Correction of batch effects in high throughput proximity extension assays for proteomic studies using bridging controls: the BAMBOO method.

Correction of batch effects in high throughput proximity extension assays for proteomic studies using bridging controls: the BAMBOO method. | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Correction of batch effects in high throughput proximity extension assays for proteomic studies using bridging controls: the BAMBOO method. H.M. Smits, E.M. Delemarre, A. Pandit, A.H. Schoneveld, B. Oldenburg, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4044125/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background : The proximity extension assay (PEA) facilitates large-scale proteomic studies involving a large number of proteins and samples. However, inevitable discrepancies in day-to-day measurements may introduce the inherent risk of undesirable variation, known as batch effects, which may impact down-stream statistical analyses and increase the chances of false discoveries. The implementation of bridging controls on each plate has been suggested to mitigate this complication, but a clear method on how to use this strategy is still lacking. In this study, we characterized potential batch effects in proteomics using PEAs and generated guidelines to mitigate batch effects using bridging controls. Results : This study characterized three distinct types of batch effects (protein-specific, sample-specific, and plate-wide) in PEA proteomic studies. We developed a new method, BAMBOO (Batch AdjustMents using Bridging cOntrOls), based on a robust regression model. In a simulation study, we compared BAMBOO with established batch correction techniques; median centering, median of the difference (MOD), and ComBat. We observed that median centering and ComBat were significantly impacted by outliers within the bridging controls, whereas BAMBOO and MOD were more robust when no plate-wide batch effects were introduced. Moreover, upon introduction of plate-wide batch effects, BAMBOO was performing better than MOD in terms of accuracy, true negative rate and true positive rate. Inclusion of 10-12 bridging controls was found to optimally correct for batch effects. Applying the different methods to experimental data showed that BAMBOO and MOD result in a reduced incidence of false discoveries compared to the alternative methods. Conclusion : Our study underscores the prevalent existence of batch effects in PEA proteomic studies, which can be corrected using bridging controls using an innovative, robust and effective tool, BAMBOO. The use of BAMBOO may enhance the reliability of large-scale analyses in the proteomic field using PEA. proteomics large proteomic study batch effects batch effects correction bridging controls Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Background Identifying a phenotype from a set of biomarkers can greatly improve our understanding of biological processes in health and disease. The identification and validation of proteomic biomarkers have become an essential area of research in the field of personalized medicine, as they hold great potential for improving disease detection, monitoring, and therapeutic decision-making [1]. The challenge is to identify the specific protein(s) or protein pattern(s) associated with a specific phase of a disease. Proximity extension assays (PEA), like Olink’s (Uppsalla, Sweden) target panel, are proteomics measurement techniques that allow a large number of proteins to be measured in many samples simultaneously. In brief, this technique uses pairs of oligonucleotide-conjugated antibodies. Upon binding with the protein of interest, the matching oligonucleotides on the antibody pairs form an amplicon which can be subsequently amplified and measured using qPCR. It enables accurate and consistent measurements of proteins without cross-reactivity at a relatively low cost in volumes as low as 1 µl of various matrices like serum, plasma, synovial fluid and dried blood spots [2, 3]. The standardization and scalability of PEA techniques are key features, making them a compelling technology for (large) proteomic studies. However, comparing or pooling data from different centers, or data derived from measurements over prolonged periods of time, remains a challenge, due to technical variations and the introduction of inter-plate variability. These so-called batch effects increase the risk of false discoveries in downstream statistical analyses [4]. To mitigate batch effects in multicenter studies or repeated measurements of a longer period of time, it has been suggested to include at least 8 so-called “bridging controls” (BCs) in every measurement, referring to the practice of including the same samples (with identical freeze-thaw cycle) on every plate [5]. The analyses of differences between these technical replicates, allow correction of batch effects across different plates and time points. Various methods have been developed to address batch effects in transcriptomic data and mass spectrometry data, including RUV [6], ComBat [7, 8], median centering method [9], and Median of the difference (MOD) [10]. Although some of these methods have been used to correct for batch effects in PEA studies [9, 11, 12], little is known regarding the nature of these batch effects or the number of bridging controls required for optimal correction. To our knowledge no comprehensive study has been published comparing the accuracy of these existing methods using bridging controls for analyses of PEA data. In this manuscript, we aimed to characterize batch effects in a proteomic study applying the Olink Target panel. We found 3 distinct batch effects and developed a new correction method called BAMBOO for Batch Adjustment using Bridging cOntrOls. In a simulation study, we compared BAMBOO with 3 existing correction methods and showed that overall BAMBOO is the current most robust method. We also observed that BAMBOO can effectively reduce false discovery rates using experimental data in comparison to other methods. Methods PEA measurements using Olink technology Relative protein concentrations were measured using PEA technology based Proseek Multiplex panels (Olink Proteomics), performed by the Olink service provider, Arcadia, in the UMC Utrecht, the Netherlands. In short, upon binding of antibody pairs to their respective targets, DNA reporter molecules conjugated to the antibodies give rise to new antigen specific DNA amplicons. Subsequently, amplicons are quantified using real-time PCR. The raw quantification cycle values are normalized and converted into normalized protein expression (NPX) units. The NPX values are expressed on a log2 scale in which one unit increase in NPX values represents a doubling of the protein concentration. Different quality controls were measured on every sample and plate using Olink’s standard quality control protocol [13]. Bridging controls and experimental data To characterize batch effects, we analyzed a selection of 8 healthy controls (HC) samples and 16 samples from patients with autoimmune disease to maximize the ranges of values. All samples were measured twice on separate plates. We obtained informed consent for all HC and patients. The institutional ethics committee of UMC Utrecht (the Netherlands) approved blood draws for all studies (07/125 for HC, NL61114.041.17. for IBD patients and NL47875.041.14 for JDM patients). To evaluate batch correction methods on actual experimental data, we measured serum samples from 14 participants that experienced a virus infection included within the RESCEU project (ref 17/069 and NL60910.041.17), along with 31 serum samples from healthy controls, using Olink’s Target 96 Immuno-oncology panel. After blood draw, serum samples were allowed to stand for at least 30 minutes and maximum of 4 hours before centrifugation at 3000 RPM for 10 minutes and stored at -80℃. Sodium heparin plasma samples were obtained by spinning at 1000g for 10 minutes. Healthy control serum samples were directly aliquoted into micronic tubes at a volume of 50 µl each and stored at -80℃ prior to measurement. Patient samples, used as bridging controls, were initially stored at -80℃, thawed, aliquoted in 20 µl amounts, and refrozen at -80℃ before measurement. Simulated data To compare our new approach to existing methods, we performed a simulation study. Each simulation involved two plates, each containing 88 samples for measurement of 92 proteins. Each protein \(i (i=1,\dots ,92)\) was assumed to follow a normal distribution \(N({\mu }_{i},{\sigma }_{i})\) , where \({\mu }_{i}∼U\left(\text{0,15}\right)\) and \({\sigma }_{i}∼U\left(\text{0.1,2}\right)\) . To introduce biological variability (for instance healthy controls vs. diseased individuals), we assumed that a certain number of proteins have different means ( \({\mu }_{i}^{BG}\) , where \(BG\) denotes the different biological groups). The number of proteins for which we assumed biological variability, and the differences in mean were tunable parameters ( \({N}_{BV}\) and \({\varDelta }_{BV}\) ) in our simulations. Each sample was defined by randomly drawing values from these 92 normal distributions. To simulate the bringing controls, a number of samples ( \({N}_{BC}\) ) were identical on both plates. Subsequently, batch effects were added to the simulated plates. Random noise was added to each protein following a normal distribution \(N(0, {\sigma }_{i}^{noise})\) . For a number of proteins ( \({N}_{BE}\) ), additional noise was added by changing the mean of the distribution from which the random noise was drawn to \(N({\mu }_{i}^{BE},{\sigma }_{i}^{noise}\) ). In addition, a selected number of samples ( \({N}_{OS}\) ) were introduced as potential outliers ( \(OS\) ) on one of the two simulated plates. Those samples were created by randomly adding or subtracting to the NPX of all protein one value from the following list: \(-3, -2.5, -1.5, 1.5, 2.5, 3\) . Finaly, we introduced noise to all values on one plate by using a linear function (intercept ꞵ0 and slope ꞵ1) as follows: \({NPX}_{D}={\beta }_{0}+{\beta }_{1}NPX\) . Table 1 shows the parameter values used for the simulations. Each possible parameter combination was simulated 50 times. Table 1 Variables and values used in the simulation study. Variable Meaning Value \({N}_{BC}\) Number of Bridging controls 3, 5, 10, 15, 24 \({N}_{BV}\) Number of proteins significantly different between the 2 groups of samples 0, 5,10,15 \({\varDelta }_{BV}\) Difference in mean NPX between the 2 groups of samples 0, 2.5, 5 \({N}_{BE}\) Number of proteins with a batch effect on the mean of the normal distribution 0, 10, 20 \({{\mu }_{i}^{BE}}_{}\) Mean of the normal distribution followed by the proteins with a batch effect 0, 2.5, 5 \({{\sigma }_{i}^{noise}}_{}\) Standard deviation of the normal distribution followed by the proteins with a batch effect 0, 0.15 \({\beta }_{1}\) Slope of the plate specific batch effect 0, 0.025, 0.05, 0.1 Comparison of the methods The simulated and experimental plates were corrected for batch effects using 4 different methods: our new method called BAMBOO (Batch Adjustment using Bridging cOntrOls), the median centering of the protein NPX values (also called intensity normalization) [9, 13], the MOD method (also called reference sample normalization) which is the method recommended by Olink [13], and SVA’s ComBat [7, 8] for which we set one of the covariates in the model matrix to the sample identification variable to use the bridging controls. The quality of batch effect correction in the simulated data was determined by computing accuracy (percentage of proteins correctly identified as significantly different), the true positive rate (TPR) and the false negative rate (TNR). True differential proteins were identified using t-tests between the two different biological groups using a statistically significant threshold after FDR correction of 0.05. Results Identification of 3 types of batch effects We measured a set of 24 samples on two different plates to identify potential batch effects in PEA studies. To visualize potential batch effects, we plotted both plate measurements against each other. If no batch effect was present, one would expect a perfect agreement between the two measurements of each sample and protein (i.e. all the data on the first diagonal x = y). Based on the differences between the measurements, we were able to identify three distinct types of batch effects. Firstly, we color-coded the 92 proteins and we observed that protein measurements were grouped together (Fig. 1A). For certain proteins, specifically those noted P1, P2, P3 and P4 in Fig. 1A, there is a general deviation from the first diagonal. This indicates that after measuring these proteins on the second plate the NPX values for the 24 samples were higher or lower compared to the first time. We called this batch effect a "protein specific batch effect". Secondly, when we color-coded the 24 samples instead of the proteins (Fig. 1B), a distinct deviation from the first diagonal was observed, most noticeable for the purple and red sample. This disparity strongly suggests that all values for a specific sample can be offset with a certain amount between measurements. We called this effect a "sample specific batch effect". Lastly, we looked at the measurements of the entire plate (Fig. 1C). A notable deviation from the first diagonal can be observed for lower NPX values. To confirm this, a regression model was fitted to the data and investigated if this regression line was significantly different from the first diagonal. To make sure that the above-mentioned batch effects (protein- and sample-specific) did not influence the regression, we used a robust linear regression l (intercept = -0.5; SE = 0.0178; slope = 1.04; SE = 0.0024). We found that the intercept was significantly different from 0 (p < 0.01) and the slope was significantly different from 1 (p < 0.01). This implies that besides the first two described batch effects, there is an overall deviation from the first diagonal influencing all proteins of all samples on the plate equally. We called this a “plate-wide” batch effect. Figure 1. NPX values of 24 samples measured on two different plates. a) The protein specific batch effects shown in four proteins (p1, p2, p3, p4). Colors highlight the different proteins, values below LOD in one of the two plates are indicated with an open symbol. b) Example of the sample-specific batch effect for two samples (blue and orange). c) Visualization of plate-wide effect as shown by a robust linear regression line (blue) fitted to the data. BAMBOO: a new batch effect correction method for PEA study Based on the identified batch effects, we developed a new correction method called BAMBOO for B atch A djust M ents using B ridging c O ntr O ls. This approach uses bridging controls to adjust measurements from one plate to a reference plate in 4 steps. The first step is quality filtering, in which the amount of batch effect is determined for each BC \(j\) using the following formula: \({BE}_{j}={\sum }_{i=1}^{{N}_{BC}}{NPX}_{i,1}^{j}-{NPX}_{i,2}^{j}\) . Using the Interquartile Range ( \(\left[{Q}_{1};{Q}_{3}\right]\) ) on the \({BE}_{j}s\) , all BCs with a \({BE}_{j}\) lower than \({Q}_{1}-1.5({Q}_{3}-{Q}_{1})\) or higher than \({Q}_{3}+1.5({Q}_{3}-{Q}_{1})\) can be considered as outliers and are removed. In addition, values below the limit of detection (LOD) are removed as they have a higher chance of being on the non-linear phase of the S-curve [14]. However, if this results in less than 6 BCs measurements for a protein, values below LOD are kept but the protein is flagged to indicate that any statistical result(s) coming from this protein should be interpreted with caution. In the second step, we estimate the plate-wide batch effects using a robust linear regression model on the bridging control data: \({NPX}_{i ,1 }^{j} = {b}_{0 }+{b}_{1}{NPX}_{i , 2 }^{j}\) , where \({b}_{0 }\) and \({b}_{1}\) are used as adjustment factors for plate-wide batch effects. In the third step, we estimate the adjustment factor for protein specific batch effects ( \({AF}_{i})\) as follows: \({AF}_{i} =median({NPXj}_{i, 1 }^{j}- ({b}_{0 }+{b}_{1}{NPX}_{i , 2 }^{j}\left)\right)\) . Lastly, using all the adjustment factors, we adjust the non-bridging control samples to the reference plate: \(adj.NP{X}_{i, 2}^{j} = ({b}_{0 }+{b}_{1}{NPX}_{i, 2 }^{j}) + {AF}_{i}\) . Comparing BAMBOO to other methods: a simulation study To evaluate our new approach in comparison to existing ones, we performed a simulation study tuning the strength of the different batch effects described above, the number of BCs, the number of outliers within the BCs, plate wide batch effect and other variables (Table 1 ). We compared BAMBOO with 3 other existing approaches (ComBat, median centering and MOD) using qualitative measures such as accuracy (percentage of significantly different proteins simulated and still identified as such after batch effect correction), true positive rate (TPR, proteins that were not significantly different in the true dataset but became significantly different after batch effect correction), and true negative rate (TNR, protein that were significantly different in the true dataset and became non-significantly different after batch effect correction). The values chosen to simulate the different batch effect parameters were in line with what we observed in Fig. 1 with the exception of the plate-wide effect for which we considered the extreme value of 0.1. First, we compared accuracy for the 4 batch correction approaches without introducing a plate-wide effect nor outliers within the BCs (Fig. 2 A). Overall, all 4 methods show high accuracy (> 95%) however the median centering method resulted in lower accuracy regardless of the number of BCs (96.8 to 97.2%). BAMBOO and MOD showed similar accuracies while ComBat reached slightly higher values. Using more than 10 BCs did not increase the accuracy for BAMBOO, MOD and ComBat. Since BAMBOO was designed to also correct for plate-wide batch effects, we investigated accuracy when plate-wide effects were introduced. We considered 3 different scenarios: a small, moderate, and large plate-wide effect (Fig. 2 B, Supplementary Fig. 2B). As for when no plate-wide effect was present, the median centering method achieved the lowest accuracies (although still acceptable values > 90%) regardless of the scenario and number of BCs used. BAMBOO and ComBat produced similar accuracies when low plate-wide effects were included, while MOD showed lower accuracies overall. When the plate-wide effect was moderate or large, a clear superiority of BAMBOO over ComBat and MOD methods was observed (Fig. 2 B, Supplementary Fig. 2B). Next, we introduced outliers among the BCs and investigated the accuracy when no plate-wide effect was present. Interestingly, when 1, 2 or 3 outliers were included the median centering method and ComBat performed poorly with accuracies as low as 60–80% in cases with less than 10 BCs. In contrast, both BAMBOO and MOD showed high accuracies (> 90%) in all cases (Fig. 2 C). Similar results were found when introducing plate-wide effects (small, moderate, and large). Notably, BAMBOO outperformed MOD when large plate-wide effects were present (Supplemental Fig. 1). Since BAMBOO and MOD performed the best based on accuracy to correct batch effects in the presence and absence of outliers, we investigated the TPR and TPR. As we observed that accuracy did not increase with more than 10 BCs, and to limit the number of simulations, we now only considered two scenarios. One with 10 BCs and one with 5 BCs to investigate a more cost-effective study setup (i.e. using less BCs to have more “real” samples measured on each plate). When using 10 BCs and no plate-wide effect and outliers were simulated, we observed similar TPR and TNR for BAMBOO and MOD (TPR: 99% and TNR: 97%; Fig. 3 and Fig. 4 ). Similarly, when we simulated outliers, both methods performed equally well (TPR > 98% and TPN > 96%). However, when we simulated plate-wide effects with and without outliers, MOD had lower TPR and TNR compared to cases without plate-wide effects while BAMBOO kept similar rates (Fig. 3 and Fig. 4 ). In addition, we observed that in scenarios with plate-wide effects MOD identified false positives that have a larger mean difference compared to the true data and false negatives that have a small mean difference compared to the true data. We observed similar results when we used only 5 BCs (Supplemental Fig. 3 and Supplemental Fig. 4). Surprisingly, we did not observe differences in TPR and TNR when using 5 BCs or 10 BCs when no outliers and no plate-wide effects were present for both methods. However, MOD had lower TPR and TNR compared to cases with 10 BCs when outliers and/or plate-wide were simulated. In conclusion, both BAMBOO and MOD perform well in removing batch effects when no outlier within the BCs and/or no (or small) plate-wide effect are present. But BAMBOO outperforms MOD when plate-wide effect and/or outliers are introduced and even more when a small number of BCs were measured. Application to experimental data: Healthy controls vs viral infected individuals To validate our method on real sample data, we compared 31 healthy controls (HC, measured on plate A) and 14 viral infected individuals (measured on plate B). These data were obtained from different studies and were measured on separate plates months apart. To correct for the batch effects, a set of 10 BCs were included on both plates. We measured the 92 proteins using the Olink T96 Immuno-Oncology panel. To visually assess the presence of batch effects, we first plotted the 10 BCs of each plate against each other (Supplemental Fig. 5). We observed protein specific batch effects as well as a plate-wide specific batch effect. The presence of these batch effects was confirmed using a hierarchical cluster analysis where we observed a clear separation of both plates (Fig. 5 ). We corrected the data using 4 different approaches: BAMBOO, MOD, the median centering and ComBat. The batch adjusted data was used to identify differentially expressed proteins (using the Wilcoxon rank sum test with an FDR cut-off at 0.05). All 4 methods found the same 60 proteins to be significantly different between the two groups of individuals (Supplementary Fig. 6). Nine proteins were found significantly different after batch effects correction only by one of the four methods: 5 after using ComBat, 3 after using median centering method, 1 after using BAMBOO and none after using MOD. The protein found significant after using BAMBOO had more than 6 measured values below LOD and was therefore flagged by BAMBOO to indicate that results should be interpreted with caution (see methods). For these 9 proteins, we investigated if their discovery could be due to improper or incomplete removal of batch effects. This was done by looking into the paired bridging control measurements after batch correction (Fig. 6 ). For the 5 proteins called significant by only ComBat, 3 proteins showed a clear deviation from the first diagonal indicating improper batch correction. Additionally, we observed that 4 of these 5 proteins had one measurement that could be classified as an outlier. For the 3 proteins found significant only by median centering method, we also observed a deviation from the first diagonal for 2 of them. Additionally, we observed that the 3 proteins present a bimodal distribution with a median value that could be defined as an outlier. Based on the analysis of experimental data, we can conclude that ComBat and median centering greatly suffer from the presence of outliers within the BCs and that BAMBOO is able to flag potential false discoveries due to low measured values. Discussion Here, we investigated batch effects occurring in proteomic studies using Olink PEA technologies. We developed a new method, called BAMBOO, which can correct for the identified batch effects using a minimal number of bridging controls. We compared this new method to existing alternatives using a simulation study and an experimental dataset. In both cases, BAMBOO corrected well for the batch effects and had potentially less false discoveries. With the emerging technologies and increasing prevalence of large-scale proteomic studies, efforts to characterize batch effects are crucial. However, in many cases, the methodology for their assessment remains unclear or even unattainable when no bridging controls are included. A recent comprehensive study by Eldjarn et al. , investigated the reproducibility of Olink and SomaScan, using the ratio of the coefficient of variation (CV) of repeated measurements to the CV of the assay [15]. Their findings revealed that the Olink Discovery assays exhibit greater precision than SomaScan. Interestingly, imperfect CV ratios suggested the potential presence of batch effects, in contrast to previous studies with smaller sample sizes [16–18]. In another study, Haslam et al. , evaluated Olink’s reproducibility using a triplicate of plasma samples among other analyses [19]. They found that approximately half of the proteins measured demonstrated excellent stability (Spearman r > 0.75) while about a third exhibited good stability (Spearman 0.40 < r < 0.75). These findings align with our results, indicating that most proteins measured in technical replicates display a good correlation between plates. However, it is noteworthy that some proteins show protein-specific batch effects. A recent paper by Dammer et al. , presents a comprehensive overview of current available methods to correct for batch effects that might be due to variations in sample preparation, batching, platform settings, personnel, and other experimental procedures [20]. They also proposed a new version of the median polish approach initially described by John Tukey in 1977 [21]. This new method is called TAMPOR and it can be used with or without bridging controls. While this method appears efficient to compare data from different platforms, data are transformed by an abundance normalization and therefore lose their original log2 scale (in case of Olink), complicating data interpretation. It seems that methods such as BAMBOO and MOD are preferable for large scale studies as data will keep their original scale and TAMPOR might be preferred when comparing or combining data from different platforms. We performed a simulation study to compare our new approach, BAMBOO, with existing approaches. The most basic batch correction method, median centering, did not perform well even in scenarios without plate-wide effect and outliers. Subsequently, ComBat, originally designed for processing transcriptomics data performed equally well as BAMBOO in the absence of plate-wide effects and outliers. However, its performance suffered when these factors were present. Although originally developed for microarray data correction, ComBat is widely used for analyses in other fields of omics data, such as Olink studies [12, 22, 23]. Lastly, MOD, a simple method in which the median of the paired-differences between bridging controls is used as a correction factor, showed comparable performance to BAMBOO in scenarios with outliers. However, this method was not robust against plate-wide batch effects. We showed that in scenarios with plate-wide effects, MOD identified more false positives with relatively large effect sizes and more false negatives with small effect sizes. It is possible that MOD over-corrects for batch effects and hence leads to more false positives and negatives in statistical analysis. In both our simulation study and the analysis of experimental data, we saw that both ComBat and median centering are impacted by outliers. Proteins called significantly different after correction with one of these methods showed a clear deviation from the first diagonal. Even though the experimental data did not contain a complete sample as outliers (all proteins of a sample), some individual proteins could be identified as such (outside the expected range). Interestingly, most studies made on microarray data show that ComBat can deal well with outliers [7, 8, 24]. When looking at other types of data, such as imaging, Han et al. , showed that using ComBat without identifying outliers could lead to false discoveries [25]. This suggests that the type of data used for ComBat can also influence its performance. It is advised to take along at least 8 bridging controls per plate for correcting batch effects [5]. Logically, the more bridging controls are used, the better batch effects are corrected. However, there is a balance between the number of experimental samples that can be measured and how precisely batch effects need to be corrected, also in terms of the available budget. Our simulation study showed that 10 BCs are sufficient to accurately correct for batch effects even when there is a strong plate-wide effect, when using BAMBOO. However, even in economical scenarios with 5 BCs, we showed that BAMBOO still adjusts well for batch effects, even with strong plate-wide effects (Accuracy > 96%). However, its performances dropped with the addition of one outlier. Hence, we advise to take along 10–12 BCs to account for the removal of potential outliers when using BAMBOO. Additionally, we recommend using a biologically heterogeneous group of samples (i.e. healthy and diseased) to increase the ranges of measurements and making sure that the majority will be above the LOD. One of the novelties of our approach is to flag proteins for which BCs are below the limit of detection. In this situation, it is difficult to compute adjustment factors as the difference between two plates for those BCs will be null. Hence, those proteins might still show a batch effect in the downstream analyses. Another novelty of our approach is the ability of BAMBOO to detect outliers within the BCs and to exclude them from correction. Conclusions In conclusion, we have identified the different batch effects that can be observed in proteomic studies and developed a new method to correct for them and compared it with 3 commonly used methods. We showed that 10–12 bridging controls is the optimal number of BCs to take along to accurately correct for batch effects. ComBat and median centering cannot properly correct for them, and we therefore advise to not use them for PEA studies. One method (MOD) was influenced by plate-wide batch effects and is therefore not recommended to use when such batch effect is present in the data. We therefore advise to use BAMBOO in all studies; which is available on GitHub ( https://github.com/CIC-UMCutrecht/BAMBOO/ ) Abbreviations PEA - Proximity extension assay BAMBOO - Batch AdjustMents using Bridging cOntrOls MOD - Median of the difference TNR - True negative rate TPR - True positive rate (q)PCR - (quantitative) Polymerase chain reaction BC - Bridging control RUV - Remove Unwanted Variation SVA - Surrogate variable analysis MOD - Median of the difference DNA - Deoxyribonucleic acid NPX - Normalized protein expression HC - Healthy control IBD - Inflammatory bowel disease JDM - Juvenile dermatomyositis RPM - Rounds per minute FDR - False discovery rate LOD - Limit of detection CV - Coefficient of variation Declarations Ethics approval and consent to participate Informed consent was obtained from all individuals included. The different studies were approved by the ethics committee of the UMC Utrecht (the Netherlands): 07/125 for HC, NL61114.041.17. for IBD patients,NL47875.041.14 for JDM patients and NL60910.041.17 for virus infection patients. Funding None Consent for publication: Not applicable Availability of data and materials The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. Competing interests The authors declare no competing interests. Authors' contributions HMS contributed to the analysis, interpretation of the data and the development of the software under the mentorship of JD. EMD and SN contributed to the design of the study and acquisition of the data. AS and BO contributed to the acquisition of the data. AP and FvW contributed to the interpretation of the data. All authors contributed to the revision of the manuscript drafted by HMS and JD. 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White paper 2021, https://www.olink.com/content/uploads/2021/09/olink-data-normalization-white-paper-v2.0.pdf [ https://olink.com/faq/how-is-the-limit-of-detection-lod-estimated-and-handled/ ] Eldjarn GH, Ferkingstad E, Lund SH, Helgason H, Magnusson OT, Gunnarsdottir K, Olafsdottir TA, Halldorsson BV, Olason PI, Zink F, Gudjonsson SA, Sveinbjornsson G, Magnusson MI, Helgason A, Oddsson A, Halldorsson GH, Magnusson MK, Saevarsdottir S, Eiriksdottir T, Masson G, Stefansson H, Jonsdottir I, Holm H, Rafnar T, Melsted P, Saemundsdottir J, Norddahl GL, Thorleifsson G, Ulfarsson MO, Gudbjartsson DF, Thorsteinsdottir U, Sulem P, Stefansson K: Large-scale plasma proteomics comparisons through genetics and disease associations. Nature 2023, 622(7982):348-358. 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Frontiers in Systems Biology 2023, 3. Tukey, J. W. Exploratory data analysis. Reading, MA: Addison-Wesley; 1977. Åkesson J, Hojjati S, Hellberg S, Raffetseder J, Khademi M, Rynkowski R, Kockum I, Altafini C, Lubovac-Pilav Z, Mellergård J, Jenmalm MC, Piehl F, Olsson T, Ernerudh J, Gustafsson M: Proteomics reveal biomarkers for diagnosis, disease activity and long-term disability outcomes in multiple sclerosis. Nature Communications 2023, 14(1). Angerfors A, Brännmark C, Lagging C, Tai K, Månsby Svedberg R, Andersson B, Jern C, Stanne TM: Proteomic profiling identifies novel inflammation-related plasma proteins associated with ischemic stroke outcome. Journal of Neuroinflammation 2023, 20(1). Chen C, Grennan K, Badner J, Zhang D, Gershon E, Jin L, Liu C: Removing batch effects in analysis of expression microarray data: An evaluation of six batch adjustment methods. PLoS ONE 2011, 6(2). Han Q, Xiao X, Wang S, Qin W, Yu C, Liang M: Characterization of the effects of outliers on ComBat harmonization for removing inter-site data heterogeneity in multisite neuroimaging studies. Frontiers in Neuroscience 2023, 17. Additional Declarations No competing interests reported. Supplementary Files SuppFiguresandTablesBAMBOOBMCgenomics.pptx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4044125","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":282553526,"identity":"c303e1d8-e0af-4356-a786-01b12ac03429","order_by":0,"name":"H.M. Smits","email":"","orcid":"","institution":"Center for Translational Immunology, University Medical Center Utrecht","correspondingAuthor":false,"prefix":"","firstName":"H.M.","middleName":"","lastName":"Smits","suffix":""},{"id":282553528,"identity":"fa0942d9-73fc-48c0-b8bc-92da2e663c82","order_by":1,"name":"E.M. Delemarre","email":"","orcid":"","institution":"Center for Translational Immunology, University Medical Center Utrecht","correspondingAuthor":false,"prefix":"","firstName":"E.M.","middleName":"","lastName":"Delemarre","suffix":""},{"id":282553530,"identity":"db396507-af77-4b1b-8c70-218c14095bbd","order_by":2,"name":"A. Pandit","email":"","orcid":"","institution":"Center for Translational Immunology, University Medical Center Utrecht","correspondingAuthor":false,"prefix":"","firstName":"A.","middleName":"","lastName":"Pandit","suffix":""},{"id":282553532,"identity":"024216e3-b8d7-4082-ac97-3b84362a8365","order_by":3,"name":"A.H. Schoneveld","email":"","orcid":"","institution":"Central Diagnostic Laboratory, University Medical Center Utrecht","correspondingAuthor":false,"prefix":"","firstName":"A.H.","middleName":"","lastName":"Schoneveld","suffix":""},{"id":282553534,"identity":"6177f47a-293c-4085-8e39-79c7c7972b65","order_by":4,"name":"B. Oldenburg","email":"","orcid":"","institution":"Department of Gastroenterology and Hepatology, University Medical Center Utrecht","correspondingAuthor":false,"prefix":"","firstName":"B.","middleName":"","lastName":"Oldenburg","suffix":""},{"id":282553535,"identity":"3a4cce2d-46ed-40e7-9560-a308008144d5","order_by":5,"name":"F. van Wijk","email":"","orcid":"","institution":"Center for Translational Immunology, University Medical Center Utrecht","correspondingAuthor":false,"prefix":"","firstName":"F.","middleName":"van","lastName":"Wijk","suffix":""},{"id":282553538,"identity":"f0e1cfe0-5b7e-4f10-bddc-0c2fee120549","order_by":6,"name":"S. Nierkens","email":"","orcid":"","institution":"Center for Translational Immunology, University Medical Center Utrecht","correspondingAuthor":false,"prefix":"","firstName":"S.","middleName":"","lastName":"Nierkens","suffix":""},{"id":282553539,"identity":"baf8f828-0e6a-45b8-b674-815b7f0029ed","order_by":7,"name":"J. Drylewicz","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAUlEQVRIie3OMUvDQBTA8RcfnMtru0aC9CucBDqFfJYcgZtUlCyFDgYClyXUtdD2UxSytqVgF7+Bi12cFISAdLOXVDcvdHS4/3Ac7/HjDsBm+4c5KXCAOwCm76+/U6yPbivhDUFeT6ghUTMxdSQ65p5EMMWyIh6I8fn2bdS5DsXS26yr+z3cmoiTsmRKXApFkXzplLEoujL2JhEkZkI+Et/cKBeeNFmJgmiAFIFQ7eRbE0clR9L7OoWsNEGGP6+wdpKxxJnx+EGRxIt5GfvFM/M9kq6RXOXZAt6Hod/Pt7vPjzK8zAvcVRQE4tFEMoAz+mPhGgBAv/7c3ri22Ww2m+4A8KNKE1RP8dgAAAAASUVORK5CYII=","orcid":"","institution":"Center for Translational Immunology, University Medical Center Utrecht","correspondingAuthor":true,"prefix":"","firstName":"J.","middleName":"","lastName":"Drylewicz","suffix":""}],"badges":[],"createdAt":"2024-03-08 13:17:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4044125/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4044125/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53450991,"identity":"ff7ccbea-e58e-48ac-b487-5860d5141917","added_by":"auto","created_at":"2024-03-26 06:40:03","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":372100,"visible":true,"origin":"","legend":"\u003cp\u003eNPX values of 24 samples measured on two different plates. a) The protein specific batch effects shown in four proteins (p1, p2, p3, p4). Colors highlight the different proteins, values below LOD in one of the two plates are indicated with an open symbol. b) Example of the sample-specific batch effect for two samples (blue and orange). c) Visualization of plate-wide effect as shown by a robust linear regression line (blue) fitted to the data.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4044125/v1/0d012da73680968808349a03.png"},{"id":53450992,"identity":"b0c9dfa7-e092-471f-a503-a08fd69602de","added_by":"auto","created_at":"2024-03-26 06:40:03","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":204010,"visible":true,"origin":"","legend":"\u003cp\u003eAccuracies of the four batch correction methods. a) The accuracies of the four methods without plate-wide batch effects or outliers. b) Accuracies of the four methods with a plate-wide effect of 0.0025, 0.05 and 0.1. c) Accuracies of the four methods with 1, 2 or 3 outliers. Lines represent mean of the accuracy over all the simulations.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4044125/v1/e3de6726deea83bf7596b3f6.png"},{"id":53450993,"identity":"7e27fd3a-263b-4f2a-9aa2-904181652da4","added_by":"auto","created_at":"2024-03-26 06:40:03","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":382428,"visible":true,"origin":"","legend":"\u003cp\u003eTrue negative rate\u003cstrong\u003e \u003c/strong\u003efor BAMBOO and MOD using 10 bridging controls. The effect size between the two groups after batch correction are on the x-axis and the effect size in the “true” data (i.e. before batch introduction on the simulated data) are on the y-axis. Columns show the number of outliers in the simulations and the rows the strength of the plate-wide effect. False positives (proteins that were not significantly different in the true data and found statistically significant after batch effects correction) are in red and true negatives (proteins that were not significantly different in the true data and still not statistically significant after batch effects correction) are in grey.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4044125/v1/6e2be4ed93c051fc07670646.png"},{"id":53450997,"identity":"f99604eb-0ab1-458f-a80e-8facae89904f","added_by":"auto","created_at":"2024-03-26 06:40:03","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":325516,"visible":true,"origin":"","legend":"\u003cp\u003eTrue positive rate\u003cstrong\u003e \u003c/strong\u003efor BAMBOO and MOD using 10 bridging controls. Left figure (BAMBOO), right figure (MOD). The effect size between the two groups after batch correction are on the x-axis and the effect size in the “true” data (i.e. before batch introduction on the simulated data) are on the y-axis. Columns show the number of outliers in the simulations and the rows the strength of the plate-wide effect. False negatives (proteins that were significantly different in the true data and found not statistically significant after batch effects correction) are in orange and true positives (proteins that were significantly different in the true data and still statistically significant after batch effects correction) are in grey.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4044125/v1/34d64b28ee0f0211b69caf1d.png"},{"id":53450994,"identity":"f5042f4b-bfe2-4329-a3c5-fdc22483fdfb","added_by":"auto","created_at":"2024-03-26 06:40:03","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":66434,"visible":true,"origin":"","legend":"\u003cp\u003eHeatmap of the NPX values of HC and viral infection samples measured on plate A and plate B. NPX values were transformed as Z-scores. Each row represents a protein, and each column a sample. Clustering was performed using Wards-d2 clustering algorithm with the Euclidean distance.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4044125/v1/93173b3dd3edde61f2dcec94.png"},{"id":53450995,"identity":"10bf2454-2566-4146-a68d-e8cf5cd7ff78","added_by":"auto","created_at":"2024-03-26 06:40:03","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":189721,"visible":true,"origin":"","legend":"\u003cp\u003eNPX values of the BCs for the proteins found significant by only one of the four methods after batch correction. a) NPX values of the bridging controls for the protein found significant only after batch correction with BAMBOO. b) NPX values of the bridging controls for the 3 proteins found significant only after batch correction with median centering normalization. c) NPX values of the bridging controls for the 5 proteins found significant only after batch correction with ComBat.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4044125/v1/e12ad9884c2e04a7e76cb609.png"},{"id":55899561,"identity":"f6666186-23cf-4e5d-a121-4cf125f0354c","added_by":"auto","created_at":"2024-05-06 05:07:47","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1532294,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4044125/v1/d9686f7a-a09d-4a1a-98bb-29511e48d13d.pdf"},{"id":53450996,"identity":"0aea5c18-28e4-4bd3-b8af-0874c363d162","added_by":"auto","created_at":"2024-03-26 06:40:03","extension":"pptx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1765515,"visible":true,"origin":"","legend":"","description":"","filename":"SuppFiguresandTablesBAMBOOBMCgenomics.pptx","url":"https://assets-eu.researchsquare.com/files/rs-4044125/v1/00453b15a3876cc482bb9a60.pptx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Correction of batch effects in high throughput proximity extension assays for proteomic studies using bridging controls: the BAMBOO method.","fulltext":[{"header":"Background","content":"\u003cp\u003eIdentifying a phenotype from a set of biomarkers can greatly improve our understanding of biological processes in health and disease. The identification and validation of proteomic biomarkers have become an essential area of research in the field of personalized medicine, as they hold great potential for improving disease detection, monitoring, and therapeutic decision-making [1]. The challenge is to identify the specific protein(s) or protein pattern(s) associated with a specific phase of a disease.\u003c/p\u003e \u003cp\u003eProximity extension assays (PEA), like Olink\u0026rsquo;s (Uppsalla, Sweden) target panel, are proteomics measurement techniques that allow a large number of proteins to be measured in many samples simultaneously. In brief, this technique uses pairs of oligonucleotide-conjugated antibodies. Upon binding with the protein of interest, the matching oligonucleotides on the antibody pairs form an amplicon which can be subsequently amplified and measured using qPCR. It enables accurate and consistent measurements of proteins without cross-reactivity at a relatively low cost in volumes as low as 1 \u0026micro;l of various matrices like serum, plasma, synovial fluid and dried blood spots [2, 3]. The standardization and scalability of PEA techniques are key features, making them a compelling technology for (large) proteomic studies. However, comparing or pooling data from different centers, or data derived from measurements over prolonged periods of time, remains a challenge, due to technical variations and the introduction of inter-plate variability. These so-called batch effects increase the risk of false discoveries in downstream statistical analyses [4].\u003c/p\u003e \u003cp\u003eTo mitigate batch effects in multicenter studies or repeated measurements of a longer period of time, it has been suggested to include at least 8 so-called \u0026ldquo;bridging controls\u0026rdquo; (BCs) in every measurement, referring to the practice of including the same samples (with identical freeze-thaw cycle) on every plate [5]. The analyses of differences between these technical replicates, allow correction of batch effects across different plates and time points. Various methods have been developed to address batch effects in transcriptomic data and mass spectrometry data, including RUV [6], ComBat [7, 8], median centering method [9], and Median of the difference (MOD) [10]. Although some of these methods have been used to correct for batch effects in PEA studies [9, 11, 12], little is known regarding the nature of these batch effects or the number of bridging controls required for optimal correction. To our knowledge no comprehensive study has been published comparing the accuracy of these existing methods using bridging controls for analyses of PEA data.\u003c/p\u003e \u003cp\u003eIn this manuscript, we aimed to characterize batch effects in a proteomic study applying the Olink Target panel. We found 3 distinct batch effects and developed a new correction method called BAMBOO for Batch Adjustment using Bridging cOntrOls. In a simulation study, we compared BAMBOO with 3 existing correction methods and showed that overall BAMBOO is the current most robust method. We also observed that BAMBOO can effectively reduce false discovery rates using experimental data in comparison to other methods.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003ePEA measurements using Olink technology\u003c/h2\u003e\n \u003cp\u003eRelative protein concentrations were measured using PEA technology based Proseek Multiplex panels (Olink Proteomics), performed by the Olink service provider, Arcadia, in the UMC Utrecht, the Netherlands. In short, upon binding of antibody pairs to their respective targets, DNA reporter molecules conjugated to the antibodies give rise to new antigen specific DNA amplicons. Subsequently, amplicons are quantified using real-time PCR. The raw quantification cycle values are normalized and converted into normalized protein expression (NPX) units. The NPX values are expressed on a log2 scale in which one unit increase in NPX values represents a doubling of the protein concentration. Different quality controls were measured on every sample and plate using Olink\u0026rsquo;s standard quality control protocol [13].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003eBridging controls and experimental data\u003c/h2\u003e\n \u003cp\u003eTo characterize batch effects, we analyzed a selection of 8 healthy controls (HC) samples and 16 samples from patients with autoimmune disease to maximize the ranges of values. All samples were measured twice on separate plates. We obtained informed consent for all HC and patients. The institutional ethics committee of UMC Utrecht (the Netherlands) approved blood draws for all studies (07/125 for HC, NL61114.041.17. for IBD patients and NL47875.041.14 for JDM patients). To evaluate batch correction methods on actual experimental data, we measured serum samples from 14 participants that experienced a virus infection included within the RESCEU project (ref 17/069 and NL60910.041.17), along with 31 serum samples from healthy controls, using Olink\u0026rsquo;s Target 96 Immuno-oncology panel.\u003c/p\u003e\n \u003cp\u003eAfter blood draw, serum samples were allowed to stand for at least 30 minutes and maximum of 4 hours before centrifugation at 3000 RPM for 10 minutes and stored at -80℃. Sodium heparin plasma samples were obtained by spinning at 1000g for 10 minutes. Healthy control serum samples were directly aliquoted into micronic tubes at a volume of 50 \u0026micro;l each and stored at -80℃ prior to measurement. Patient samples, used as bridging controls, were initially stored at -80℃, thawed, aliquoted in 20 \u0026micro;l amounts, and refrozen at -80℃ before measurement.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003eSimulated data\u003c/h2\u003e\n \u003cp\u003eTo compare our new approach to existing methods, we performed a simulation study. Each simulation involved two plates, each containing 88 samples for measurement of 92 proteins. Each protein \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i (i=1,\\dots ,92)\\)\u003c/span\u003e\u003c/span\u003e was assumed to follow a normal distribution \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N({\\mu }_{i},{\\sigma }_{i})\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }_{i}\u0026sim;U\\left(\\text{0,15}\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{i}\u0026sim;U\\left(\\text{0.1,2}\\right)\\)\u003c/span\u003e\u003c/span\u003e. To introduce biological variability (for instance healthy controls vs. diseased individuals), we assumed that a certain number of proteins have different means (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }_{i}^{BG}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(BG\\)\u003c/span\u003e\u003c/span\u003e denotes the different biological groups). The number of proteins for which we assumed biological variability, and the differences in mean were tunable parameters (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{BV}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varDelta }_{BV}\\)\u003c/span\u003e\u003c/span\u003e) in our simulations. Each sample was defined by randomly drawing values from these 92 normal distributions. To simulate the bringing controls, a number of samples (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{BC}\\)\u003c/span\u003e\u003c/span\u003e) were identical on both plates.\u003c/p\u003e\n \u003cp\u003eSubsequently, batch effects were added to the simulated plates. Random noise was added to each protein following a normal distribution \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N(0, {\\sigma }_{i}^{noise})\\)\u003c/span\u003e\u003c/span\u003e. For a number of proteins (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{BE}\\)\u003c/span\u003e\u003c/span\u003e), additional noise was added by changing the mean of the distribution from which the random noise was drawn to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(N({\\mu }_{i}^{BE},{\\sigma }_{i}^{noise}\\)\u003c/span\u003e\u003c/span\u003e). In addition, a selected number of samples (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{OS}\\)\u003c/span\u003e\u003c/span\u003e) were introduced as potential outliers (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(OS\\)\u003c/span\u003e\u003c/span\u003e) on one of the two simulated plates. Those samples were created by randomly adding or subtracting to the NPX of all protein one value from the following list: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(-3, -2.5, -1.5, 1.5, 2.5, 3\\)\u003c/span\u003e\u003c/span\u003e. Finaly, we introduced noise to all values on one plate by using a linear function (intercept ꞵ0 and slope ꞵ1) as follows: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({NPX}_{D}={\\beta }_{0}+{\\beta }_{1}NPX\\)\u003c/span\u003e\u003c/span\u003e. Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the parameter values used for the simulations. Each possible parameter combination was simulated 50 times.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eVariables and values used in the simulation study.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVariable\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMeaning\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eValue\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{BC}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of Bridging controls\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3, 5, 10, 15, 24\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{BV}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of proteins significantly different between the 2 groups of samples\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0, 5,10,15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varDelta }_{BV}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDifference in mean NPX between the 2 groups of samples\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0, 2.5, 5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({N}_{BE}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of proteins with a batch effect on the mean of the normal distribution\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0, 10, 20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\mu }_{i}^{BE}}_{}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMean of the normal distribution followed by the proteins with a batch effect\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0, 2.5, 5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\sigma }_{i}^{noise}}_{}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStandard deviation of the normal distribution followed by the proteins with a batch effect\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0, 0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSlope of the plate specific batch effect\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0, 0.025, 0.05, 0.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003eComparison of the methods\u003c/h2\u003e\n \u003cp\u003eThe simulated and experimental plates were corrected for batch effects using 4 different methods: our new method called BAMBOO (Batch Adjustment using Bridging cOntrOls), the median centering of the protein NPX values (also called intensity normalization) [9, 13], the MOD method (also called reference sample normalization) which is the method recommended by Olink [13], and SVA\u0026rsquo;s ComBat [7, 8] for which we set one of the covariates in the model matrix to the sample identification variable to use the bridging controls.\u003c/p\u003e\n \u003cp\u003eThe quality of batch effect correction in the simulated data was determined by computing accuracy (percentage of proteins correctly identified as significantly different), the true positive rate (TPR) and the false negative rate (TNR). True differential proteins were identified using t-tests between the two different biological groups using a statistically significant threshold after FDR correction of 0.05.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eIdentification of 3 types of batch effects\u003c/h2\u003e \u003cp\u003eWe measured a set of 24 samples on two different plates to identify potential batch effects in PEA studies. To visualize potential batch effects, we plotted both plate measurements against each other. If no batch effect was present, one would expect a perfect agreement between the two measurements of each sample and protein (i.e. all the data on the first diagonal x\u0026thinsp;=\u0026thinsp;y). Based on the differences between the measurements, we were able to identify three distinct types of batch effects.\u003c/p\u003e \u003cp\u003eFirstly, we color-coded the 92 proteins and we observed that protein measurements were grouped together (Fig.\u0026nbsp;1A). For certain proteins, specifically those noted P1, P2, P3 and P4 in Fig.\u0026nbsp;1A, there is a general deviation from the first diagonal. This indicates that after measuring these proteins on the second plate the NPX values for the 24 samples were higher or lower compared to the first time. We called this batch effect a \"protein specific batch effect\".\u003c/p\u003e \u003cp\u003eSecondly, when we color-coded the 24 samples instead of the proteins (Fig.\u0026nbsp;1B), a distinct deviation from the first diagonal was observed, most noticeable for the purple and red sample. This disparity strongly suggests that all values for a specific sample can be offset with a certain amount between measurements. We called this effect a \"sample specific batch effect\".\u003c/p\u003e \u003cp\u003eLastly, we looked at the measurements of the entire plate (Fig.\u0026nbsp;1C). A notable deviation from the first diagonal can be observed for lower NPX values. To confirm this, a regression model was fitted to the data and investigated if this regression line was significantly different from the first diagonal. To make sure that the above-mentioned batch effects (protein- and sample-specific) did not influence the regression, we used a robust linear regression l (intercept = -0.5; SE\u0026thinsp;=\u0026thinsp;0.0178; slope\u0026thinsp;=\u0026thinsp;1.04; SE\u0026thinsp;=\u0026thinsp;0.0024). We found that the intercept was significantly different from 0 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.01) and the slope was significantly different from 1 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.01). This implies that besides the first two described batch effects, there is an overall deviation from the first diagonal influencing all proteins of all samples on the plate equally. We called this a \u0026ldquo;plate-wide\u0026rdquo; batch effect.\u003c/p\u003e \u003cp\u003e \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eFigure 1.\u003c/span\u003e NPX values of 24 samples measured on two different plates. a) The protein specific batch effects shown in four proteins (p1, p2, p3, p4). Colors highlight the different proteins, values below LOD in one of the two plates are indicated with an open symbol. b) Example of the sample-specific batch effect for two samples (blue and orange). c) Visualization of plate-wide effect as shown by a robust linear regression line (blue) fitted to the data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eBAMBOO: a new batch effect correction method for PEA study\u003c/h2\u003e \u003cp\u003eBased on the identified batch effects, we developed a new correction method called BAMBOO for \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eB\u003c/span\u003eatch \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eA\u003c/span\u003edjust\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eM\u003c/span\u003eents using \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eB\u003c/span\u003eridging c\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eO\u003c/span\u003entr\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eO\u003c/span\u003els. This approach uses bridging controls to adjust measurements from one plate to a reference plate in 4 steps.\u003c/p\u003e \u003cp\u003eThe first step is quality filtering, in which the amount of batch effect is determined for each BC \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(j\\)\u003c/span\u003e\u003c/span\u003e using the following formula: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({BE}_{j}={\\sum }_{i=1}^{{N}_{BC}}{NPX}_{i,1}^{j}-{NPX}_{i,2}^{j}\\)\u003c/span\u003e\u003c/span\u003e. Using the Interquartile Range (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left[{Q}_{1};{Q}_{3}\\right]\\)\u003c/span\u003e\u003c/span\u003e) on the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({BE}_{j}s\\)\u003c/span\u003e\u003c/span\u003e, all BCs with a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({BE}_{j}\\)\u003c/span\u003e\u003c/span\u003e lower than \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{1}-1.5({Q}_{3}-{Q}_{1})\\)\u003c/span\u003e\u003c/span\u003e or higher than \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{3}+1.5({Q}_{3}-{Q}_{1})\\)\u003c/span\u003e\u003c/span\u003e can be considered as outliers and are removed. In addition, values below the limit of detection (LOD) are removed as they have a higher chance of being on the non-linear phase of the S-curve [14]. However, if this results in less than 6 BCs measurements for a protein, values below LOD are kept but the protein is flagged to indicate that any statistical result(s) coming from this protein should be interpreted with caution.\u003c/p\u003e \u003cp\u003eIn the second step, we estimate the plate-wide batch effects using a robust linear regression model on the bridging control data: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({NPX}_{i ,1 }^{j} = {b}_{0 }+{b}_{1}{NPX}_{i , 2 }^{j}\\)\u003c/span\u003e\u003c/span\u003e, where\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{0 }\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{1}\\)\u003c/span\u003e\u003c/span\u003e are used as adjustment factors for plate-wide batch effects.\u003c/p\u003e \u003cp\u003eIn the third step, we estimate the adjustment factor for protein specific batch effects (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({AF}_{i})\\)\u003c/span\u003e\u003c/span\u003e as follows: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({AF}_{i} =median({NPXj}_{i, 1 }^{j}- ({b}_{0 }+{b}_{1}{NPX}_{i , 2 }^{j}\\left)\\right)\\)\u003c/span\u003e\u003c/span\u003e. Lastly, using all the adjustment factors, we adjust the non-bridging control samples to the reference plate: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(adj.NP{X}_{i, 2}^{j} = ({b}_{0 }+{b}_{1}{NPX}_{i, 2 }^{j}) + {AF}_{i}\\)\u003c/span\u003e\u003c/span\u003e .\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eComparing BAMBOO to other methods: a simulation study\u003c/h2\u003e \u003cp\u003eTo evaluate our new approach in comparison to existing ones, we performed a simulation study tuning the strength of the different batch effects described above, the number of BCs, the number of outliers within the BCs, plate wide batch effect and other variables (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). We compared BAMBOO with 3 other existing approaches (ComBat, median centering and MOD) using qualitative measures such as accuracy (percentage of significantly different proteins simulated and still identified as such after batch effect correction), true positive rate (TPR, proteins that were not significantly different in the true dataset but became significantly different after batch effect correction), and true negative rate (TNR, protein that were significantly different in the true dataset and became non-significantly different after batch effect correction). The values chosen to simulate the different batch effect parameters were in line with what we observed in Fig.\u0026nbsp;1 with the exception of the plate-wide effect for which we considered the extreme value of 0.1.\u003c/p\u003e \u003cp\u003eFirst, we compared accuracy for the 4 batch correction approaches without introducing a plate-wide effect nor outliers within the BCs (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003eA). Overall, all 4 methods show high accuracy (\u0026gt;\u0026thinsp;95%) however the median centering method resulted in lower accuracy regardless of the number of BCs (96.8 to 97.2%). BAMBOO and MOD showed similar accuracies while ComBat reached slightly higher values. Using more than 10 BCs did not increase the accuracy for BAMBOO, MOD and ComBat.\u003c/p\u003e \u003cp\u003eSince BAMBOO was designed to also correct for plate-wide batch effects, we investigated accuracy when plate-wide effects were introduced. We considered 3 different scenarios: a small, moderate, and large plate-wide effect (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003eB, Supplementary Fig.\u0026nbsp;2B). As for when no plate-wide effect was present, the median centering method achieved the lowest accuracies (although still acceptable values\u0026thinsp;\u0026gt;\u0026thinsp;90%) regardless of the scenario and number of BCs used. BAMBOO and ComBat produced similar accuracies when low plate-wide effects were included, while MOD showed lower accuracies overall. When the plate-wide effect was moderate or large, a clear superiority of BAMBOO over ComBat and MOD methods was observed (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003eB, Supplementary Fig.\u0026nbsp;2B).\u003c/p\u003e \u003cp\u003eNext, we introduced outliers among the BCs and investigated the accuracy when no plate-wide effect was present. Interestingly, when 1, 2 or 3 outliers were included the median centering method and ComBat performed poorly with accuracies as low as 60\u0026ndash;80% in cases with less than 10 BCs. In contrast, both BAMBOO and MOD showed high accuracies (\u0026gt;\u0026thinsp;90%) in all cases (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003eC). Similar results were found when introducing plate-wide effects (small, moderate, and large). Notably, BAMBOO outperformed MOD when large plate-wide effects were present (Supplemental Fig.\u0026nbsp;1).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSince BAMBOO and MOD performed the best based on accuracy to correct batch effects in the presence and absence of outliers, we investigated the TPR and TPR. As we observed that accuracy did not increase with more than 10 BCs, and to limit the number of simulations, we now only considered two scenarios. One with 10 BCs and one with 5 BCs to investigate a more cost-effective study setup (i.e. using less BCs to have more \u0026ldquo;real\u0026rdquo; samples measured on each plate).\u003c/p\u003e \u003cp\u003eWhen using 10 BCs and no plate-wide effect and outliers were simulated, we observed similar TPR and TNR for BAMBOO and MOD (TPR: 99% and TNR: 97%; Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Similarly, when we simulated outliers, both methods performed equally well (TPR\u0026thinsp;\u0026gt;\u0026thinsp;98% and TPN\u0026thinsp;\u0026gt;\u0026thinsp;96%). However, when we simulated plate-wide effects with and without outliers, MOD had lower TPR and TNR compared to cases without plate-wide effects while BAMBOO kept similar rates (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e). In addition, we observed that in scenarios with plate-wide effects MOD identified false positives that have a larger mean difference compared to the true data and false negatives that have a small mean difference compared to the true data. We observed similar results when we used only 5 BCs (Supplemental Fig.\u0026nbsp;3 and Supplemental Fig.\u0026nbsp;4). Surprisingly, we did not observe differences in TPR and TNR when using 5 BCs or 10 BCs when no outliers and no plate-wide effects were present for both methods. However, MOD had lower TPR and TNR compared to cases with 10 BCs when outliers and/or plate-wide were simulated.\u003c/p\u003e \u003cp\u003eIn conclusion, both BAMBOO and MOD perform well in removing batch effects when no outlier within the BCs and/or no (or small) plate-wide effect are present. But BAMBOO outperforms MOD when plate-wide effect and/or outliers are introduced and even more when a small number of BCs were measured.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eApplication to experimental data: Healthy controls vs viral infected individuals\u003c/h2\u003e \u003cp\u003eTo validate our method on real sample data, we compared 31 healthy controls (HC, measured on plate A) and 14 viral infected individuals (measured on plate B). These data were obtained from different studies and were measured on separate plates months apart. To correct for the batch effects, a set of 10 BCs were included on both plates. We measured the 92 proteins using the Olink T96 Immuno-Oncology panel.\u003c/p\u003e \u003cp\u003eTo visually assess the presence of batch effects, we first plotted the 10 BCs of each plate against each other (Supplemental Fig.\u0026nbsp;5). We observed protein specific batch effects as well as a plate-wide specific batch effect. The presence of these batch effects was confirmed using a hierarchical cluster analysis where we observed a clear separation of both plates (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e). We corrected the data using 4 different approaches: BAMBOO, MOD, the median centering and ComBat.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe batch adjusted data was used to identify differentially expressed proteins (using the Wilcoxon rank sum test with an FDR cut-off at 0.05). All 4 methods found the same 60 proteins to be significantly different between the two groups of individuals (Supplementary Fig.\u0026nbsp;6). Nine proteins were found significantly different after batch effects correction only by one of the four methods: 5 after using ComBat, 3 after using median centering method, 1 after using BAMBOO and none after using MOD. The protein found significant after using BAMBOO had more than 6 measured values below LOD and was therefore flagged by BAMBOO to indicate that results should be interpreted with caution (see methods).\u003c/p\u003e \u003cp\u003eFor these 9 proteins, we investigated if their discovery could be due to improper or incomplete removal of batch effects. This was done by looking into the paired bridging control measurements after batch correction (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e). For the 5 proteins called significant by only ComBat, 3 proteins showed a clear deviation from the first diagonal indicating improper batch correction. Additionally, we observed that 4 of these 5 proteins had one measurement that could be classified as an outlier. For the 3 proteins found significant only by median centering method, we also observed a deviation from the first diagonal for 2 of them. Additionally, we observed that the 3 proteins present a bimodal distribution with a median value that could be defined as an outlier.\u003c/p\u003e \u003cp\u003eBased on the analysis of experimental data, we can conclude that ComBat and median centering greatly suffer from the presence of outliers within the BCs and that BAMBOO is able to flag potential false discoveries due to low measured values.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eHere, we investigated batch effects occurring in proteomic studies using Olink PEA technologies. We developed a new method, called BAMBOO, which can correct for the identified batch effects using a minimal number of bridging controls. We compared this new method to existing alternatives using a simulation study and an experimental dataset. In both cases, BAMBOO corrected well for the batch effects and had potentially less false discoveries.\u003c/p\u003e \u003cp\u003eWith the emerging technologies and increasing prevalence of large-scale proteomic studies, efforts to characterize batch effects are crucial. However, in many cases, the methodology for their assessment remains unclear or even unattainable when no bridging controls are included. A recent comprehensive study by Eldjarn \u003cem\u003eet al.\u003c/em\u003e, investigated the reproducibility of Olink and SomaScan, using the ratio of the coefficient of variation (CV) of repeated measurements to the CV of the assay [15]. Their findings revealed that the Olink Discovery assays exhibit greater precision than SomaScan. Interestingly, imperfect CV ratios suggested the potential presence of batch effects, in contrast to previous studies with smaller sample sizes [16\u0026ndash;18]. In another study, Haslam \u003cem\u003eet al.\u003c/em\u003e, evaluated Olink\u0026rsquo;s reproducibility using a triplicate of plasma samples among other analyses [19]. They found that approximately half of the proteins measured demonstrated excellent stability (Spearman r\u0026thinsp;\u0026gt;\u0026thinsp;0.75) while about a third exhibited good stability (Spearman 0.40\u0026thinsp;\u0026lt;\u0026thinsp;r\u0026thinsp;\u0026lt;\u0026thinsp;0.75). These findings align with our results, indicating that most proteins measured in technical replicates display a good correlation between plates. However, it is noteworthy that some proteins show protein-specific batch effects.\u003c/p\u003e \u003cp\u003eA recent paper by Dammer \u003cem\u003eet al.\u003c/em\u003e, presents a comprehensive overview of current available methods to correct for batch effects that might be due to variations in sample preparation, batching, platform settings, personnel, and other experimental procedures [20]. They also proposed a new version of the median polish approach initially described by John Tukey in 1977 [21]. This new method is called TAMPOR and it can be used with or without bridging controls. While this method appears efficient to compare data from different platforms, data are transformed by an abundance normalization and therefore lose their original log2 scale (in case of Olink), complicating data interpretation. It seems that methods such as BAMBOO and MOD are preferable for large scale studies as data will keep their original scale and TAMPOR might be preferred when comparing or combining data from different platforms.\u003c/p\u003e \u003cp\u003eWe performed a simulation study to compare our new approach, BAMBOO, with existing approaches. The most basic batch correction method, median centering, did not perform well even in scenarios without plate-wide effect and outliers. Subsequently, ComBat, originally designed for processing transcriptomics data performed equally well as BAMBOO in the absence of plate-wide effects and outliers. However, its performance suffered when these factors were present. Although originally developed for microarray data correction, ComBat is widely used for analyses in other fields of omics data, such as Olink studies [12, 22, 23]. Lastly, MOD, a simple method in which the median of the paired-differences between bridging controls is used as a correction factor, showed comparable performance to BAMBOO in scenarios with outliers. However, this method was not robust against plate-wide batch effects. We showed that in scenarios with plate-wide effects, MOD identified more false positives with relatively large effect sizes and more false negatives with small effect sizes. It is possible that MOD over-corrects for batch effects and hence leads to more false positives and negatives in statistical analysis.\u003c/p\u003e \u003cp\u003eIn both our simulation study and the analysis of experimental data, we saw that both ComBat and median centering are impacted by outliers. Proteins called significantly different after correction with one of these methods showed a clear deviation from the first diagonal. Even though the experimental data did not contain a complete sample as outliers (all proteins of a sample), some individual proteins could be identified as such (outside the expected range). Interestingly, most studies made on microarray data show that ComBat can deal well with outliers [7, 8, 24]. When looking at other types of data, such as imaging, Han \u003cem\u003eet al.\u003c/em\u003e, showed that using ComBat without identifying outliers could lead to false discoveries [25]. This suggests that the type of data used for ComBat can also influence its performance.\u003c/p\u003e \u003cp\u003eIt is advised to take along at least 8 bridging controls per plate for correcting batch effects [5]. Logically, the more bridging controls are used, the better batch effects are corrected. However, there is a balance between the number of experimental samples that can be measured and how precisely batch effects need to be corrected, also in terms of the available budget. Our simulation study showed that 10 BCs are sufficient to accurately correct for batch effects even when there is a strong plate-wide effect, when using BAMBOO. However, even in economical scenarios with 5 BCs, we showed that BAMBOO still adjusts well for batch effects, even with strong plate-wide effects (Accuracy\u0026thinsp;\u0026gt;\u0026thinsp;96%). However, its performances dropped with the addition of one outlier. Hence, we advise to take along 10\u0026ndash;12 BCs to account for the removal of potential outliers when using BAMBOO. Additionally, we recommend using a biologically heterogeneous group of samples (i.e. healthy and diseased) to increase the ranges of measurements and making sure that the majority will be above the LOD.\u003c/p\u003e \u003cp\u003eOne of the novelties of our approach is to flag proteins for which BCs are below the limit of detection. In this situation, it is difficult to compute adjustment factors as the difference between two plates for those BCs will be null. Hence, those proteins might still show a batch effect in the downstream analyses. Another novelty of our approach is the ability of BAMBOO to detect outliers within the BCs and to exclude them from correction.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn conclusion, we have identified the different batch effects that can be observed in proteomic studies and developed a new method to correct for them and compared it with 3 commonly used methods. We showed that 10\u0026ndash;12 bridging controls is the optimal number of BCs to take along to accurately correct for batch effects. ComBat and median centering cannot properly correct for them, and we therefore advise to not use them for PEA studies. One method (MOD) was influenced by plate-wide batch effects and is therefore not recommended to use when such batch effect is present in the data. We therefore advise to use BAMBOO in all studies; which is available on GitHub (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/CIC-UMCutrecht/BAMBOO/\u003c/span\u003e\u003cspan address=\"https://github.com/CIC-UMCutrecht/BAMBOO/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003ePEA - Proximity extension assay\u003c/p\u003e\n\u003cp\u003eBAMBOO - Batch AdjustMents using Bridging cOntrOls\u003c/p\u003e\n\u003cp\u003eMOD - Median of the difference\u003c/p\u003e\n\u003cp\u003eTNR - True negative rate\u003c/p\u003e\n\u003cp\u003eTPR - True positive rate\u003c/p\u003e\n\u003cp\u003e(q)PCR - (quantitative) Polymerase chain reaction\u003c/p\u003e\n\u003cp\u003eBC - Bridging control\u003c/p\u003e\n\u003cp\u003eRUV - Remove Unwanted Variation\u003c/p\u003e\n\u003cp\u003eSVA - Surrogate variable analysis\u003c/p\u003e\n\u003cp\u003eMOD - Median of the difference\u003c/p\u003e\n\u003cp\u003eDNA - Deoxyribonucleic acid\u003c/p\u003e\n\u003cp\u003eNPX - Normalized protein expression\u003c/p\u003e\n\u003cp\u003eHC - Healthy control\u003c/p\u003e\n\u003cp\u003eIBD - Inflammatory bowel disease\u003c/p\u003e\n\u003cp\u003eJDM - Juvenile dermatomyositis\u003c/p\u003e\n\u003cp\u003eRPM - Rounds per minute\u003c/p\u003e\n\u003cp\u003eFDR - False discovery rate\u003c/p\u003e\n\u003cp\u003eLOD - Limit of detection\u003c/p\u003e\n\u003cp\u003eCV - Coefficient of variation\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cem\u003eEthics approval and consent to participate\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eInformed consent was obtained from all individuals included. The different studies were approved by the ethics committee of the UMC Utrecht (the Netherlands): 07/125 for HC, NL61114.041.17. for IBD patients,NL47875.041.14 for JDM patients and NL60910.041.17 for virus infection patients. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eFunding\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eNone\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u0026nbsp; Consent for publication:\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u0026nbsp;\u0026nbsp;\u003c/em\u003eNot applicable\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eAvailability of data and materials\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eCompeting interests\u0026nbsp;\u003c/em\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eAuthors\u0026apos;\u0026nbsp;\u003c/em\u003econtributions\u003c/p\u003e\n\u003cp\u003eHMS contributed to the analysis, interpretation of the data and the development of the software under the mentorship of JD. EMD and SN contributed to the design of the study and acquisition of the data. \u0026nbsp;AS and BO contributed to the acquisition of the data. AP and FvW contributed to the interpretation of the data. All authors contributed to the revision of the manuscript drafted by HMS and JD.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eAcknowledgements\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to acknowledge Louis Bont for providing the viral infected samples used as experimental data.\u003cbr\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col start=\"1\" type=\"1\"\u003e\n \u003cli\u003eCaliff RM: Biomarker definitions and their applications. 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Proteomics 2022, 22(13-14).\u003c/li\u003e\n \u003cli\u003e\u0026nbsp;Dammer EB, Seyfried NT, Johnson ECB: Batch correction and harmonization of \u0026ndash;Omics datasets with a tunable median polish of ratio. Frontiers in Systems Biology 2023, 3.\u003c/li\u003e\n \u003cli\u003e\u0026nbsp;Tukey, J. W. Exploratory data analysis. Reading, MA: Addison-Wesley; 1977.\u003c/li\u003e\n \u003cli\u003e\u0026nbsp;\u0026Aring;kesson J, Hojjati S, Hellberg S, Raffetseder J, Khademi M, Rynkowski R, Kockum I, Altafini C, Lubovac-Pilav Z, Mellerg\u0026aring;rd J, Jenmalm MC, Piehl F, Olsson T, Ernerudh J, Gustafsson M: Proteomics reveal biomarkers for diagnosis, disease activity and long-term disability outcomes in multiple sclerosis. Nature Communications 2023, 14(1).\u003c/li\u003e\n \u003cli\u003e\u0026nbsp;Angerfors A, Br\u0026auml;nnmark C, Lagging C, Tai K, M\u0026aring;nsby Svedberg R, Andersson B, Jern C, Stanne TM: Proteomic profiling identifies novel inflammation-related plasma proteins associated with ischemic stroke outcome. Journal of Neuroinflammation 2023, 20(1).\u003c/li\u003e\n \u003cli\u003e\u0026nbsp;Chen C, Grennan K, Badner J, Zhang D, Gershon E, Jin L, Liu C: Removing batch effects in analysis of expression microarray data: An evaluation of six batch adjustment methods. PLoS ONE 2011, 6(2).\u003c/li\u003e\n \u003cli\u003e\u0026nbsp;Han Q, Xiao X, Wang S, Qin W, Yu C, Liang M: Characterization of the effects of outliers on ComBat harmonization for removing inter-site data heterogeneity in multisite neuroimaging studies. Frontiers in Neuroscience 2023, 17.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"proteomics, large proteomic study, batch effects, batch effects correction, bridging controls","lastPublishedDoi":"10.21203/rs.3.rs-4044125/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4044125/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground\u003c/strong\u003e: The proximity extension assay (PEA) facilitates large-scale proteomic studies involving a large number of proteins and samples. However, inevitable discrepancies in day-to-day measurements may introduce the inherent risk of undesirable variation, known as batch effects, which may impact down-stream statistical analyses and increase the chances of false discoveries. The implementation of bridging controls on each plate has been suggested to mitigate this complication, but a clear method on how to use this strategy is still lacking. In this study, we characterized potential batch effects in proteomics using PEAs and generated guidelines to mitigate batch effects using bridging controls.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e: This study characterized three distinct types of batch effects (protein-specific, sample-specific, and plate-wide) in PEA proteomic studies. We developed a new method, BAMBOO (Batch AdjustMents using Bridging cOntrOls), based on a robust regression model. In a simulation study, we compared BAMBOO with established batch correction techniques; median centering, median of the difference (MOD), and ComBat. We observed that median centering and ComBat were significantly impacted by outliers within the bridging controls, whereas BAMBOO and MOD were more robust when no plate-wide batch effects were introduced. Moreover, upon introduction of plate-wide batch effects, BAMBOO was performing better than MOD in terms of accuracy, true negative rate and true positive rate. Inclusion of 10-12 bridging controls was found to optimally correct for batch effects. Applying the different methods to experimental data showed that BAMBOO and MOD result in a reduced incidence of false discoveries compared to the alternative methods.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusion\u003c/strong\u003e: Our study underscores the prevalent existence of batch effects in PEA proteomic studies, which can be corrected using bridging controls using an innovative, robust and effective tool, BAMBOO. The use of BAMBOO may enhance the reliability of large-scale analyses in the proteomic field using PEA.\u0026nbsp;\u003c/p\u003e","manuscriptTitle":"Correction of batch effects in high throughput proximity extension assays for proteomic studies using bridging controls: the BAMBOO method.","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-26 06:39:58","doi":"10.21203/rs.3.rs-4044125/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1b05a529-aa0f-49dd-a833-4609495b0462","owner":[],"postedDate":"March 26th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-05-06T04:59:28+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-26 06:39:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4044125","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4044125","identity":"rs-4044125","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}