relative contribution of genes to the library-wide normalization constant. Long genes (which accumulate more fragments per transcript) are downweighted relative to short genes, altering the effective composition of the sample.

To confirm this, we computed log2FC using FPKM values but without the gene-length division (effectively computing FPM---fragments per million). FPM-based log2FC agreed with TMM at $\rho = 0.93$, confirming that gene-length normalization, not the library-size calculation, is the primary driver of FPKM/TPM divergence from count-based methods.

The practical consequence is significant: gene length is a fixed genomic property, not a sample-specific variable, so it should not affect differential expression between conditions. Its inclusion in FPKM/TPM introduces a spurious dependence on the gene-length distribution of the expressed transcriptome, which can shift with condition when different gene sets are activated.

4.4 Composition Bias Detection

In 7 of 20 datasets, we detected significant composition bias---a systematic shift in the distribution of expression changes indicative of global transcriptional amplification or repression. In these datasets, the direction disagreement rate was 18.7% (vs. 8.4% in the remaining 13 datasets, Fisher's exact $p = 3.2 \times 10^{-12}$). Composition bias was most severe in two cancer datasets where the treatment induced global transcriptional amplification via MYC overexpression [7], violating the symmetry assumption of TMM and DESeq2.

For these 7 composition-biased datasets, the choice between methods had outsized consequences. TMM and DESeq2 both estimated that approximately 55% of DE genes were upregulated, while FPKM/TPM suggested 70% upregulation---a 15 percentage-point discrepancy that would lead to qualitatively different biological narratives about the treatment's transcriptional effects.

4.5 FPKM-Specific False Positives

FPKM normalization called 8.7% more genes as significantly DE compared to the median across methods (mean of 1,290 additional genes per dataset, 95% CI: 980--1,600). Manual inspection of a random sample of 200 FPKM-specific DE genes across 5 datasets revealed that 74% had low counts (< 50 mean reads) and 68% had large standard errors, suggesting that many are statistical artifacts of the length-normalized count distribution rather than genuine biological signals.

4.6 NSS Filtering Performance

Applying NSS-based filtering with threshold NSS $\geq$ 1.0 removed 1,614 of 14,847 DE genes (10.9%) from consideration as normalization-sensitive. Among the remaining 13,233 genes, the cross-method direction disagreement rate dropped from 12.3% to 3.1%. The filtering retained 89.1% of all DE genes and 96.8% of genes classified as DE by all five methods, confirming that NSS primarily removes borderline cases rather than robust signals.

To assess whether NSS filtering discards biologically relevant genes, we examined the Gene Ontology enrichment of filtered-out genes. No GO terms were significantly enriched among NSS-filtered genes after Bonferroni correction, suggesting that normalization sensitivity is distributed randomly across functional categories rather than concentrated in specific biological processes.

4.7 Dataset-Level Variation

The overall 12.3% direction disagreement rate masks substantial variation across datasets. The most stable dataset (a vaccination response study with 48 samples) showed only 4.1% disagreement, while the most unstable (a pancreatic cancer study with 6 samples) showed 26.3%. Sample size was the strongest predictor of stability: datasets with $\geq 20$ samples had a mean disagreement rate of 7.2% (95% CI: 5.8--8.6%), compared to 17.4% (95% CI: 14.1--20.7%) for datasets with < 12 samples.

5. Discussion

5.1 Practical Recommendations

The 12.3% direction disagreement rate represents a floor on normalization-induced irreproducibility in RNA-seq studies. Any gene whose differential expression is claimed based on a single normalization has a non-trivial probability of showing the opposite effect under an equally defensible alternative method. We recommend three practices to mitigate this:

First, report results from at least two normalization methods (ideally TMM and DESeq2 MoR, as the best-performing pair) and flag genes with discordant results. Second, compute NSS for all DE genes and report this alongside adjusted p-values, enabling readers to assess normalization robustness. Third, validate direction-unstable genes by RT-qPCR or proteomics before building biological narratives around their regulation.

5.2 Which Normalization Is "Best"?

Our results do not identify a single best normalization. TMM and DESeq2 MoR agree closely and both rest on well-characterized statistical assumptions, making them the safest default choice for standard differential expression analyses. FPKM and TPM should not be used for differential expression analysis---a recommendation already made by Love et al. [2] and Soneson et al. [12] but still routinely violated in practice. Upper quartile normalization performs comparably to TMM and DESeq2 for most datasets but shows greater sensitivity to composition bias.

For datasets with suspected global transcriptional changes (e.g., MYC amplification, cell cycle arrest), none of the tested methods is fully appropriate. Spike-in normalization [7] or methods specifically designed for asymmetric differential expression [13] should be used instead.

5.3 The Low-Count Problem

The concentration of disagreement in low-count genes (31% reversal rate for genes with < 50 mean reads) highlights a fundamental tension in RNA-seq analysis: low-count genes are where novel biology often hides (weakly expressed transcription factors, signaling molecules, non-coding RNAs), but they are also where statistical methods are least reliable. Independent filtering based on count thresholds (as implemented in DESeq2's default pipeline) removes many of these genes, but the threshold is itself a methodological choice that affects which genes are testable.

Our NSS metric provides an alternative to hard count filtering. Rather than removing all low-count genes indiscriminately, NSS identifies the specific subset whose differential expression is normalization-sensitive, preserving low-count genes that happen to show consistent signals across methods.

5.4 Limitations

First, we used DESeq2 as the sole differential expression engine; pairing different normalizations with different DE methods (e.g., TMM with edgeR, FPKM with limma-voom) would introduce additional variability that we did not measure. Second, our dataset selection focused on two-group comparisons with clear contrasts; more complex experimental designs (time series, multi-factorial) may show different patterns of normalization sensitivity. Third, the NSS threshold of 1.0 was chosen heuristically based on the observed distribution; formal optimization of this threshold using external validation (e.g., RT-qPCR ground truth) would strengthen the recommendation. Fourth, we did not evaluate newer normalization methods such as SCnorm [14] or PsiNorm, which may reduce sensitivity. Fifth, our analysis considered bulk RNA-seq exclusively; single-cell RNA-seq introduces additional normalization challenges (dropout, cell-size variation) that require separate investigation.

6. Conclusion

Normalization choice is a consequential analytical decision that reverses the direction of differential expression for 12.3% of genes across standard RNA-seq datasets. This rate is not uniformly distributed: it is concentrated in low-count genes, amplified in datasets with composition bias, and driven primarily by the divergence between gene-length-normalized methods (FPKM/TPM) and count-based methods (TMM/DESeq2/UQ). The Normalization Sensitivity Score provides a per-gene measure of this instability, enabling targeted validation and more transparent reporting. RNA-seq differential expression results that are not accompanied by normalization sensitivity analysis should be interpreted with the understanding that roughly one in eight significant findings may not survive a change of normalization method.

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