Different from other reviews in this field, we emphasize background intuition and the statistical principle of each method to help biologists better understand it. Finally, we discuss data mining problems for BCR-seq data and with a highlight on recently emerging multiple-sample analysis.High-throughput sequencing for B cell receptor (BCR) repertoire provides useful insights for the adaptive immune system. With the continuous development of the BCR-seq technology, many efforts have been made to develop methods for analyzing the ever-increasing BCR repertoire data. In this review, we comprehensively outline different BCR repertoire library preparation protocols and summarize three major steps of BCR-seq data analysis, IgH locus is located at 14q32.33, andIgκ andIgλ are located at 2p11.2 and 22q11.2, respectivelyThe antigen receptor on B cells, B cell receptor (BCR), recognizes the antigen and plays key roles in B cell development, survival and activation. The secreted form of BCR is also called antibody, which contains two identical immunoglobulin (Ig) heavy (IgH) chains and two identical Ig light (IgL) chainsi.e., V(D)J sequence annotation, clonal phylogenetic inference, and BCR repertoire profiling and mining are summarized.In this review, different BCR repertoire library preparation protocols are outlined and three major steps of BCR-seq data analysis,Ig genes undergo two layers of diversification processes to contribute to the total BCR/antibody repertoire, including the antigen-independent and antigen-dependent processes.To recognize different antigens, in each B cell,IgV exon to shape a primary antibody repertoire. In this antigen-independent process, the germline variable (V), diversity (D), and joining (J) gene segments are assembled in an ordered manner from a panel of gene segments spanning in theIg locus. The diversity of primary BCR repertoire comes from the numbers of V/D/J gene segments and is also contributed by the insertion and deletion (indel) at the joining junctioni.e., starting with a cysteine (C) and ending with phenylalanine (F) or tryptophan (W), as highlighted in the sequence annotation from IMGT V(D)J recombination, occurring during B cell development in the omentum, fetal liver, or adult bone marrow, assembles theUpon antigen stimulation, BCR undergoes another layer of diversification, including IgH class-switch recombination (CSR) and IgV somatic hypermutation (SHM), both of which are initiated by activation-induced cytidine deaminase (AID) ,9 . In To present a landscape of BCR repertoire, researchers have developed diverse approaches to prepare such a library , which cIg gene constant exon. Degenerated primer sets targeting the V gene segments [The mRNA from a pool of B cells can be subject to library preparation with a multiplex PCR strategy. The complementary DNA (cDNA) can be prepared with a random hexamer or primers annealing to theegments ,15 are egments  . Regardegments ,20 . InWhen genomic DNA was used as an input, both multiplex and one-side PCR can be applied. In multiplexed PCR, forward primer sets annealing to the V segments and reverse primers annealing to J segments are usually usedThe emerging single-cell methods enable the analysis of BCR at the single-cell level. Multiplex PCR can be apply to a single B cell to amplify the IgH and IgL chainsThe BCR repertoire sequencing (BCR-seq) libraries are usually sequenced through high-throughput sequencing (HTS) to generate data in FASTQ format. Different from other types of HTS data, the BCR-seq data analysis can be summarized into the following three major steps –30 : 1. In the As the first step, V(D)J sequence annotation infers the V(D)J gene segments and CDR3 nucleotide/amino acid sequences from the preprocessed BCR-seq data. Generally, there are two ways to annotate the sequence: alignment-based and model-based algorithms, both of which use germline Ig sequences as reference. In this task, IMGTSequence alignment, an algorithm to compare two or more biological sequences, is probably the most fundamental procedure in data analyses –33 . Ite.g., IghutilNeedleman-Wunsch alignment algorithm aims to calculate the best overall similarity score between the query sequence and a target sequence by a dynamic programming algorithm. On the contrary, the Smith-Waterman algorithm does not devote to comparing the entire sequence, but to finding the fragments with high similarity in two sequences. Both algorithms are successfully applied to DNA and protein sequence analyses, while the local algorithm is more frequently used in BCR-seq analysis. For example, Bolotin et al.i.e., classical probabilistic model and Hidden Markov Model (HMM).Due to the complexity of the BCR repertoire, researchers further introduced statistic-based methods to precisely annotate V(D)J sequences. Two types of models are frequently used in this category,Classical probabilistic model describes the biological process by a series of dependent or independent probabilistic events, and parameters can be estimated by maximizing the likelihood function of the observed data. This kind of model is widely used in many tools including ImmuneDB, VDJServer, and MIGEC. Among them, ImmuneDBi.e., germline Ig segments choice, insertion, and deletion (without consideration of mutation events). These interconnected events were described as a conditional probability density function, which is also applied by other toolsWe take IGoR as an example to illustrate the classical probabilistic model in detail. IGoRx, denote the objective function of it asPrcomb, whereθ represents the set of parameters to be determined. When obtaining the value ofθ, each query sequence can be easily annotated as the V(D)J gene segment that gives the highest observation probability. In detail, it first performs a local or global alignment between the query sequencexi and the germline gene sequencejg. Second, it marks each nucleotide as one of the basic types  of recombination. Third, IGoR substitutes the parameters (θ) and observed values from the last step into the objective function so that we would get the probabilityi·jp (the query sequencexi is expanded from the germline gene sequencejg). Fourth, IGoR repeats the above steps until all the germline gene sequences are traversed. Then the query sequenceix will be annotated as the germline gene sequencej*g with the highest probabilityi·j*p among allj germline gene sequences.For each V(D)J sequenceθ. Parameterθ can be obtained from previous experiments or estimated with the following procedure (for most cases). Based on available observations, one can calculate the likelihood function based on the probabilistic model and maximize the likelihood function to find the best parameters, and the difference between probabilistic and likelihood models is described in Box 1 (Supplementary Data). IGoR utilized Expectation Maximum (EM) algorithm to calculate the MLE estimation of parameter. The EM algorithm is a powerful statistical method in biological data analysis with latent variables, which is shown as a “coin” example in Box 2 (Supplementary Data). Briefly, the recombination event (latent variable) is an analogy to the side of “coins”, and the probability of head-side up (the observable variable) is affected by parameterθ. After repeating the E and M steps iteratively, both parameterθ and recombination events will be obtained. Once we have the parameterθ, recombination events of other homogeneous samples can be inferred with ML- or Bayesian-based method directly.The key step of this method is how to optimize the parameterDue to the huge amount of reads in a typical BCR experiment, a classical probabilistic model usually takes substantial computation time. In order to save the computation time and reduce the inference error, other researchers claimed to cluster the sequences first and annotated sequences in the same cluster as one clonal typeobserved series . The entire modeling process is named as Markov process. Different from classical probabilistic models, HMM is built up with two probability matrices:transition matrix andemission matrix.Hidden Markov Model (HMM) is another popular annotation algorithm implemented in SoDAhidden stage of a nucleotide is C, it will mostly emit a C, but it will also emit to other nucleotides such as T with a small probability, indicating a C>T mutation event. In thetransition matrix, each entry quantifies the transition probability of thei-thhidden stage to the (i+1)-thhidden stage, which can be understood as a simple Markov property. In BCR-seq analysis, the indel events further complicate the model from classical HMM. For deletion events, eachhidden stagecan either be transited from the initial state or skip all stages behind it to the next gene segment. Naturally, the closer to the start (or end) of gene segment (J or V) that stage position is, the more probably the deletion event would happen. For insertion events, an N-region topology is inserted at the junction site, which is made up of four stages (A/G/C/T) and forms a self-transition structure. Thus, thetransition matrixdefines the pair-wise transition probabilities between two nucleotides and a loop-break probability at each position.For one germline sequence, each nucleotide of it corresponds to a hidden stage, which will ‘emit’ an observation among A, T, G, and C. In particular, if theThere are several ways to improve the classical HMM model, e.g., one can use a blank stage between gene segments to block the dependence of cross-segment probabilities  and decrease the computing complexity ,58 ). AUpon antigen stimulation, B cells undergo clonal expansion in germinal center reaction and are selected by their affinitiesClustering is an unsupervised learning method to divide the unlabeled data into several classes and thus can show the unknown data structure and topology. In BCR-seq analysis, clustering is the key step to define a clonotype cluster that potentially represents B cell clonal expansion from one ancestor. As previously demonstrated, the highest abundance antibody usually is not a high-affinity antibody in a BCR repertoireClustering is usually performed in BCR-seq analysis in both annotation and phylogenetic inference steps. In BCR-seq, both PCR-amplification and sequencing steps could introduce errors ,48 . Ini.e., partition-, model-, density-, hierarchical-, and spectral-based. Basically, all methods aim to find a partition of samples in a way that samples from the same clusters are as similar as possible, while those from different clusters are as different as possible. Many classical algorithms were developed in each group. For example, in single-cell transcriptome data analysis, hundreds of clustering algorithms were developed, most of which require explicit specification of the cluster numberkk, which indicates the number of cell types, is usually less than 100kis often infeasible for B-cell repertoire clustering due to the huge number of clonal typesClustering algorithms can be roughly divided into the following five groups,et al.i.e., 2.4 mismatch in a CDR3 of 16 aa.Most clustering algorithms require a distance matrix as the input. Distance between two sequences is calculated based on their similarity or alignment score of either nucleotide or amino acid sequences. Nucleotide sequences could contain mutation hotspot information, while amino acid sequences have a much clear biological significance ,72 . AtHamming distance and Minimum edit distance (MED) are usually used to define the distance between two sequences. Hamming distance is the simplest algorithm that only counts the number of mismatches in the alignment ,77,78 e.g., IGRECk-mers between reads and germline sequences as a new filtration strategy to cluster sequences.The distance matrix requires a great deal of computing resources especially for the high-throughput BCR-seq data. In practice, this problem can be alleviated by either using an approximate algorithm or further dividing the dataset into subgroups. For sub-grouping methods, clonotypes can be grouped based on the combination of V and J gene segments or sequence length. Other methods in this line include IgRepertoireConstructor, which constructs a Hamming Graph with many sub-graphs that are defined by a threshold of hamming distanceMaximum likelihood (ML) and maximum parsimony (MP) are the most popular methods to construct a phylogenetic tree inside a clonotype cluster and infer the common ancestor, which was originally developed in evolutionary biologyp andq are introduced, wherep defines whether the node bifurcates, andq defines whether the descendant contains a mutant. These two parameters were assumed as independent in calculating the likelihood of a GCtree, which is defined by multiplying the likelihood function of each node (clonotype)latent variable, and the parameterp,q) asobservable variables. Using the initial tree topology and the observed abundance, we can get the estimated parameterThe ML method is used in both classical probabilistic model-based annotation and phylogenetic tree construction. We take GCtreeet al.et al.Tools for inferring phylogenetic tree by the ML framework based on different model assumptions. For example, TreeSimMaximum parsimony (MP), also called the minimum spanning method, is an approximate algorithm for phylogenetic tree construction. The main procedure of MP usually starts with inferring an undirected tree by a certain distance metric and is followed by an iterative step of trimming and rewiring the phylogenetic tree. The undirected tree can be constructed by the Kruskal’s algorithmet al.et al.Some existing MP-based tools, such as GLaMSTThese two types of methods have their advantage and disadvantage. ML methods can bring the best result under its model assumption, while MP methods have a significant advantage in computation time. For both types of methods, we can use the conservative tree estimation process to obtain a more confident result of both the structure of the tree and other analyses such as substitution model. For instance, we can exclude nodes without descendants or just remove trees with only a two-tier structure.The BCR-seq data contain multiple layers of information, which can be displayed in various ways. Here, we review the popular single-sample profiling approaches and also introduce the emerging profiling and data-mining approaches for multiple-sample analysis.Outcomes of BCR-seq analysis mainly include the following categories: profiling, diversity estimation, mutation frequencies (substitution model), similarity analysis to known antibodies, public (shared) clonotypes, convergent among samples, and so on ,99,100BCR repertoire can be profiled in the following ways. First, the V, D, and J gene segment usage (distribution) can be visualized by using a simple bar plot or scatter plot as well as the Ig class ,102 . Tevaluation problem), the parameterq in the Hill index can be set as 2 or +∞. To infer the diversity of the whole repertoire (estimate problem),i.e., the total number of clonotypes, the parameterq in Hill index should be set as 0. For example, Bashford-Rogerset al.et al.Diversity of a BCR repertoire is an important feature of antibody diversification. Traditionally, diversity can be evaluated with three commonly used indexes: species richness, Simpson′s index, and Shannon′s entropyet al.Currently, the BCR-seq technology is widely used in profiling the different BCR repertoires from multiple individuals or samples collected at different time points. However, tumor-infiltrate BCR repertoires are found to be heterogeneous and convergent among different cancer types, healthy degrees, and pathological stages ,122 . DIn clinical scenarios, multiple samples can be either time-point samples or sectional samples. The former corresponds to samples of an individual in different time points, presenting a dynamic profile. The latter refers to samples from different individuals at one time point. For example, time-point samples can be obtained in vaccine research, and the BCR dynamic profiles can be applied to predict vaccine response. For sectional samples, public clonotypes could reveal a convergent response, which was reported in several studies ,125 .et al.et al.In the past few decades, many efforts have been made to the annotation and phylogenetic inference for BCR repertoire analysis. With the continuous development of the BCR-seq technology, methods for extra-large data set are urgently needed. Compared to other types of biological big-data, BCR-seq data need more stable and accurate statistical models to describe the BCR repertoire in a quantitative way. Due to the large sample size (number of BCRs) in a typical experiment, deep learning models are promising to participant in different tasks of BCR-seq data analyses and mining. For example, Chen


It has been well established that the dysfunctional placenta plays an important role in the pathogenesis of preeclampsia (PE), a hypertensive disorder in pregnancy. However, it is not well understood how individual cell types in the placenta are involved in placenta dysfunction because of limited single-cell studies of placenta with PE. Given that a high-resolution single-cell atlas in the placenta is now available, deconvolution of publicly available bulk PE transcriptome data may provide us with the opportunity to investigate the contribution of individual placental cell types to PE. Recent benchmark studies on deconvolution have provided suggestions on the strategy of marker gene selection and the choice of methodologies. In this study, we experimented with these suggestions by using real bulk data with known cell-type proportions and established a deconvolution pipeline using CIBERSORT. Applying the deconvolution pipeline to a large cohort of PE placental microarray data, we found that the proportions of trophoblast cells in the placenta were significantly different between PE and normal controls. We then predicted cell-type-level expression profiles for each sample using CIBERSORTx and found that the activities of several canonical PE-related pathways were significantly altered in specific subtypes of trophoblasts in PE. Finally, we constructed an integrated expression profile for each PE sample by combining the predicted cell-type-level expression profiles of several clinically relevant placental cell types and identified four clusters likely representing four PE subtypes with clinically distinct features. As such, our study showed that deconvolution of a large cohort of placental microarray provided new insights about the molecular mechanism of PE that would not be obtained by analyzing bulk expression profiles. Preeclampsia (PE) is a hypertensive disorder of pregnancy and is the main reason for maternal and fetal morbidity and mortality . AbnormaNumerous deconvolution methods have been developed , and theP) and the Pearson correlation coefficient between the predicted and true bulk transcripts (PCCT). As PCCT can be directly calculated from a deconvolution, it has been suggested to be potentially useful for improving the performance of deconvolution  for evaluating the performance of deconvolution. We found that with the increase of SecondFC, the average correlation between cell types in the signature gene matrix decreases, but PCCP increases; when the similarity decreases to an inflection point, PCCP would reach a high level  bulk data produced by gh level . AccordiT) can then be calculated. It is assumed that the closer the estimated cell-type proportions to true cell-type proportions, that is, a higher PCCP, the closer the predicted expression of bulk transcripts to true expression, that is, a higher PCCT. It has thus been proposed that maximizing PCCT may have the effect of maximizing PCCP  and late-onset PE (LOPE) depending on the gestational age (GA) (34 weeks) of disease onset . FollowiTOP2A and MIK67, both of which are related to cell proliferation, and the keratin gene KRT7 is highly expressed in EVT too. The other marker genes of EVT are HLA-G, which is involved in the immune tolerance process , the cell undergoes phenotypic changes termed the EMT process in order to gain the invasive ability . It has Placenta hypoxia is one of the most significant clinical manifestations of PE . This waIt has been reported that the placenta of PE is likely hormonally compensated in response to development deficiency . Here, wROC less than 0.9, indicating that PE is a heterogeneous and complex disease that may involve multiple subtypes and cannot be easily described by using one model.As the predicted cell-type-level expression profiles were biologically relevant and provided more details about the altered PE canonical pathways, we explored whether they could better distinguish PE from normal controls than the bulk expression profiles did. For each of the six above-mentioned cell types, we used 80% samples to train an SVM model to distinguish PE from normal samples by using the predicted cell-type-level expression profiles and then tested it using the 20% remaining samples see . HoweverAlthough EOPE is generally considered more severe than LOPE, the real situation is usually more complex and severe and nonsevere PE types are actually difficult to distinguish by their subjective clinical indicators . The cohAs a comparison, we first conducted unsupervised clustering of PE samples based on their bulk expression profiles by using negative matrix factorization (NMF) see . BecauseWe next conducted unsupervised clustering of PE samples using the predicted cell-type-level expression profiles of each of the six cell types and investigated their association with clinical features. We found that the clustering results of all six cell types except for SCT were all significantly associated with some clinical features . The reaGiven that the predicted cell-type-level expression profiles of the above five cell types were strongly linked to clinical features, we constructed an integrated expression profile for each sample by combining the predicted expression profiles of the highly variable genes of each cell type and then conducted unsupervised clustering see  and founFor example, Cluster 1 has a significantly higher proportion of intrauterine growth retardation (IUGR), which consists of the higher “mean umbilical PI”—a potential IUGR predictor , compareIn conclusion, by using the integrated expression profiles, we obtained four clinically distinct PE subtypes that are significantly associated with not only fetal state-related but also maternal state-related clinical features that would not be observed by using the bulk expression profiles , highlighttps://singlecell.broadinstitute.org/single_cell/study/SCP424) that includes single-cell data produced by 10X, Drop-seq, and inDrops sequencing platforms. The cohort of placenta microarray dataset was built by https://www.ebi.ac.uk/arrayexpress/experiments, E-MTAB-6678, E-MTAB-6701). Datasets from GEO were downloaded with accessions above through the website (https://www.ncbi.nlm.nih.gov/geo).A number of PBMC datasets were used for developing the deconvolution pipeline. The bulk PBMC datasets included Finotello’s PBMC RNA-seq dataset  GSE1075 GSE6513 with celWe followed Francisco’s recommended strategy on marker gene selection. Given a single-cell reference gene expression matrix, we applied the following parameters to select the marker gene set: logFC ≥ 1 and logCPM ≥ 1. For SecondFC, we determined the relationship between SecondFC and the average correlation between cell types in the signature gene matrix, setting it to no less than 6. Here, logFC means log fold change between the highest expressed cell type and the average expression of other cell types, logCPM means the log average normalized expression level among all cell types, and SecondFC means the average expression fold change of a given marker gene between the highest expressed cell type and the second-highest expressed cell type. When evaluating different deconvolution methods, we ranked the marker genes by logFC and selected a given fraction of top-ranked genes, for example, top 5%, 10%, … 100%, and averaged the expression counts of all cells in each cell type to construct the signature gene matrix for the selected marker genes.https://CRAN.R-project.org/package=nnls), ordinary least squares (OLS) (https://www.R-project.org/), robust linear regression (RLR) (https://www.stats.ox.ac.uk/pub/MASS4/), FARDEEP (https://github.com/YuningHao/FARDEEP), and CIBERSORT (https://cibersort.stanford.edu/), while the three single-cell reference-based methods are DWLS (https://github.com/dtsoucas/DWLS), MuSiC (https://github.com/xuranw/MuSiC), and SCDC (https://github.com/meichendong/SCDC). In addition, we added CIBERSORTx (https://cibersortx.stanford.edu/), which is based on CIBERSORT’s improved method of using single-cell data as input.We evaluated nine deconvolution methods in this study, among which five bulk reference-based methods and three single-cell reference-based methods were recommended by Francisco et al. . The fivThe single-cell reference expression matrix used for the deconvolution of placental microarray data was constructed from the single-cell placental atlas produced by We randomly selected 80% of the samples (training set) to train an SVM model and tested the model using the 20% remaining samples. When training the SVM model, we first identified the differentially expressed genes (DEGs) between PE and normal controls by controlling log CPM >4 using the package of “edgeR” in R. The log-normalized expression profiles of DEGs were then used as the input to train SVM model. For the SVM model, we used svm.SVC classifiers from the scikit-learn library in Python. For the kernel, we chose “linear”. For other parameters like degree and gamma, we used the default parameters in the function svm.SVC. For the hyperparameter, C was grid searching between 0 and 2, with 0.2 intervals, and fivefold cross-validation was performed on the training set to find the most appropriate hyperparameter C. The hyperparameter C was determined and then retrained for the whole training set and tested on the test set.We first log-normalized raw expression counts and selected highly variable genes by using the “mean.var.plot” method in the Seurat package, with the parameter “mean.cutoff” > 0.5. The “dispersion.cutoff” parameter was tried between 1 and 2.5, with 0.1 intervals, to ensure the stability of unsupervised clustering results. Next, we used the “ScaleData” method to scale the data to maximize the variation between samples. Finally, we used the negative matrix factorization (NMF) to do unsupervised clustering. The input of NMF was the scaled data, and the output of the NMF was the specified k clusters, where k is given artificially. To determine the optimal number of clusters, we iteratively tested k from 2 to 10. In each iteration, we calculated the cophenetic coefficient (CC) of the clusters, which represents the stability of clustering. Ideally, CC remains stable initially when k increases from 2 and then drops quickly when k continues to increase, and the k before the quick drop of CC would be selected. In practice, we would try different values for “dispersion.cutoff” when selecting highly variable genes and selected the one where we could identify the best k.t-test to check the difference between pairs of clusters, where p values were corrected by FDR; when the data type is categorical, we used the Chi-Square test.Most of the clinical features are in numerical values. To test the significance of the association of a clinical feature with the clustering of PE samples, when the data type of the clinical feature is numerical, we used analysis of variance (ANOVA) to inspect whether there is any difference in the mean of the clinical features in between clusters, and used T, the PCC between the predicted expression and true expression of bulk transcripts that can be calculated given estimated cell-type proportions. To have an approximate solution to this problem, we designed several benchmark tests that likely have a similar degree of challenges to the deconvolution of PE placental microarray data and found CIBERSORT performed the best across these tests. CIBERSORT was therefore chosen as the deconvolution method of our study. The successful validation of the biological relevance of the predicted cell-type-level expression profiles of the major placental cell types using their marker genes also confirmed that the deconvolution results by CIBERSORT can be trusted. Based on our experience, the CIBERSORT-based practical pipeline may also well be suited for the deconvolution of other microarray datasets.In this study, we aimed to reanalyze a large cohort of PE placental microarray data through deconvolution. For this purpose, we first attempted to develop a practical pipeline by experimenting with the strategies for marker gene selection and several deconvolution methods recommended by Francisco’s benchmark study . While tIn this study, the deconvolution of PE placental microarray data has resulted in several important findings of PE. First, the proportions of EVT and VCT in the placenta are significantly altered in PE, but in different directions, with EVT increasing and VCT decreasing. It has been shown that the differentiation of VCT to EVT and the transition of EVT to gain invasive ability are both inhibited by PE . ConsistThe discovery of clinically distinct clusters by this study is of great value to the field of PE. For example, a new diagnostic model can be developed based on the classification of these clinically distinct clusters, such that PE patients can be assigned into different groups and different treatment plans can be applied. New therapeutic drugs targeting the most severe PE may also be developed by selecting drug target genes from the marker genes from the PE cluster with the most severe outcomes. Moreover, there is a rich trove of bulk RNA-seq or microarray data in the public domain, with many having disease-related clinical information. The fact that the deconvolution of PE placental microarray data led to several new findings on the disease strongly suggests that similar deconvolution studies should be conducted to reanalyze disease-related bulk data to generate new insights into the molecular mechanisms of diseases.


As the cost of RNA-sequencing decreases, complex study designs, including paired, longitudinal, and other correlated designs, become increasingly feasible. These studies often include multiple hypotheses and thus multiple degree of freedom tests, or tests that evaluate multiple hypotheses jointly, are often useful for filtering the gene list to a set of interesting features for further exploration while controlling the false discovery rate. Though there are several methods which have been proposed for analyzing correlated RNA-sequencing data, there has been little research evaluating and comparing the performance of multiple degree of freedom tests across methods.We evaluated 11 different methods for modelling correlated RNA-sequencing data by performing a simulation study to compare the false discovery rate, power, and model convergence rate across several hypothesis tests and sample size scenarios. We also applied each method to a real longitudinal RNA-sequencing dataset.Linear mixed modelling using transformed data had the best false discovery rate control while maintaining relatively high power. However, this method had high model non-convergence, particularly at small sample sizes. No method had high power at the lowest sample size. We found a mix of conservative and anti-conservative behavior across the other methods, which was influenced by the sample size and the hypothesis being evaluated. The patterns observed in the simulation study were largely replicated in the analysis of a longitudinal study including data from intensive care unit patients experiencing cardiogenic or septic shock.Multiple degree of freedom testing is a valuable tool in longitudinal and other correlated RNA-sequencing experiments. Of the methods that we investigated, linear mixed modelling had the best overall combination of power and false discovery rate control. Other methods may also be appropriate in some scenarios.The online version contains supplementary material available at (10.1186/s12874-022-01615-8). RNA-sequencing (RNA-seq) technology has revolutionized how we study and understand the underlying pathobiology of disease. Recently, declining sequencing costs have allowed for more complex investigations, including correlated and longitudinal study designs. In particular, longitudinal designs have become increasingly popular, as they allow researchers to understand the dynamics of gene expression across time and how these dynamics differ between groups of subjects. However, complex study designs demand more sophisticated analysis methods. As with single timepoint designs, careful pre-processing of longitudinal RNA-seq data is still necessary prior to analysis to remove artifacts produced during sequencing , 2. FollIn longitudinal RNA-seq studies, researchers are often interested in multiple hypotheses. For example, many longitudinal RNA-seq studies include repeated measures from each subject over time, with subjects coming from multiple treatment groups. This allows for the investigation of between-subject comparisons, such as a test for differences in gene expression between treatment groups at a particular timepoint; within-subject comparisons, such as a test for differences in gene expression across two timepoints in a single treatment group; or interaction effects to compare changes over time between groups. Furthermore, studies with more than two timepoints per subject might involve multiple comparisons across different timepoints in order to characterize how gene expression changes across time.In the situation where there are multiple hypotheses to be tested for each gene, the ability to perform an omnibus test, or a test where multiple hypotheses are evaluated, is valuable for controlling false discovery rates. For example, in a study with multiple timepoints per subject in which time is treated categorically, a researcher might wish to compile a list of genes that change over time for further investigation. In such a situation, one could perform a series of hypothesis tests to identify the differentially expressed genes (DEGs) between each pair of timepoints and perform a multiple testing correction to each hypothesis test individually to control the false discovery rate to 5%, for example. However, because each hypothesis test may produce different false positive genes, when lists of significant genes are aggregated across multiple hypotheses, the percentage of false positives in the aggregated list will be greater than 5% without additional adjustment . Thus, pSeveral different methods have been proposed for the analysis of longitudinal RNA-seq data. Popular analysis packages such as edgeR , 5 and DThe limma  package,Recently, several methods have been proposed for longitudinal and other correlated RNA-seq studies. These methods generally use random effects or covariance structures to account for the correlation in the data while also considering the unique characteristics of RNA-seq data such as overdispersion. Many methods developed for correlated RNA-seq data are limited by the fact that they do not allow for multiple treatment groups or additional covariates . Finally, we provide recommendations as to which models are most appropriate under various circumstances.We compared methods which have been proposed for correlated RNA-seq experiments and that allow for multiple treatment groups, covariates and/or timepoints, and can be used to perform multiple DF tests. We describe the selected methods below. Additional information on each method is available in Standard RNA-seq analysis tools generally use a linear modelling framework with transformed data, or a generalized linear model (GLM) framework, assuming a negative binomial distribution. In studies with correlated designs, these methods can be implemented with the caveat that the model assumptions, such as the independence of observations, will not be met, or adjustments can be made to attempt to account for the correlation of the data. In this study, we tested three of the methods from the most popular RNA-seq analysis packages: limma, edgeR, and DESeq2.The R package limma was originally created for the analysis of microarray expression data, which are approximately normally distributed . limma eThe edgeR and DESeq2 packages both employ a negative binomial GLM framework to address overdispersion –6. Both Generalized estimating equations (GEE) are a semi-parametric extension of GLM that can account for correlation between observations . This meOne drawback to GEE models is that sandwich estimators have poor performance at small sample sizes. To address this issue, we used the small sample size adjustment proposed by Wang and Long , which uGeneralized linear mixed models (GLMM) are an extension of GLMs that use random effects to account for correlation. Similar to the methods implemented in edgeR and DESeq2, in using the GLMM framework, the gene expression for each gene can be modeled using a negative binomial distribution, which accounts for the overdispersion.When using negative binomial mixed modelling (NBMM), parameter estimation can be analytically complex and there are multiple approaches that can be used. We consider two maximum likelihood estimation approaches, Laplace (NBMM-LP) and adaptive Gaussian quadrature (NBMM-AGQ) as well as the pseudolikelihood approach (NBMM-PL).The rmRNAseq package employs a method similar to the limma+voom method in which the data are first transformed using the voom approach and then a linear model is fit for each gene using the transformed data. However, within the rmRNAseq framework, models are fit using a continuous autoregressive correlation structure to account for correlation in the data.A similar approach is to use linear mixed modelling (LMM) with random effects to account for correlated data after applying a normalizing transformation. We test this approach using a variance stabilizing transformation (VST), as demonstrated in Vestal et al. .https://github.com/ewynn610/corrRNASeq.We implemented each method using R (version 4.0.2). All analysis was carried out on a Linux high performance computing (HPC) cluster and parallel processing with 8 cores was used for all methods besides limma, DESeq2, and edgeR. Table Offsets to adjust for differences in library size were included in models for all except three methods Table . The tra∗ and DESeq2 ∗). When including this extra fixed effect, the group term was not included in the model as it is inestimable.The models using the edgeR and DESeq2 packages were fit in two ways. First, correlation was ignored and a model was fit with an intercept, time and group main effects, and an interaction term. Second, a fixed effect for subject was included in the model  for the edgeR, DESeq2, NBMM-LP and NBMM-AGQ analyses. For all of these methods excluding edgeR, this required fitting two models for each test, a full model as well as a reduced model. The GLMMadaptive package used for fitting NBMM-LP models offers the option of using a multivariate Wald test instead of an LRT test. However Tsonaka & Spitali  found thχ2 test as implemented by the esticon function in the doBy package [F-statistic outlined by Smyth [p-values are computed using an F-test with augmented degrees of freedom. The rmRNASeq package calculates p-values by building a distribution of null test statistics from data generated by a parametric bootstrap procedure and then computing the proportion of null statistics greater than or equal to the observed F-statistic.Hypothesis testing for GEE was done using a Wald  package . F-tests package , 34. Theby Smyth  for hypoY. Let Ygij be the expression level of gene g for the ith subject and jth observation, with E(Ygij)=μgij. Further, let αg be a dispersion parameter for gene g with In order to evaluate and compare the testing characteristics of the previously described methods, we performed a simulation study. We used a two group design (e.g. treatment and control) with four observations per subject. A negative binomial distribution was used to simulate a matrix of counts Xi1 is an indicator variable signifying whether the ith subject is in the treatment group or not, and Xij2, Xij3 and Xij4 are indicator variables representing whether observation j was taken at the 2nd, 3rd, or 4th timepoint respectively. Each βgk,k∈0,...,7 is a fixed effect regression coefficient specific to gene g. Finally, bgi is the random intercept for gene g and subject i which is normally distributed with a mean of 0 and a variance of where N samples had less than 1 count per million (CPM), where N was equal to the number of samples collected for a single group and timepoint. We simulated datasets to contain a mix of null and differentially expressed genes by changing the interaction coefficients for 20% of genes. In order to mimic real data, βg0,αg and βg0 was derived by scaling the randomly drawn CPM values to add up to one million and then multiplying each scaled value by a total library size of 25 million. Then, βg0 was set to the log of this value.Table measures , 37. Thep-values [We analyzed simulated data using each method as described in the implementation section. Models for each gene were fit using fixed effects for group and time variables, which were both treated as categorical, as well as the interaction between group and time. A random intercept for each subject was included in models for methods in which random effects are possible. After the models were fit, the percentage of models that successfully converged for each method was calculated, and non-converged models were removed. Then the false discovery rate (FDR) and power were calculated for four different multiple DF tests: a between-subject test, a within-subject test, an interaction test, and a global test Table . Power ap-values  and a siN=21) or cardiogenic shock . Further information on the study design and methods is available in Braga et al. [We applied the analysis methods previously outlined to a publicly available, longitudinal RNA-seq dataset of 96 whole blood samples from 32 patients experiencing circulatory shock who were admitted into the ICU (GEO Dataset: GSE131411). For each patient, three blood samples were collected: one within 16 hours after ICU admission, one 48 hours after admission, and one seven days after admission or at discharge. Subjects were categorized by whether they experienced septic shock , which reduced the total number of genes analyzed to 14,340.The goal of our analysis was to investigate how the gene expression of shock patients changed over time and how these changes differed between patients with SS versus CS. To accomplish this, for each method we fit a model with fixed effects for the type of shock and timepoint  as well as the interaction between the two variables. A random intercept for each subject was included in models for methods in which random effects are possible. All models were fit as described in the implementation section. As with the simulation study, the percentage of models that failed to converge for each method was calculated and non-converged models were removed.p-values for multiple comparisons and the DEGs for each method and test were identified using a 0.05 FDR threshold.For each model, we ran four different multiple DF hypothesis tests: a between-subject test to assess if there was a difference in gene expression between the SS and CS groups at any timepoint, two within-subject tests to assess if there was a change in gene expression over time in the SS group or the CS group, and a test to assess if any of the interaction coefficients were significant. The Benjamini Hochberg method was used to adjust Because LMM exhibited comparatively good behavior in the simulation study, we used the results from this method to explore the patterns in the changes in gene expression over time in the SS and CS groups. All analysis was done for each group separately. First, we subset the data to include only genes that were significant in the multiple DF test for difference in gene expression at any timepoint in the SS group or CS group. For these genes, we computed the predicted gene expression  for each gene at each of the three timepoints for the group in question. We then constructed heatmaps for these genes, with genes clustered hierarchically using a correlation distance metric and a complete linkage clustering method. We visually inspected the heatmaps to decide where to cut each clustering tree to identify clusters that represented distinct profiles of change over time.After clustering, we ran functional enrichment analysis on the genes in each cluster to better understand the functional role of genes with different expression profiles over time. Analysis was executed using the topGO package in R  using bi% for any of the sample sizes tested. Figure p-value for the corresponding hypothesis tests could not be calculated. The transparent portion of the bars in Fig. Of the 11 methods evaluated, only 3 methods  had average non-convergence rates above 0.1N=3 per group, about 21% of the full models did not converge and the reduced model(s) for an additional 10% of genes did not converge. Comparatively, at N=3 per group around 16% and 15% of models did not converge for NBMM-PL and LMM respectively. For all three methods, non-convergence rates decreased with increasing sample size, though the magnitude of the decrease was larger for NBMM-PL and LMM than for NBMM-LP. At N=10 per group, NBMM-PL and LMM both had non-convergence rates around 4% while NBMM-LP had a non-convergence rate of 11% with at least one reduced model failing to converge for an additional 15% of genes.NBMM-LP had the highest non-convergence rates at all sample sizes, even when only considering cases in which only the full model did not converge. At For all three methods and at all sample sizes, at least 90% of convergence failures were due to model singularities, with remaining non-converged models reaching model iteration limits or experiencing other errors which prevented the model from fitting properly. On average, the random intercept variance used to simulate the data was lower for genes that did not converge while the dispersion was generally higher . These rN=3 per group), but the FDR was increasingly inflated for the larger sample sizes. Conversely, DESeq2* and edgeR* had an inflated FDR at N=3 and N=5 per group, but at N=10 per group the rate was close to the nominal value. DESeq2 and edgeR (ignoring correlation) both had conservative FDR for the interaction and within-subject test, but showed inflated rates for the between-subject test and test for any significant coefficient. Across all of the tests, LMM was slightly conservative while NBMM-PL was slightly inflated except for the between-subject test, in which it was conservative. Finally, rmRNASeq had very conservative FDR values across all tests. For the majority of methods and tests, FDR approached the nominal rate (dashed line) and had increasing power with increasing sample size.Figure N=10 per group, showed similar power to LMM and NBMM-PL at this sample size. Similarly, limma, which had close to nominal FDR at N=3 per group, had comparable power to LMM and NBMM-PL for most tests at this sample size and had more power than either method for the between-subject test.Of the methods that had FDR values which were conservative or close to the nominal rate across all sample sizes and conditions, LMM and NBMM-PL generally had the highest power. rmRNASeq, which showed conservative FDR values, had low power, particularly at the smaller sample sizes. For the within-subject test and the test for significant interaction effects in which edgeR and DESeq2 (ignoring correlation) exhibited conservative FDR values, both methods were less powered than LMM and NBMM-PL at all sample sizes. DESeq2* and edgeR*, which had close to nominal FDR values at N=3 per group, no method that had conservative or close to nominal FDR had high power. For the within-subject test, LMM, NBMM-PL and limma had power values near 60% at N=3 per group, but no other tests showed power values this high for methods without severely inflated FDR. The power values at N=5 and N=10 per group were much stronger with LMM and NBMM-PL having power values near or above 80% for all tests at N=10 per group.At the smallest sample size, p-values from the null features in each simulated dataset are shown for each combination of method, test, and sample size in The distributions of the raw Table NBMM-LP had the largest percentage of non-converged models with 4.33% of the full model fits not converging . However, in the analysis of the reduced dataset in which each group was filtered to ten random subjects, this test still had the most DEGs across methods, while the test for differences across time in the CS group had the least amount of DEGs. This may indicate that the changes in gene expression over the course of treatment are more prevalent in SS patients than CS patients.Table N=10 per group) all three methods exhibited FDR values close to the nominal rate with LMM showing conservative rates compared to the other three methods.The differences in the number of DEGs for each method was generally what would be expected based on the results of the simulation study. NBMM-AGQ showed relatively inflated FDR values in the simulation study, and in this analysis this method found more DEGs than most other methods, particularly for the within-subject and interaction tests. DESeq2 and edgeR (ignoring correlation) had high DEG counts for the between-subject test and low DEG counts for the within-subject and interaction tests, which is also in line with the simulation results. limma also showed a mix of conservative and anti-conservative behavior in terms of the number of DEGs for each test. Finally, DESeq2*,edgeR*, NBMM-PL, NBMM-LP and LMM all had relatively moderate numbers of DEGs across all tests, with DESeq2*, edgeR*, NBMM-LP and NBMM-PL generally finding slightly more DEGs than LMM. This also corresponds to the simulation results in which in the largest sample size scenario  at least one GO term was significantly enriched. Table In RNA-seq studies with longitudinal and other correlated designs, researchers are often interested in multiple hypotheses. Multiple DF tests allow researchers to assess multiple hypotheses at once, which is a useful method for selecting lists of genes for further exploration and can also be valuable in FDR control. Recently, several researchers have developed and compared analysis methods for analyzing longitudinal RNA-seq data. However, there has been little research evaluating and comparing these methods in the context of multiple DF testing. Understanding the comparative performance of various multiple DF hypothesis testing methods is becoming increasingly important as complex study designs become more common in correlated RNA-seq designs.N=10 per group). Conversely, limma had optimal FDR values at the smallest sample size, but these increased for the larger sample sizes. DESeq2 and edgeR (ignoring correlation) showed a mix of conservative and anti-conservative behavior. rmRNAseq had conservative FDR values, but was also extremely underpowered, particularly at the lower sample sizes. LMM and NBMM-PL generally had the highest power of the methods that had FDR values which were conservative or close to the nominal rate across all sample sizes and conditions.Of the methods compared in this study, LMM using data transformed using VST generally exhibited FDR closest to the nominal rate across the different sample sizes and multiple DF tests. NBMM-PL generally resulted in FDR values close to nominal as well, though slightly more inflated than LMM. GEE, NBMM-AGQ, and NBMM-LP had high FDR values across all simulation scenarios. DESeq2* and edgeR* had inflated FDR values at small sample sizes, but were relatively close to the nominal value for the highest sample size . In analysis of the shock dataset, which may have a correlation structure that is not strictly compound symmetric, rmRNAseq did behave more similarly to other methods than in the simulation study, though we found that this was driven partially by sample size. Still, because complex RNA-seq studies are becoming more common, future research concerning the performance of multiple DF tests on data with different correlation structures and models with more complex random effects structures would be beneficial.We did not explore the use of multiple DF tests in the context of single cell RNA-sequencing (scRNA-seq). Because gene expression of cells from the same sample or subject is more similar than cells from different samples , multi-sN=3 per group, so we suggest that at least five subjects be included per group when possible.As the cost of RNA-seq experiments decreases, it becomes increasingly feasible to perform experiments using correlated designs, including longitudinal studies. Because these studies often involve multiple hypotheses and also require initial filtration to a set of genes for further exploration, multiple DF tests are a valuable tool for correlated RNA-seq data. In this work, we tested several modelling methods for longitudinal RNA-seq data with an emphasis on multiple DF hypotheses tests. Through a simulation study, we found that overall, LMM exhibited the best performance in terms of controlling FDR at nominal levels while maintaining the power to detect differential expression, though there were convergence issues at low sample sizes. limma offers a good alternative for small studies since it did not have convergence issues and had adequate FDR control at the smallest sample size. However, all methods were underpowered at Multiple DF testing is a valuable tool for selecting interesting genes for downstream analysis while also controlling the FDR. However, as we show in this study, there are many methods that allow for multiple DF testing all with different levels of efficacy. Making an informed decision when choosing a method based on the study goals as well as design elements such as sample size is key in producing useful, meaningful findings.Additional file 1 Supplementary methods, results, tables, and figures.


Each type of omics data including genomics, epigenomics, transcriptomics, proteomics, metabolomics, and metagenomics mainly provides the profile of one particular layer for a cell or sample . IntegraSince multi-omics strategies could be more powerful than single omics, combining different types of single-cell or bulk sequencing data for a more comprehensive exploration has become increasingly popular and important . In thisGuo et al. found that the mutations in TP53 and KRAS were significantly associated with the poor prognosis of intrahepatic cholangiocarcinoma (ICC). They further classified the ICC patients into different subgroups based on the mutation feature of TP53 and KRAS, which could benefit the clinical management of ICC. Johann et al. uncovered that the mutations of AKT1 and TP53 signaling pathways were closely associated with the pulmonary sclerosing pneumocytoma (PSP) through integrative analysis of genomic, transcriptomic, radiomic, and pathomic data. The insights into the underlying etiology and molecular behavior of PSP gained in this study may benefit corresponding therapy. Gao et al. constructed an effective prognostic model for breast cancer using the differentially expressed genes among distinct glycosylation patterns. Their results highlight the value and importance of risk score characterization based on glycosylation patterns for predicting the overall survival and immune infiltration of breast cancer patients. Hao et al. identified two subgroups of MYC signaling inhibition and activation for lung adenocarcinoma (LUAD) through joint analysis of genomics, transcriptomics, and single-cell sequencing data from multiple cohorts. The two LUAD subgroups discovered by them exhibited significant differences in terms of prognosis, genomic variations, immune microenvironment, as well as clinical features. Additionally, Jiang et al. built and validated a model for predicting the prognosis of LUAD by integrating bulk and single-cell RNA-seq data. They also detected two distinct subtypes of LUAD patients that differed in prognosis and immune characteristics. Sun et al. systematically analyzed the transcriptome of synovial sarcoma in terms of gene expression, alternative splicing, gene fusion, and circular RNAs. Their integrative analysis provided new insights into the transcriptomic profile and the underlying molecular mechanism of synovial sarcoma. Wang et al. constructed a clinical diagnostic map and a cluster prediction model for glioblastoma based on the methylation, expression, and single-cell sequencing data. The classification method developed by them could potentially promote the analysis of methylation heterogeneity for the promoter CpG islands in glioblastoma. Zhao et al. revealed high cellular heterogeneity in both malignant and immune cells of diffuse large B-cell lymphoma (DLBCL). They provided novel insights into the transcriptional dynamics of the tumor microenvironment for DLBCL. Zhang et al. established a prognostic model based on eight genes  for predicting the overall survival of head and neck squamous cell carcinoma (HNSCC) patients. The low-risk and high-risk groups of HNSCC separately showed higher and lower immune scores, thus those eight gene signatures have the potential to be used in the clinical management of HNSCC. Li et al. classified hepatocellular carcinoma patients into high-necroptosis and low-necroptosis groups, which had a significant difference in survival time. They found that the high-necroptosis patients were with an enriched expression of immune checkpoint-related genes and could benefit from certain immunotherapy. Wang et al. uncovered four dysregulated oncogenic signaling pathways and identified related potential prognostic biomarkers for pan-cancer through systematic analysis of the TCGA multi-omics data. Their results could facilitate a better understanding of the function of oncogenic signaling pathways in human pan-cancer. Kujawa et al. systematically evaluated the influence of six different data integration methods on single-cell analysis. They found that ComBat-seq  for mouse endothelial cells based on the sequencing data of 203 samples from 71 different conditions. ECO could enable researchers to friendly explore endothelial expression profiles of diverse tissues in conditions of certain genetic modifications, disease models, and other stimulations in vivo.mBat-seq , limma (mBat-seq , and MNNmBat-seq  could efThe studies published on this Research Topic discovered meaningful results and offered new insights into corresponding biomedical research. As we all know that the cost of sequencing technologies is gradually decreasing, which can facilitate the conduction of multi-omics investigations. Bulk and single-cell protocols have their own advantages and limitations. Compared to single-cell sequencing methods, bulk approaches do not need living cells and the experimental procedures are usually simpler . DissectCollectively, joint analysis of bulk and single-cell multi-omics data can help us gain a more comprehensive and systematic view of biological and clinical samples. The innovation of various omics profiling technologies and related machine learning methods for integrating different types of data will further make multi-omics exploration more feasible and easier. We hope the studies published on this Research Topic will inspire related biomedical researchers to better understand the benefit and value of multi-omics strategies.


The central role of proteins in diseases has made them increasingly attractive as therapeutic targets and indicators of cellular processes. Protein microarrays are emerging as an important means of characterising protein activity. Their accurate downstream analysis to produce biologically significant conclusions is largely dependent on proper pre-processing of extracted signal intensities. However, existing computational tools are not specifically tailored to the nature of these data and lack unanimity.Here, we present the single-channel Protein Microarray Analysis Pipeline, a tailored computational tool for analysis of single-channel protein microarrays enabling biomarker identification, implemented in R, and as an interactive web application. We compared four existing background correction and normalization methods as well as three array filtering techniques, applied to four real datasets with two microarray designs, extracted using two software programs. The normexp, cyclic loess, and array weighting methods were most effective for background correction, normalization, and filtering respectively.https://metaomics.uct.ac.za/shinyapps/Pro-MAP/.) for those not well versed in the R programming language.Thus, here we provided a versatile and effective pre-processing and differential analysis workflow for single-channel protein microarray data in form of an R script and web application (The online version contains supplementary material available at 10.1186/s12859-022-05095-x. Protein microarray technology enables the simultaneous monitoring of expression levels for hundreds to thousands of proteins, to quantify their interactions and associated functions . In partThe design of high-throughput protein microarrays is based on, and therefore bears several similarities to, the established gene expression microarrays. As a result, researchers have often adapted methodologies and computational tools originally developed for gene expression microarrays to protein microarrays. However, as has become increasingly apparent, there are several distinct features that distinguish both arrays and should subsequently affect their analysis. For instance, most protein arrays have much fewer probes than gene expression arrays , 11 thusnormexp background correction and batch filtering on provided data. It also offers the user with option of comparing MA plots to determine which normalization techniques  best suit the data. However, this pipeline requires intermediate programming skills at least, thereby limiting the user pool. In contrast, PMA is built in JAVA and can be used via a fairly simple graphical user interface. It conducts neighbourhood background correction and net intensity correction, enables the user to define noise threshold and replicate CV thresholds, and finally runs intensity and quantile normalization amongst sub- and whole arrays. Finally, ProCAT uses neighbourhood background correction, data filtering, and scale normalization to pre-process microarray data. However, with these last two pipelines, there is no justification provided as to why these methods have been selected above other available methods. Furthermore, these tools have several limitations, including the file formats recognized and array layouts accepted by the pipelines, which we address in our current pipeline.To the best of our knowledge, there are currently three major tools available for single channel protein microarray analysis: Protein Array Analyzer (PAA) , ProteinIn this study, we explore the various methods available for the analysis of single channel protein microarray data, largely focusing on background correction, normalization, and array filtering. Based on our findings, we have developed a robust and flexible statistical pipeline suitable for use in the pre-processing of all single channel protein microarrays regardless of array design, data extraction software used, or file format. The proposed single-channel Protein Microarray Analysis Pipeline (Pro-MAP) follows the logical steps involved in the analysis of microarray data , 16 and To develop our pipeline, we compared four datasets, with two array designs, extracted using two image software programs, producing two file types. We compared four background correction, four normalization, and three array filtering methods to determine the most effective combination for the pre-processing of single-channel microarray data.Following extraction of pixelated data from raw image files, the usual first step succeeding spot filtering in protein microarray data analysis involves the subtraction of the background signal from the foreground signals to generate net intensities for each spot. However, heterogeneity in the surrounding background signal makes background subtraction less robust than it might at first sight appear. Using MA (mean difference) plots, which depict differential expression, we therefore compared four different background correction methods on the PDAC technical replicates (TR) cohort dataset. The normalized M-values for one, randomly selected, array from the TR cohort, are shown in Fig. The differences between the background correction methods for the same raw data are conspicuous. Interestingly, some background correction methods produce more variable M-values than others, particularly at low A values. The M-values for the arrays were as large as 6.21, 6.06, 5.94, and 5.625 for rawdata, movingminimum, subtraction, and normexp, respectively  patient samples, was used to determine the precision of each background correction method relative to the dataset. The residual variance for each probe shows how accurately each expression value fits the proposed model. Figure Most of the background methods showed low variance denoting a high precision, with normexp background correction showing the highest precision. No background correction resulted in the highest variance and lowest precision Fig. a, b. TheAs a prelude to data analysis, it is common to normalize protein microarray datasets, in order to ensure that subsequent differential expression is focused on true biological signal and not skewed by systematic technical variation in signal intensities. However, the differing underlying structure of protein microarray datasets means that normalisation methods which are commonly used in genomic experiments are not necessarily well suited to normalisation of protein microarray datasets. We therefore compared the performance of four different normalization methods in order to objectively identify the most appropriate method for inclusion in our pipeline.The datasets compared here were background corrected using the normexp method available in limma, based on the findings above. We calculated the coefficient of variation (CV) of the normalized intensity values for all the AlexaFluor-BSA controls for each of the arrays in the JHB cohort and the first three IgG controls in the GSH (PDAC versus chronic pancreatitis [CP]) cohort. A low CV between controls of known concentrations denotes minimal systematic bias and technical variation, suggesting a better performing normalization method. We therefore compared the CVs of the controls after application of no normalization, scale, quantile, and cyclic loess normalization methods. Cyclicloess normalization resulted in replicate data with the lowest CVs Fig. c, d suggp < 0.001), for the JHB cohort alone. To further investigate these differences, we ran a Tukey’s multiple pairwise comparisons test and found that the significant differences in CVs were between cylicloess normalization and the other three normalization methods (p < 0.001). Thus, based on these data, cyclic loess normalization was the method selected for our Pro-MAP pipeline.Subsequently, we ran a one-way ANOVA comparing the means of the CVs for each normalization method in both cohorts  as GPR or TXT files are uploaded into the Shiny app by either dragging and dropping files into the upload area or selecting them from the file system. Upon upload, default median foreground, background and annotation columns are automatically identified by the application but can be manually changed by the user based on preference. The main panel of the app is organized as tabs through which the user navigates to modify imputed data and view results. Subsequently, file details are automatically checked, and an error message arises if any disparate files are identified. The next tab produces a target file (metadata) with pre-set headers that can be downloaded and modified by the user to include disease conditions and any other defining factors deemed vital by the user for pre-processing and downstream analysis, then re-uploaded to match file names to column names in the final matrix. Metadata is also modifiable in the shiny. Following this, the user has the option of selecting probes to be removed at the final data condensation stage, this may include controls and empty slots. Alternatively, an annotated protein/probe list can be uploaded and probes to be removed selected based on a defined category e.g., “controls” Fig. a, b.Once the data has been prepared, spot filtering, background correction, normalization steps, and array weight calculations are performed automatically as described below, and plots are generated Fig. c, d.On most arrays, non-empty spots are represented in triplicate or more to ensure the reliability of the data attained. A quality index for each spot is then used as a noise threshold below which undesirable spots, categorized as non-specific binding, are discarded. The noise threshold for Pro-MAP is determined as intensities < 2SD of the median background intensity and spots classified as such are discarded as “noisy”, represented as an ‘NA’ in the data table produced , 17.To further minimize the consequences of spatial heterogeneity across arrays due to processing effects, such as wash solution deposits or optical noise from the scanner, the data is normexp background corrected. This method uses a model-based adjustment based on a normal plus exponential convolution model fitted to the background subtracted signal. A maximum-likelihood estimation is then used to determine the corrected foreground intensities; thus, all corrected intensities are positive.To combat systematic experimental bias and technical variation in factors, such as sample labelling efficiency, scanner readout efficiency, and microarray quality without losing biological signals of interest, microarrays are normalized. In Pro-MAP, the data is “fast” cyclic loess normalized. Each array is normalized with a reference array, which is an average of all arrays, by applying a correction factor which is obtained from a loess curve fit through MA plots of the arrays.Each array is weighted using an REML algorithm and weights are thereafter incorporated into downstream differential expression analysis models.Following pre-processing, interactive plots of the expression intensities of the raw data, log intensities of the normalized data, array weights, and mean log expression intensities of the condensed data are generated in a colour scheme that is user-defined. A txt file of the array weights to be used for downstream differential analysis is downloadable by the user. Furthermore, the final pe-processed array dataset, consolidated into mean intensities with columns and rows representing arrays and proteins, respectively, and unwanted probes removed is downloadable as a data table or expression set. Finally, the plots are downloadable as png files.p < 0.05 set as the default.The final step in the Pro-MAP pipeline is the optional differential expression for the identification of potential protein biomarkers Fig. e. A lineWe developed the Pro-MAP web tool that covers all the necessary steps in the pre-processing and analysis of single channel protein microarrays. Its core has been implemented using R (version 4.0) using shiny, limma  for readThis study highlights some of the pitfalls of previously used pre-processing techniques as they pertain to single-channel protein microarrays. Here, using real datasets, commonly used pre-processing methods are compared to determine which are the most accurate for use in pre-processing single-channel protein microarrays. From this, we created a robust single-channel protein microarray analysis pipeline, Pro-MAP, in R.Our study showed that the various background correction methods tested differed in terms of how accurately and precisely they portrayed the data. We compared no background correction, subtraction, moving minimum, and normexp background correction methods. We found, using a small technical replicate (TR cohort) dataset that where the log intensity should have been minimal, using the normexp background correction most accurately depicted this in terms of log intensity ratios (M) as it resulted in the smallest M values. Subsequently, we measured the precision of each correction method using residual log variances and found that the normexp correction method produced the lowest variances and therefore was the most “precise”. We also found that next to rawdata, the commonly used subtraction method was markedly worse than the other background correction methods. This is similar to findings by Ritchie et al.  who alsoTo determine the optimal normalization methods for our arrays, we corrected the background of our dataset using the normexp method in limma. Subsequently, we compared the no normalization, scale, quantile, and cyclic loess normalization methods. We found that scale normalization resulted in the highest CVs of all the normalization methods suggesting it had the least ability to correct for technical variation and systematic bias in our data. In contrast, cyclic loess showed an apparent improvement over all other methods in terms of reproducibility, with CVs < 15% in both datasets used.Finally, we tested the effect of equal array weights, array filtering of low weighted arrays, and the incorporation of array weights into differential expression analysis  on the aOur pipeline provides a robust pre-processing analysis workflow for the preparation of single-channel protein microarray data for a variety of array designs, scanned and extracted using different scanner types and image analysis software programs. We filter the extracted data based on a noise threshold of < 2SD of the background. Subsequently, the data is normexp background corrected and cyclic loess normalized, and array weights are calculated. Finally, the data is consolidated into a dataset consisting of columns representing samples and rows representing proteins, with all the controls filtered out in readiness for downstream analysis. The use of a single pipeline for all single-channel protein arrays will facilitate future data sharing and research collaborations, which is currently limited in the field.From this pipeline, we have developed Pro-MAP, a state-of-the-art single channel protein microarray analysis pipeline with a user-friendly web interface. The results at each step, pre-processing and differential analysis, are downloadable, including publication-ready plots in user-defined colour themes. To encourage further development of single-channel protein microarray analysis and enable users to run their analysis locally at their personal devices, considering confidential patient level data is often analysed, the base R script  and the Committee of Health and Social Care of Guernsey Ethics (IJG/C5.4). Moreover, written informed consent was obtained from all individuals, from which patient samples were derived for the study. All arrays were assayed as previously described , 29.The datasets selected here were the most appropriate ones from the pool available to us. The first dataset included 4 PDAC patient samples assayed in 2019 and again in 2021. The arrays were printed using the CT100+ design developed by Blackburn et al., [The second dataset was derived from a Johannesburg (JHB) pancreatic cancer cohort consisting of 10 pancreatic ductal adenocarcinoma (PDAC) samples and 10 controls, which included other non-PDAC pancreatic cancer patient samples. The arrays were printed, scanned, and data was extracted similarly to the TR cohort dataset. This dataset was used to compare variance/precision between the four background correction methods as well as the control CVs produced by each of the four normalization methods compared  cohort consisting of four arrays each with five PDAC patient pools per array and two arrays each with four chronic pancreatitis (CP) patient pools per array. The arrays used were pre-printed Sengenics Immunome slides and each array consisted of 1622 distinct proteins with 7 negative and 29 positive controls, including Ig and Cy3 BSA proteins. These arrays were also scanned on an Inopsys scanner, and the data was extracted using the Mapix software. We used this data to determine the effects of the different normalization methods on the CVs of a different set of controls from those used in the CT100+ arrays to confirm our results  cohort consisting of 20 prostate cancer patients and 20 controls (benign prostate disease patients). The CT100+ design was used to print the arrays that produced this dataset and scanned using the Inopsys scanner. These data were extracted using GenePix Pro v 6.1 software . As the largest dataset, this was most suitable for comparison of the moderated t-statistics and false discovery rates produced by the three array filtering techniques compared as a removal of arrays did not significantly affect the data  which is then subtracted from the foreground. This is done to avoid skewed background intensities due to artefacts or dust particles .This method uses a model-based adjustment based on a normal plus exponential convolution model , 35. TheNormalization accounts for systematic experimental bias and technical variation in factors, such as sample labelling efficiency, scanner readout efficiency, and microarray quality while maintaining biological signals of interest . SeveralHere, the data was normexp background corrected and no normalization step was applied.This method is the standard method of normalization for microarrays and is performed on a linear scale as opposed to a log scale. Scaling transforms each array so that the median for each array is equal , 40. HowThis is the most popular normalization method used in microarray studies due to its low computational load. This method is based on the idea that quantile–quantile plots show an equal distribution of two data vectors if the plot produces a straight line. Thus, the method “forces” an equal distribution for the probe intensities for each array in a dataset . HoweverCyclic loess normalizes two arrays at a time by applying a correction factor which is obtained from a loess curve fit through MA plots of the arrays. In this study, we utilized the “fast cyclic loess” method for our pipeline. This is a less aggressive method than the quantile normalization method and is a non-linear loess method where, in the case of the “fast method” arrays are normalized to a reference array, which is the average of all arrays . In receDespite background correction and normalization, variations in data quality may remain, affecting downstream analyses , 42. ProFollowing background correction and normalization, all arrays are used equally in the analyses.Here, following background correction ad normalization, the array weights are estimated using the REML algorithm created by Ritchie et al.  and thesHere, following background correction and normalization, the two arrays with the lowest calculated array weights/quality scores are removed prior to further analyses. It is important to note here that the cut-off for array filtering is investigator and data dependent. For this study, two arrays with the lowest weights were filtered out.To compare background correction methods, we spot-filtered extracted data from the TR and JHB cohorts and applied all four background correction methods. For the TR cohort, we used the corrected intensities to generate mean difference plots and calculate the log intensity ratios (M) = log2(X − Y)/log2 Y and log intensity averages (A) = 1/2 (log2 X + log2 Y). As these were replicates of patients with the same disease, we expected the most effective background correction methods to have the smallest M and A values, denoting minimal differential expression between replicates. Subsequently, in the JHB cohort, we calculated residual standard deviation value or variance, (σ) which is a goodness-of-fit measure that shows how well a set of data points fit the actual model. The smaller the variance, the more predictive or “precise” and useful the model. The JHB cohort was quantile normalized as a normalization method had yet to be chosen and the data were analysed by fitting a probe-wise linear model to all arrays to estimate variability. The A-values were standardized to be the same for each correction method to enable comparability. The correction method with the smallest MA values and highest precision was chosen for the pipeline.To compare our four normalization methods, the JHB and GSH cohorts were normexp background corrected following which all normalization methods were applied to the data. To determine which method best minimized technical variation and systematic experimental bias in the data, we calculated the coefficients of variation (CVs) of the AF Cy5 biotin BSA controls and IgG controls of the JHB and the GSH arrays, respectively. A lower CV of controls denoted a greater ability to minimize variation due to systematic experimental bias and technical variation without masking biologically relevant and interesting data. Thus, the method that consistently produced the lowest control CVs was used in the pipeline.p values calculated using the Benjamin Hochberg adjustment [To compare our three filtering methods, we applied the most effective background correction and normalization methods, based on our comparative analyses, and each array filtering method to the EUR cohort data. We then compared moderated t-statistics for each class of probes among each method. A higher moderated t-statistic suggested an increase in statistical power to detect true differential expression without increasing the false discovery rate (FDR). To validate these findings, we then compared false discovery rates  for eachjustment .All statistical analyses and plots were conducted and created using R (v 4.0) and ggplot2 , respectAdditional file 1. Supplementary figures and tables cited in the text.Additional file 2. A visual user guide  highlighting the Pro-MAP methodology’s critical steps.