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Batch effect

In high-throughput biological experiments, such as those involving genomics, transcriptomics, or proteomics, a batch effect refers to systematic, non-biological variations in data that arise from technical factors unrelated to the biological signals of interest, often due to samples being processed in separate batches over time or across different laboratories, instruments, or protocols.^[1] These effects manifest as unwanted shifts in data distribution, such as changes in mean expression levels or variance, which can obscure true biological differences and confound downstream analyses.^[2] Batch effects commonly originate from variations in experimental conditions, including differences in reagent lots, sample storage and preparation protocols, sequencing platforms, operator handling, or even environmental factors like ambient temperature and ozone exposure during microarray hybridization.^[1] In large-scale omics studies, they are exacerbated by the integration of datasets from multiple sources, leading to increased data heterogeneity that persists even in the era of big data and single-cell technologies.^[3] For instance, in microarray gene expression experiments, batch effects have been shown to stem from chip manufacturing variations, RNA isolation methods, or scanner settings, potentially masking subtle biological signals in multi-site studies.^[2] The impacts of uncorrected batch effects are profound, as they can inflate variability, diminish statistical power, and yield misleading conclusions, such as false associations between variables or irreproducible findings that have led to retracted publications and economic losses in biomedical research.^[1] In clinical contexts, they have contributed to errors like the misclassification of patient outcomes in predictive models, underscoring their relevance in translational applications.^[3] Despite advances in experimental design—such as randomized batch assignment or inclusion of technical replicates—batch effects remain a persistent challenge, particularly in single-cell RNA sequencing where cell isolation and library preparation introduce additional layers of technical noise.^[1] To mitigate batch effects, researchers employ computational correction methods that adjust data while preserving biological variance, including location-scale approaches like ComBat, which models and removes additive and multiplicative batch-related effects; surrogate variable analysis (SVA) and removal of unwanted variation (RUV), which identify hidden factors through matrix factorization; and more recent deep learning-based techniques such as scVI for single-cell data integration, with ongoing advances as of 2025 including BERT for multi-omics integration, BAMBOO using bridging controls, and single-cell foundation models (scFMs).^[2]^[1]^[4]^[5]^[6] These methods, often implemented in R or Python packages, have been benchmarked in initiatives like the MicroArray Quality Control (MAQC) project, demonstrating improved prediction accuracy and cross-batch comparability when applied judiciously.^[2] Ongoing efforts, including standardization by consortia like Sequencing Quality Control (SEQC), continue to refine best practices for prevention and correction in evolving high-throughput workflows.^[1]

Definition and Background

Definition

A batch effect is a systematic, non-biological variation in high-throughput experimental data that arises from technical differences between groups of samples processed together, known as batches, such as differences in reagent lots, instrument calibration runs, or laboratory conditions.^[7] These variations are unrelated to the biological variables under study and can introduce sub-groups of measurements with qualitatively distinct behavior across experimental conditions.^[7] Core characteristics of batch effects include their consistent influence on multiple samples within a single batch, which often results in shifts in the mean, variance, or distributional properties of the data across batches, thereby confounding the detection of true biological signals.^[7] When correlated with the outcomes of interest, such as disease status or treatment groups, these effects can lead to erroneous scientific conclusions by masking or mimicking biological differences.^[7] A common manifestation of batch effects is observed in exploratory analyses, where samples cluster by batch identifier rather than by biological grouping in principal component analysis (PCA) plots.^[8] This separation underscores how batch effects can dominate the overall data structure, overriding expected patterns driven by the study's biological hypotheses. In distinction from random technical noise, batch effects are structured and reproducible within specific batches, rather than being unsystematic or unpredictable across individual measurements.^[7] This organized nature makes batch effects particularly insidious in omics datasets, where they can propagate through downstream analyses if unaddressed.^[7]

Historical Development

The concept of batch effects in gene expression studies emerged in the late 1990s alongside the development of DNA microarray technology, where researchers quickly observed systematic non-biological variations between experimental runs, often attributed to differences in reagent lots, equipment calibration, or laboratory conditions.^[9] These early recognitions were implicit in discussions of technical variability during the initial adoption of high-density microarrays for genome-wide profiling, as noted in foundational overviews of the technology's challenges. Although the term "batch effect" was not yet standardized, such variations were evident in pioneering experiments that highlighted the need for normalization to ensure reproducibility across datasets.^[10] A key milestone came in 2003 with the identification of batch effects in microarray gene expression data, where Fare et al. demonstrated how atmospheric ozone exposure led to systematic degradation of Cy5-labeled samples, causing spurious inter-batch variations that confounded signal intensities.^[11] This work underscored the confounding influence of environmental factors on diagnostic models and spurred broader awareness in high-throughput genomics. By the mid-2000s, batch effects were explicitly addressed in gene expression studies; for instance, the MicroArray Quality Control (MAQC) project in 2006 revealed significant inter-laboratory and inter-platform variability, emphasizing the need for standardized protocols to combat such issues in large-scale microarray analyses. The introduction of the ComBat algorithm in 2007 marked a pivotal shift toward standardized correction methods, employing empirical Bayes frameworks to adjust for known batch covariates in microarray data while preserving biological signals, as demonstrated on datasets from diverse experimental conditions.^[9] This was further solidified by the influential 2010 review by Leek et al., which defined batch effects and their pervasive impact across high-throughput data, guiding subsequent research and tool development.^[7] In the 2010s, the rise of next-generation sequencing (NGS) amplified awareness of batch effects in even larger-scale genomics initiatives, such as The Cancer Genome Atlas (TCGA), launched in 2006 but yielding extensive data by the early 2010s. Analyses of TCGA datasets revealed how sequencing center, run date, and library preparation confounded cancer subtype classifications and somatic variant calls, necessitating advanced removal techniques to avoid false biological inferences.^[12] These challenges in NGS-era projects solidified batch effect correction as a cornerstone of reproducible omics research.^[13]

Causes of Batch Effects

Experimental Design Factors

Batch effects in experimental design often arise from the uneven distribution of biological samples across batches, which can confound biological signals with technical variations. For instance, if all control samples are processed in one batch while treatment samples are concentrated in another, any observed differences may reflect batch-specific artifacts rather than true treatment effects. This imbalance reduces statistical power and can lead to spurious associations, particularly when sample classes are unevenly represented across batches.^[1] Temporal factors during multi-day or multi-week experiments further contribute to batch effects through changes in personnel, environmental conditions, or seasonal variations. Shifts in laboratory personnel can introduce subtle differences in protocol execution, while fluctuations in temperature, humidity, or air quality across batches alter sample stability and instrument performance. For example, variations in atmospheric conditions, such as ozone levels, have been shown to impact microarray data quality in high-throughput experiments. These temporal drifts are especially problematic in longitudinal studies, where processing order correlates with exposure time, making it difficult to disentangle biological changes from technical ones.^[7]^[1] Differences in sample handling protocols between batches, including variations in storage duration, freeze-thaw cycles, and pipetting techniques, exacerbate batch effects by introducing inconsistencies in molecular profiling. Prolonged storage or multiple freeze-thaw cycles can degrade RNA, proteins, or metabolites, leading to systematic biases, while manual pipetting variability among operators—due to differences in technique or cumulative volume errors—affects assay precision. Such handling disparities are common in omics studies and can propagate non-biological variation throughout the data.^[1] In clinical trials, patient recruitment waves often create implicit batches that introduce demographic biases, as cohorts enrolled at different times or sites may differ in age, ethnicity, or other factors. For example, in large-scale genomics projects like The Cancer Genome Atlas (TCGA), samples from varying centers exhibit batch effects due to differences in sequencing platforms and protocols, confounding analyses of tumor heterogeneity with site-specific variations. This highlights the need for randomized allocation across processing batches to mitigate such design-induced confounders.^[13]^[1]

Data Processing Factors

Data processing factors contribute to batch effects through technical variations introduced during analytical and instrumental handling of samples post-collection. Instrument variability, such as differences in scanner calibration for microarray experiments or sequencing machine performance in next-generation sequencing (NGS) workflows, can systematically alter signal intensities across batches. Similarly, reagent variability arising from differences in dye lots, enzyme batches, or kit compositions in microarray hybridization or NGS library preparation introduces non-biological biases that propagate through the data.^[14] These factors often confound biological signals, as they correlate with processing order rather than experimental conditions. Protocol variations further exacerbate batch effects by introducing inconsistencies in post-collection workflows. For instance, minor differences in RNA extraction kits, the number of polymerase chain reaction (PCR) amplification cycles, or library preparation steps between sequential runs in RNA-seq experiments can lead to shifts in transcript abundance estimates.^[14] In NGS pipelines, variations in enzymatic reactions or buffer compositions across batches may amplify subtle technical artifacts, reducing the reproducibility of gene expression profiles.^[15] Such protocol-related discrepancies are particularly pronounced in high-throughput settings where multiple runs are required to process large sample cohorts. Computational factors in data processing pipelines represent another key source of batch effects, stemming from inconsistencies in software implementation or settings. The use of different versions of alignment tools, such as varying parameters in FASTQ processing or read mappers like STAR or HISAT2 in RNA-seq analysis, can produce divergent quantification results that mimic biological variation.^[14] Similarly, discrepancies in normalization algorithms or reference genome assemblies across processing batches introduce systematic offsets in downstream metrics like gene counts or variant calls.^[16] These computational artifacts highlight the need for standardized pipelines to minimize unintended technical stratification. A specific example of data processing-induced batch effects occurs in mass spectrometry (MS) workflows, where ion source contamination accumulates over sequential sample runs, leading to progressive shifts in peak intensities. In large-scale proteomic studies, this contamination necessitates periodic instrument cleaning and recalibration, creating discrete batches that introduce intensity drifts and impair protein quantification accuracy. For instance, in an analysis of 413 samples, signal deterioration after 50–70 samples resulted in batch-wise biases that confounded allele-specific expression patterns, underscoring the impact of instrumental maintenance on data integrity.^[17]

Detection of Batch Effects

Statistical Detection Methods

Statistical detection methods for batch effects rely on quantitative hypothesis testing and variance partitioning to identify systematic variations attributable to batches in high-dimensional datasets, such as gene expression profiles. These approaches assess whether observed differences between samples exceed what would be expected under random variation, often focusing on mean shifts, variance components, or multivariate distances. By testing null hypotheses of no batch differences, they provide p-values or effect sizes to quantify the significance and magnitude of batch effects, enabling researchers to determine if further correction is warranted.^[18] Distance-based methods compute pairwise distances, such as Euclidean or correlation-based metrics, between samples in the feature space of gene expression data to evaluate batch-induced clustering or separation. These distances are then subjected to analysis of variance (ANOVA) or related tests, like PERMANOVA for multivariate permutations, to assess whether inter-batch distances are significantly larger than intra-batch distances, with the F-statistic measuring the proportion of variance explained by batch factors. For instance, in radiomic and genomic datasets, this approach detects batch effects by permuting labels and comparing observed distance matrices to null distributions, achieving high sensitivity in simulated multi-batch scenarios. Such methods are particularly useful for confirming batch effects arising from processing variability, like differences in array hybridization.^[18]^[19] Surrogate variable analysis (SVA) identifies hidden batch factors by estimating unmodeled sources of variation through a combination of principal component analysis and empirical Bayes methods. The process involves first regressing out known covariates (e.g., biological conditions) from the expression matrix to obtain residuals, then applying singular value decomposition to capture the top principal components representing heterogeneity; these are refined into surrogate variables using a gene-by-gene protection mechanism to avoid over-adjustment for true signals. SVA is effective for detecting subtle, non-obvious batch effects in microarray and RNA-seq data, as demonstrated in studies where it recovered a high proportion of known artifacts while preserving biological variance in heterogeneous expression datasets.^[20] A basic statistical test for batch effects in gene expression data examines differences in mean expression levels across batches using a two-sample t-test. Under the null hypothesis H_0: \mu_1 = \mu_2, where \mu_1 and \mu_2 are the mean expressions for batches 1 and 2, the test statistic is given by

t = \frac{\mu_1 - \mu_2}{\sqrt{\frac{\sigma^2}{n_1} + \frac{\sigma^2}{n_2}}},

with \sigma^2 as the pooled variance and n_1, n_2 as sample sizes per batch; significant t-values (e.g., p < 0.05 after multiple testing correction) across many genes indicate pervasive batch effects. This per-gene approach is foundational for initial detection, often revealing batch influences in a substantial number of features in unnormalized datasets. Principal variance component analysis (PVCA) partitions total variance in gene expression data into components attributable to batches, biological factors, and residuals using a mixed-effects model framework integrated with principal components. It first performs PCA on the centered data to select the top principal components, then fits these as random effects in a variance components model to estimate batch contributions via restricted maximum likelihood; results are visualized as stacked bar plots showing batch proportions. PVCA excels at quantifying batch dominance in multi-factor designs, outperforming simple ANOVA in datasets with interaction terms.^[21]

Visualization Techniques

Visualization techniques play a crucial role in the exploratory analysis of high-throughput data, allowing researchers to intuitively identify batch effects through graphical representations of data structure and variation. These methods provide an initial assessment before applying formal statistical tests, revealing patterns such as unwanted clustering or distributional shifts that indicate technical artifacts rather than biological signals.^[7] Principal component analysis (PCA) is a widely used dimensionality reduction technique that projects high-dimensional data onto lower-dimensional space to highlight major sources of variance. In the context of batch effects, PCA plots often show samples clustering primarily by batch rather than by intended biological conditions, such as treatment groups or tissue types; for instance, the first two principal components (PC1 and PC2) may capture a significant proportion of variance attributable to batch. This separation underscores the dominance of technical variability, as demonstrated in analyses of microarray and sequencing data where biological signals are obscured.^[7]^[22] Heatmaps, typically generated from normalized expression matrices with row and column clustering, offer another effective visualization for detecting batch effects. These plots display features (e.g., genes) as rows and samples as columns, with color intensity representing expression levels; batch effects manifest as distinct stripes, blocks, or segregated clusters along the sample axis, indicating systematic shifts across batches rather than gradual biological gradients. Such patterns are particularly evident in gene expression data, where hierarchical clustering fails to group samples by biology due to batch-induced artifacts. Box plots and violin plots provide distributional summaries to compare feature intensities or summary statistics across batches. Box plots illustrate medians, quartiles, and outliers for metrics like gene expression levels or log-intensities per batch, revealing shifts in central tendency or increased spread that signal batch-specific biases; violin plots extend this by showing density estimates, highlighting multimodal distributions within batches. These are especially useful for initial quality checks, as they quantify how batch processing alters overall data scaling without requiring dimensionality reduction. In single-cell RNA sequencing (scRNA-seq), uniform manifold approximation and projection (UMAP) embeddings serve as a nonlinear visualization tool to uncover batch effects in cell populations. UMAP plots of integrated data may reveal batch-specific clusters emerging despite shared cell types, such as immune cells separating by processing batch rather than by disease state, thereby confirming technical confounding in high-dimensional cellular profiles.^[22]

Correction and Mitigation Strategies

Normalization Techniques

Normalization techniques aim to reduce batch effects by scaling and centering data prior to more advanced statistical adjustments, focusing on aligning distributions or removing systematic biases across batches without assuming parametric models. These methods are particularly useful in high-throughput genomics data, such as microarrays or RNA-seq, where technical variations from processing can confound biological signals. Global normalization, such as quantile normalization, aligns the distributions of expression values across batches by ensuring that each quantile in the sorted data from one batch matches the corresponding quantile in a reference distribution, typically the average across all batches. This approach makes the empirical distributions identical, mitigating additive and multiplicative batch biases while preserving relative intensities within samples. For instance, in microarray data, quantile normalization can be implemented using robust estimators like the median polish algorithm to handle outliers and compute summary statistics for probe sets. Originally developed for oligonucleotide arrays, it effectively reduces variance attributed to batch effects in comparative gene expression studies. Cyclic loess (or lowess) normalization addresses intensity-dependent batch biases, common in two-color microarray experiments, by applying local regression to adjust log-ratio versus log-intensity plots (MA-plots) iteratively across all pairs of arrays. In this method, loess smoothing fits a curve to the MA-plot for each pair of arrays from different batches, subtracting the fitted values to correct non-linear biases, with the process cycled through all arrays until convergence. This technique is robust to outliers and particularly effective for within- and between-slide variations in cDNA microarrays, improving the comparability of hybridizations performed in separate batches. A simple form of between-array normalization uses medians to center batches, given by the formula

y'_{gb} = y_{gb} - \median(y_{\cdot b}) + \median_g \median(y_{\cdot b})

for each gene g and batch b, where y_{gb} is the original expression value, \median(y_{\cdot b}) is the median across genes in batch b, and \median_g \median(y_{\cdot b}) is the median of the batch medians across all batches (serving as the reference). This additive adjustment shifts each batch's location to match the global reference without altering the relative scale, making it a lightweight preprocessing step for reducing location shifts due to batch-specific processing. Implemented in tools like the limma package, it is widely applied to microarray data to facilitate downstream analysis. For count-based data like RNA-seq, the RUVSeq package's RUVg method provides a normalization approach by modeling unwanted variation through factor analysis on negative control genes (e.g., those expected to have constant expression across conditions). RUVg estimates latent factors capturing batch-related variation and adjusts counts accordingly, preserving biological signals while removing technical noise; for example, it has been shown to improve differential expression accuracy in datasets with library preparation batches. This method extends traditional scaling by incorporating empirical control features, making it suitable for complex omics data with multiple sources of unwanted variation.

Statistical Modeling Approaches

Statistical modeling approaches employ parametric frameworks to explicitly model and adjust for batch effects, enabling precise removal of technical variation while preserving biological signals in high-dimensional data such as gene expression profiles.^[9] These methods leverage probabilistic assumptions about the data structure, often incorporating batch as a covariate in regression models to estimate and subtract its contribution.^[23] One prominent empirical Bayes method is the ComBat algorithm, which adjusts for batch effects in microarray and RNA-seq data by borrowing information across genes to estimate batch-specific means and variances. This shrinkage estimation protects against over-correction, particularly in scenarios with small sample sizes per batch, by assuming batch parameters follow prior distributions derived from the data.^[9] ComBat models the data as having additive and multiplicative batch effects, estimating location (\gamma) and scale (\delta) parameters via empirical Bayes priors to stabilize inferences. For each gene g, the corrected expression follows the form:

Y_{g,\text{corrected}} = X\beta_g + \gamma_{g,\text{batch}} + \delta_{g,\text{batch}} \cdot h_g + \varepsilon_g

where X\beta_g represents biological covariates for gene g, \gamma_{g,\text{batch}} and \delta_{g,\text{batch}} are gene- and batch-specific parameters estimated with empirical Bayes shrinkage, h_g denotes the original data for gene g adjusted for mean, and \varepsilon_g is the error term.^[9] Linear mixed models (LMMs) provide another key approach, treating batch as a random effect to account for its variability across samples while modeling fixed effects for biological factors of interest. In the limma package for differential expression analysis, batch can be incorporated as a random effect using the duplicateCorrelation function to estimate intra-batch correlations, with a design formula such as ~0 + group + batch to fit the model and adjust contrasts accordingly.^[23] This framework enhances statistical power by borrowing variance information across genes and handling unbalanced designs common in omics studies.^[23] Normalization techniques often serve as a prerequisite to these models, ensuring comparable scales before parametric adjustment.^[23]

Applications and Challenges

Applications in Omics Data

In genomics, batch effects in genome-wide association studies (GWAS) often stem from differences between genotyping platforms like Illumina and Affymetrix arrays, which can generate spurious associations due to inconsistent allele calling and coverage.^[24] For example, in Affymetrix 500K array data, batch-specific genotype calling algorithms have been shown to inflate GWAS results, particularly when samples are processed in separate runs.^[25] Correction via the genomic control lambda factor adjusts for this inflation by scaling test statistics, enabling reliable meta-analyses across diverse cohorts. In transcriptomics, the Genotype-Tissue Expression (GTEx) project's v6p analysis in 2017 examined RNA-seq data from multiple tissues and donors, where batch effects from sequencing centers and library preparations obscured biological signals in eQTL mapping. Conditional quantile normalization was applied to remove GC-content bias and other technical variations, facilitating robust identification of tissue-specific eQTLs across 44 human tissues from 449 postmortem donors. This approach preserved genetic regulatory patterns while minimizing artificial correlations between expression levels and experimental factors.^[26] Multi-omics integration in microbiome studies requires harmonizing proteomics and metabolomics datasets from different laboratories to counteract batch effects arising from mass spectrometry protocols and sample handling.^[27] In analyses of gut microbiome dysbiosis, reference-material-based ratio methods have successfully aligned such data, revealing coordinated microbial protein and metabolite shifts associated with host health outcomes without over-correcting biological variance.^[28] Statistical modeling approaches like ComBat, originally for single-omics, have been extended here for joint correction. The ENCODE project's ChIP-seq datasets for transcription factors provided a key case study, where uncorrected batch effects from different laboratories biased binding site predictions due to variability in signal distribution.^[29] Post-correction analyses using mixed-effects models to separate batch and chromatin variability demonstrated that batch effects dominated approximately 11% of high-variability binding sites, underscoring the need for rigorous harmonization to ensure accurate regulatory maps.

Remaining Challenges

One persistent challenge in batch effect correction is the risk of over-correction, where methods inadvertently remove genuine biological signals, particularly when batch structures confound with true subgroups such as rare genetic variants or disease subtypes. For instance, the ComBat algorithm, while effective for empirical Bayes adjustment, can lead to inflated significance in differential expression analyses if unknown sources of variability align with batches, thereby masking biologically relevant patterns. This issue is exacerbated in studies where batch factors correlate with experimental conditions, highlighting the need for risk-conscious approaches that balance correction with preservation of variance. Scalability remains a significant hurdle for applying batch correction to ultra-large datasets, such as those generated in spatial transcriptomics encompassing millions of cells. Statistical models like surrogate variable analysis (SVA), which estimate hidden factors through principal components, incur high computational costs in such high-dimensional settings, often rendering them impractical without substantial resources or approximations. Emerging scalable alternatives, such as Fugue, underscore the ongoing demand for efficient methods to handle the exponential growth in omics data volume while maintaining accuracy. Handling unknown or latent batch effects poses another critical limitation, especially in legacy datasets archived in public repositories like GEO or TCGA, where metadata on processing batches may be incomplete or unrecorded. These unmodeled artifacts can propagate biases across integrated analyses, complicating downstream inferences in meta-studies. Recent methods like nearest-pair matching (NPmatch) aim to address this by aligning samples without prior batch knowledge, but their robustness in diverse legacy contexts requires further validation. In the integration of batch effects with AI and machine learning pipelines for omics data, emerging challenges include domain shifts arising in federated learning scenarios across institutions. Federated frameworks, designed to train models on decentralized data for privacy, often encounter batch-induced shifts that introduce spurious correlations between local datasets, degrading model generalizability. Tools like FedscGen demonstrate progress in collaborative correction, yet the interplay between batch artifacts and ML-specific biases, such as in representation learning, calls for interdisciplinary advancements to ensure reliable predictions in multi-center omics research.

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