Heterogeneity in different genomic studies compromises the performance of machine learning models in cross-study phenotype predictions. Overcoming heterogeneity when incorporating different studies in terms of phenotype prediction is a challenging and critical step for developing machine learning algorithms with reproducible prediction performance on independent datasets. We investigated the best approaches to integrate different studies of the same type of omics data under a variety of different heterogeneities. We developed a comprehensive workflow to simulate a variety of different types of heterogeneity and evaluate the performances of different integration methods together with batch normalization by using ComBat. We also demonstrated the results through realistic applications on six colorectal cancer (CRC) metagenomic studies and six tuberculosis (TB) gene expression studies, respectively. We showed that heterogeneity in different genomic studies can markedly negatively impact the machine learning classifier’s reproducibility. ComBat normalization improved the prediction performance of machine learning classifier when heterogeneous populations are present, and could successfully remove batch effects within the same population. We also showed that the machine learning classifier’s prediction accuracy can be markedly decreased as the underlying disease model became more different in training and test populations. Comparing different merging and integration methods, we found that merging and integration methods can outperform each other in different scenarios. In the realistic applications, we observed that the prediction accuracy improved when applying ComBat normalization with merging or integration methods in both CRC and TB studies. We illustrated that batch normalization is essential for mitigating both population differences of different studies and batch effects. We also showed that both merging strategy and integration methods can achieve good performances when combined with batch normalization. In addition, we explored the potential of boosting phenotype prediction performance by rank aggregation methods and showed that rank aggregation methods had similar performance as other ensemble learning approaches. Overcoming heterogeneity when incorporating different studies in terms of phenotype prediction is a challenging and critical step for developing machine learning algorithms with reproducible prediction performance on independent datasets. We developed a comprehensive workflow to simulate a variety of different types of heterogeneity and evaluate the performances of different integration methods together with batch normalization by using ComBat. We also demonstrated the results through realistic applications on six colorectal cancer (CRC) metagenomic studies and six tuberculosis (TB) gene expression studies, respectively. From both the simulation studies and realistic applications, we showed that batch normalization is essential for improving phenotype prediction performance by machine learning classifiers when incorporating multiple heterogeneous datasets. Combined with batch normalization, merging strategy and ensemble weighted learning methods both can boost machine learning classifier’s performance in phenotype predictions. In addition, we explored that rank aggregation methods should be considered as alternative ways to boost prediction performances, given that these methods showed similar robustness as ensemble weighted learning methods. Genotype to phenotype mapping is an essential problem in the current genomic era. With the development of advanced biotechnologies, many types of genomic data such as single nucleotide polymorphisms, gene expression profiles, proteomics, metagenomics, etc. have been generated in many different studies. These omics data provide essential resources to understand the relationships between omics data and phenotypes. Despite these fundamental developments, due to the heterogeneity of data, it is challenging to integrate the omics data to understand genotype to phenotype mapping. For a single type of data such as gene expression or metagenomic data, many sources of heterogeneity can occur. For example, the samples can come from different ethnic groups with varying underlying distributions of the features. Even if the samples come from the same population, the genomic data can be generated from different laboratories and/or derived from different experimental technologies resulting in different distributions of the data. Another types of heterogeneity can be caused by the different causal mechanisms of the same phenotype in the populations under study . The objMany machine learning algorithms including linear regression, logistic regression, penalized regression, support vector machines (SVM), random forests (RF), neural networks (NN) and deep neural networks (DNN) have been used to predict phenotypes from omics data –5. Most Many studies have been carried out to mitigate the heterogeneity in cross-study phenotype predictions. Zhang et al.  focused Merging all datasets into one and treating all samples as if they are from the same study is a generally used method for cross-study predictions. With the increase of sample size and diversity in the study population, merging method has been shown to lead to better prediction performance than using only individual studies , 5, 10. ComBat  normalizOur study offers innovations through the development of a comprehensive workflow that effectively addresses heterogeneity in various types of omics data, an issue that has persistently compromised the performance of machine learning models in cross-study phenotype predictions. By investigating the optimal approaches to integrate different studies and conducting realistic applications on colorectal cancer and tuberculosis studies, we have created a robust framework that elevates the reproducibility of machine learning classifiers. Furthermore, the innovative utilization of ComBat normalization with integration methods markedly enhances prediction performance through removing heterogeneity effects. Our study also ventures into mostly uncharted territory by exploring the potential of boosting phenotype prediction performance through rank aggregation methods in handling heterogeneous omic data, a significant innovation in its own right.To investigate the prediction performance of different merging and integration methods when applied to multiple heterogeneous datasets, we developed a comprehensive workflow with three main steps to conduct the experiments.The first step in our workflow involves simulating diverse metagenomic datasets under three distinct scenarios, as illustrated in Population differences, such as variances in ethnicity, diet, and other factors, can lead to variations in the genomic features within a population. These features encompass single nucleotide polymorphisms (SNPs), expression levels, and microbial abundance in the microbiome. Consequently, when training machine learning classifiers on one population and applying them to a different population, it is crucial to account for the heterogeneity in the background distributions. Neglecting this heterogeneity can adversely affect the prediction performance.To assess how heterogeneity arising from population differences can influence the performance of machine learning classifiers, and to identify the optimal approaches for integrating prediction methods from various heterogeneous studies, we simulated three distinct populations. Each population was characterized by different background genomic distributions, and we manipulated these differences. For a detailed description of the implementation process for simulating the two training datasets and one test dataset, please refer to Scenario 1: Divergent training and test populations with varied genomic feature distribution.The second scenario of heterogeneity pertains to batch effects. In simple terms, batch effects represent non-biological disparities that emerge across separate batches of data. These discrepancies are usually a byproduct of technical variances in experimental conditions or different labs. Some contend that batch effects can compromise the replicability of genomic studies .It is commonplace to correct these batch effects in the pre-processing phase when dealing with genomic data. Recently, several methods for batch effect correction have been proposed, including ComBat , edgeR , and DESIn our study, we sought to evaluate these methods’ efficacy in reducing batch effects on the predictive performance of binary classifiers. This was achieved through simulation studies. In this particular setup, the training and test datasets originate from the same genomic feature distribution. However, upon simulating the training and test datasets, we then introduced batch effects into the training datasets, creating two distinct batches. These two batches were then used as the training datasets for the subsequent experiments. We provide a detailed description of the method in Scenario 2: Different batch effects on training data with consistent underlying population genomic feature distribution.In the aforementioned two scenarios, we examined how both the variability in the distribution of genomic features among populations and batch effects influence a classifier’s performance. Furthermore, we operated under the assumption that the disease models are consistent across either the same or different populations. However, a range of studies have suggested that the microbes linked with certain diseases can depend on the population in question. For instance, research indicates that colorectal cancer development can vary among populations with differing rates of diabetes , smokingConsequently, we have further assessed the effectiveness of merging and various integration methods when the underlying disease models differ. More specifically, the degree of overlap in disease-associated OTUs between training and test datasets are varied. This constitutes the third scenario in our research workflow. We adjusted the number of disease-related microbes that overlap in the training and test disease models, and then simulated different datasets in line with these adjustments. The methodology for this process is outlined in Scenario 3: Varying degrees of overlap in disease-associated OTUs between training and test datasets.Following the creation of the training and test datasets from the three scenarios mentioned above, depicted in Subsequent to the previous steps, the two simulated training datasets and one test dataset are used as input for the final classification step of in this workflow. At this stage, we independently train a machine learning classifier on each training dataset and subsequently apply each to the test dataset. This generates two distinct lists of prediction probabilities. Then, we apply various integration methods to these two probability lists to yield the final results.The two lists of prediction probabilities from the trained machine learning classifiers are directly employed in ensemble weighted learning methods. However, when we apply rank aggregation methods, the prediction probabilities are converted into ranks. A comprehensive explanation of the ensemble weighted learning and rank aggregation methods we used can be found in Classification stage.In addition to these integration methods, we also adopted a merging strategy. As illustrated in In the subsequent three sections, we delve into the specifics of the three stages within our workflow: the Simulation Stage, the Naive and ComBat Normalization Stage, and the Classification Stage. Each of these stages plays a crucial role in our analyses, and understanding them is fundamental to comprehending the entire process.In the first scenario, we contemplated a situation where the two training populations are distinct from each other and both are different from the test population. We adjusted our simulations to reflect the extent of these differences. To emulate this scenario, we first established the baseline abundance levels for the operational taxonomic unit (OTU) across different populations.Three probability vectors were created, each representing the underlying OTU abundance levels in three distinct populations. These were adapted from three real colorectal cancer (CRC) metagenomic datasets. We curated a total of six publicly accessible, geographically diverse CRC metagenomic datasets with download links provided in their respective original papers , 20–24. We created a PCoA plot to illustrate the population differences among these six CRC datasets, as shown in The two training datasets were pre-processed to preserve the top 1000 OTUs with the largest variance in each dataset. We then amalgamated the OTUs from the two datasets to create a comprehensive set of OTUs for the subsequent analysis. This simulation study incorporated a total of 1,267 OTUs. We maintained the OTU count of the 1,267 OTUs for the Feng dataset, which forms the background distribution for simulating the test dataset, and removed the remaining OTUs. Subsequently, the count data was converted into a relative abundance vector, calculated by dividing each OTU’s total count from all samples by the total counts of all OTUs.v1, v2, and v3 as the three background relative abundance vectors derived from the microbial abundance profiles of the healthy control samples in the pre-processed Hannigan, Yu, and Feng datasets, respectively. These three vectors share the same 1,267 dimensionality, with each dimension representing the relative abundance level for each OTU. In order to scrutinize the influence of population differences on cross-study prediction, we devised a pseudo-population with a relative abundance vector defined as follows:Let us denote v1(α) − v2 = α(v1 − v2). Consequently, the difference between the two populations simulated based on v1(α) and v2 escalates with α. When α = 0, both simulated populations share the same underlying distribution, hence eliminating population differences between the two training sets. Conversely, at α = 1, the two simulated populations exhibit the maximum difference. We employed diverse α values, ranging from 0 to 1 in increments of 0.2, to reflect varying degrees of training population differences in subsequent analyses. The relative abundance profiles v1(α) and v2 served as background relative abundance vectors for training populations, while v3 was applied to the test population.Note that ed, and hypothesized that the relative abundance of these OTUs could be represented as:From these 1,267 OTUs, we randomly selected 10 OTUs, assuming these were associated with a specific disease of interest. Given that disease-associated OTUs can either be enriched or depleted, we presumed the first 5 OTUs to be enriched and the remaining 5 to be depleted. These 10 OTUs were consistent across all subsequent experiments. To quantify the disease effect on these associated OTUs, we defined a disease effect factor, v1(α), v2, and v3 in this manner and normalized them into probability vectors, denoted as v1(α)′, ed to be 1.05, 1.075, and 1.1 in our simulation studies to assess the impact of disease effect. The larger the ed value, the more pronounced the difference between case and control samples.First, we adjusted 6) was used for all subsequent simulations. OTU pseudo counts were generated using a multinomial distribution MN where v denotes the relative abundance vector. For control sample simulations, v1(α), v2, and v3 were utilized; for case simulations, v1(α)′, v, and the resultant datasets were denoted as training1, training2, and test, respectively. Subsequently, count data were transformed into log-transformed relative abundance data. This was achieved by first dividing the sample counts, followed by applying a zero-replacement strategy proposed by Martn-Fernndez et al.  A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. 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Please don't hesitate to contact us if you have any questions or comments.Sincerely,Luis Pedro CoelhoAcademic EditorPLOS Computational BiologyEdwin WangSection EditorPLOS Computational Biology***********************The reviewers agree that there is interest in the study, but also raise important points which should be addressed before publication.Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: In this paper, Gao and Sun investigated different strategies phenotype prediction from multiple heterogeneous studies, including batch normalization, merging, ensemble and ranking aggregation. Through several simulation of three scenarios and real datasets, the authors found that using COMBAT normalization and mering can improve the phenotype prediction accuracy. This is an interesting study and here are my comments to the paper:1. The authors only test one classifier in their study. I wonder whether the same observations applied to some other classifier, e.g. SVM, lasso and XGBoost etc.2. The gap of the prediction accuracy rates between different approaches are much more dramatic in the simulated data compared to the real data. I am wondering how realistic the simulated datasets are. The authors discuss the potential reason is that as the number of training datasets increase, the gap between different approach will decrease, it will be good if the authors can explore this aspect in the simulation.3. While batch normalization can remove the batch effect and study specific variation, the current and improve the phenotype prediction. The current strategies are limited as they require the test data information and thus the training data needs to be re-adjusted and the model needs to be retrained every time when a new test dataset comes in. It will be good that the author can discuss the limitation and also this approach compared to strategies like domain adaption and methods like CPOP .https://doi.org/10.1038/s41746-022-00618-5• Wang, K.Y.X., Pupo, G.M., Tembe, V. et al. Cross-Platform Omics Prediction procedure: a statistical machine learning framework for wider implementation of precision medicine.npj Digit. Med. 5, 85 (2022). Minor comments:1. Figure 1c. To me this section is a “Classification” step, rather than an “Integration” step, as it contains model training + integration of results etc.2. It will be good that the authors can include a conclusion paragraph at the end of the manuscript to summarize the key take home messages of the paper.3. It will be good to group the different methods in Figure 3-5 like Figure 6.Reviewer #2: The paper investigates the best approaches to integrate different studies of the same type of omics data under a variety of different heterogeneities. The authors developed a comprehensive workflow to simulate a variety of different types of heterogeneity and evaluate the performances of different integration methods together with batch normalization by using ComBat. They also demonstrated the results through realistic applications on six colorectal cancer (CRC) metagenomic studies and six tuberculosis (TB) gene expression studies, respectively. They showed that heterogeneity in different genomic studies can markedly negatively impact the machine learning classifier’s reproducibility. Albeit the idea is interesting and the results look good, I am not entirely convinced by the evidence presented in the paper1.The authors indicated that the comBat normalization improved the prediction performance of machine learning classifier when heterogeneous populations presented, and could successfully remove batch effects within the same population. When “the methods” + “comBat”, the prediction performances were improved. But both “the methods” and “comBat” are existing methods, what is the biggest innovation of this study?2.I tried to understand the method details, but failed. Please provide more details of the methods, especially for the newly developed part. Otherwise, it is hard to judge whether the new approach is worthwhile.**********Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. 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Read more information on sharing protocols at  26 Jul 2023AttachmentResponse to reviewers.docSubmitted filename: Click here for additional data file. 30 Sep 2023Dear Dr. Sun,We are pleased to inform you that your manuscript 'Batch Normalization Followed by Merging is Powerful for Phenotype Prediction Integrating Multiple Heterogeneous Studies' has been provisionally accepted for publication in PLOS Computational Biology.Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. 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Although gene expression data play significant roles in biological and medical studies, their applications are hampered due to the difficulty and high expenses of gathering them through biological experiments. It is an urgent problem to generate high quality gene expression data with computational methods. WGAN-GP, a generative adversarial network-based method, has been successfully applied in augmenting gene expression data. However, mode collapse or over-fitting may take place for small training samples due to just one discriminator is adopted in the method.In this study, an improved data augmentation approach MDWGAN-GP, a generative adversarial network model with multiple discriminators, is proposed. In addition, a novel method is devised for enriching training samples based on linear graph convolutional network. Extensive experiments were implemented on real biological data.The experimental results have demonstrated that compared with other state-of-the-art methods, the MDWGAN-GP method can produce higher quality generated gene expression data in most cases. Over the last two to three decades, the rapid development of the genome sequencing technology has made it into reality to measure the expression level of thousands of genes from a biological sample simultaneously. Since gene expression data is extracted by various gene profiling technologies, direct reflecting the physiological state and disease of the human body , many coNevertheless, the gene expression profile data are fundamentally limited in sample size, diversity, and the speed at which they can be gathered , due to To the best of our knowledge, there are generally three categories of data augmentation methods for generating gene expression data, such as sample-based, simulator-based, and generative adversarial network-based. The sample-based methods include random sampling , mean saIn 2020, Chaudhari et al.  firstly The multiple discriminator WGAN-GP (MDWGAN-GP) model is proposed. It can ensure the high quality of the generated gene expression data. Multiple discriminators are adopted prevent mode collapse via providing more feedback signals to the generator.A novel approach based on linear graph convolutional network (GCN) is put forward to enrich training samples, avoiding over-fitting or mode collapse caused by small sample size in high dimensional data.The pan-cancer gene expression datasets were produced to demonstrate the effectiveness of the MDWGAN-GP approach. A data preprocess method is conducted to select the genes with high confidence or top ranking from protein-protein interaction networks, so as to relieve the curse of dimensionality encountered in the training. Extensive experiments were implemented to compare the quality of generated gene expression data between the MDWGAN-GP method and other state-of-the-art ones.In the process of training generative adversarial networks, mode collapse is a serious issue to be concerned about. It may be an effective channel to alleviate the problem to improve the diversity of training samples as well as feedback signals. Among the above mentioned approaches, the diversity of feedback signals may be constrained for just one discriminator being adopted in the GANs. Therefore, in this paper, the collaboration of multiple discriminators is explored. The main contributions of this paper are summarized as follows: G and a discrimination network D. Given some noise z and conditional information y , the generator G learns to produce synthetic samples similar to the real distribution. The discriminator D needs to distinguish whether the input sample is from authentic sample p(x) or from sample p(z) produced by the generator G. The loss function of CGAN can be formulated as:The conditional generative adversarial network (CGAN)  attemptsDifferent from CGAN, the Wasserstein generative adversarial network (WGAN)  tries toG= be an undirected graph, where V and E represent the set of nodes i=1,2,...,n) and edges  –29 are aRecently, Viñas et al.  proposedn rows (samples) and m columns (genes), where each entry represents the expression level of a given gene in a particular sample. A pair of K-Nearest Neighbors (KNN) graphs [f(I (resp. I), where It is generally regarded that enriched training samples contribute to GAN capturing the original distribution . Inspire) graphs , 35 \docIt has been regarded that the adoption of multi discriminators can improve the stability of optimization process . In thisFigure Y indicates the conditional labels. Z denotes the noise samples, In a generative adversarial network, the generator tries to produce samples that look real enough to trick the discriminator, while the discriminator attempts to distinguish the generated samples from the real ones. Here the objective functions are designed for one generator and three discriminators in MDWGAN-GP, as illustrated in Equation :6\documeEquation  and EquaEquation :7\documeformance .G receives noise vector Z and conditional label Y as input and produces vector i=1,2,3) takes either a real gene expression sample Y, and tries to distinguish whether the input sample is real or fake. Matrices Figure dist The Cancer Genome Atlas (TCGA). It is a public biospecimen repository which aims to augment the understanding of the molecular mechanisms of cancers. The database contains high-throughput genomic data from over 20,000 primary cancer and matched healthy samples spanning 33 cancer-types.(2) The Genotype-Tissue Expression (GTEx). It is also a public resource built to study tissue-specific gene expression and regulation. It contains samples collected from 54 non-diseased tissue sites across nearly 1000 individuals .(3) The String dataset. String is a database which records known and predicted protein-protein interactions, including physical as well as functional connections. The latest Human Protein Interaction Network version 11.5 was adopted in the experiments.(4) The HumanNet dataset. HumanNet  is a datThe data preparation was conducted was follows. Firstly, the raw RNA-seq sample datasets of TCGA and GTEx were acquired from Wang et al. . Fifteendist:9\documdist [K was 5 for KNN, and two hidden layers with 128 units and the ReLU activation function were adopted for MLP. For each method, the average results of ten runs are calculated and presented. It can be seen from the three tables that among the three methods the samples generated with the MDWGAN-GP model perform the best classification ability in the vast majority of cases. Furthermore, basing on the classification methods RF and KNN, the samples generated with the MDWGAN-GP model even present superior classification performance than the real samples .As illustrated in Tables rs (KNN) , and mulrs (KNN) , were adFurthermore, in order to intuitively reflect the clustering ability of the samples generated by model MDWGAN-GP, we compare the cluster results on the real samples with those on the generated ones. As shown in Figs. dist among the ten key genes. Figure Ten most frequently mutated genes in human cancers  were chop-value for each gene by using the denormalized generated expression data, and the genes with p-values less than 0.05 were selected as differentially expressed genes. For the convenience of description, we use “real-DEGs” and “fake-DEGs” to denote the DEGs ascertained based on the real and the generated datasets, respectively.As analyzed above, compared with using the real datasets, it might be better to conduct differential analysis between normal and cancer tissues using the generated ones. In this section, comparisons were further performed between the differentially expressed genes identified based on the generated datasets and those identified based on the real ones. Eighty percent of all pan-cancer samples were randomly selected as the training set, and the same number of samples were generated with model MDWGAN-GP. DESeq2 package of R was called to calculate the difference fold and As shown in Table p-values. The steelblue nodes represent the pathways, and the size of which indicates the number of DEGs enriched. Other colored small nodes represent the DEGs, and the color of which indicates its value of Secondly, package clusterProfiler of R  was callSince it is both difficult and expensive for gathering gene expression data with biological experiments, generating them through computational approaches has aroused great attentions. In this study, a generative adversarial network model MDWGAN-GP, having multiple discriminators, is put forward. A novel method is designed for enriching training samples based on linear graph convolutional network. Compared with other state-of-the-art methods, the MDWGAN-GP method can produce higher quality generated gene expression data in most cases. In addition, some critical biomarkers, enriching in some significant biological pathways, are identified based on the generated data. All of these have been verified through extensive experiments performed on real biological data.However, during the process of experiments, we found that GAN and its improved versions have the inherent defect of being difficult to train. It has been reported that the diffusion model can ensure sample diversity by means of adding and removing noise step by step . It is a


Luminal-A breast cancer is the most frequently occurring subtype which is characterized by high expression levels of hormone receptors. However, some luminal-A breast cancer patients suffer from intrinsic and/or acquired resistance to endocrine therapies which are considered as first-line treatments for luminal-A breast cancer. This heterogeneity within luminal-A breast cancer has required a more precise stratification method. Hence, our study aims to identify prognostic subgroups of luminal-A breast cancer. In this study, we discovered two prognostic subgroups of luminal-A breast cancer (BPS-LumA and WPS-LumA) using deep autoencoders and gene expressions. The deep autoencoders were trained using gene expression profiles of 679 luminal-A breast cancer samples in the METABRIC dataset. Then, latent features of each samples generated from the deep autoencoders were used for K-Means clustering to divide the samples into two subgroups, and Kaplan-Meier survival analysis was performed to compare prognosis  between them. As a result, the prognosis between the two subgroups were significantly different . This prognostic difference between two subgroups was validated using gene expression profiles of 415 luminal-A breast cancer samples in the TCGA BRCA dataset . Notably, the latent features were superior to the gene expression profiles and traditional dimensionality reduction method in terms of discovering the prognostic subgroups. Lastly, we discovered that ribosome-related biological functions could be potentially associated with the prognostic difference between them using differentially expressed genes and co-expression network analysis. Our stratification method can be contributed to understanding a complexity of luminal-A breast cancer and providing a personalized medicine. Luminal-A breast cancer is the most frequently occurring breast cancer subtype. However, it shows high variability in prognosis, and more precise stratification is needed. In this paper, we identified two prognostic subgroups of luminal-A breast cancer, BPS-LumA and WPS-LumA. To this end, we used deep autoencoders which automatically generate informative latent features that represent essential properties of gene expressions. We found that the two subgroups clustered using the latent features are significantly different in prognosis. This prognostic difference was validated with the external luminal-A breast cancer cohort. We showed that only latent features are able to discover the prognostic subgroups compared to gene expression profiles. In addition, we compare our results with the two previous luminal-A breast cancer stratification method which are complementary to each other. Finally, we suggested biological functions associated with the differentially expressed genes between the two subgroups as potential molecular mechanisms which results in the differences in the prognosis. We expect that our method could be used for the personalized medicine of luminal-A breast cancer. Personalized medicine is the ultimate goal of modern medicine . The perBreast cancer which is one of the leading causes of death among females , and it Especially, luminal-A breast cancer is the most frequently occurring subtype which accounts for about 60~70% of whole breast cancer, and it is characterized by hormone receptor-positive  and HER2 receptor-negative . Hence, Consequently, this heterogeneity within luminal-A breast cancer has required a more precise stratification method which makes it possible to predict the prognosis and provide the personalized diagnosis and treatment. Recently, several previous studies suggested prognostic subgroups of luminal-A breast cancer through machine learning and gene expressions. For example, Netanely et al. clustered luminal-A breast cancer samples into two prognostic subgroups (LumA-R1 and LumA-R2) using the most variable genes in their expressions . Later, Even though the previous studies successfully identified the prognostic subgroups of luminal-A breast cancer, they have a limitation that they required human engineering to select the features (genes) for stratifications. For example, Netanely et al. took the top 2,000 genes which show the highest variability in the expressions, and Poudel et al. selected the marker genes according to significances of microarray analysis .In the perspective of feature engineering, a deep learning which takes advantages of data-driven automatic feature learning can be a promising solution . EspeciaIn this study, we identified two prognostic subgroups of luminal-A breast cancer. To this end, we trained deep autoencoders using gene expression profiles of luminal-A breast cancer to generate informative latent features of each sample and we discovered the subgroups through the latent features and unsupervised learning. Additionally, we showed that our method has important biological contributions in realizing precision medicine of luminal-A breast cancer. First, we demonstrated that our method is feasible in an independent test set, which is the most important part to translate the deep learning approaches to clinical practices. Furthermore, we proved that the latent features are more useful than gene expression profiles and features generated by traditional dimensionality reduction method  in terms of discovering the prognostic subgroups. In addition, we suggested potential molecular mechanisms which determine the prognostic difference using differentially expressed genes between the subgroups and weighted gene co-expression network analysis. Lastly, we compared our stratification with two previous luminal-A breast cancer stratification methods.First of all, as we aimed to obtain informative latent features to identify prognostic subgroups of luminal-A breast cancer, we trained deep autoencoders which are able to automatically extract and compress important properties of gene expression profiles without additional human engineering. To this end, we obtained gene expression profiles of 679 and 415 luminal-A breast cancer samples from METABRIC and TCGA dataset to use them as training set and validation set, respectively. Before training the deep autoencoders, we chose the top 5,000 genes which show the highest variability across the samples based on the median absolute deviation (MAD) in the METABRIC dataset . Then, wAs we expected, the MSEs decreased continuously as the size of hidden layers increased in the training set , but theThe ultimate goal of our study is to identify distinct prognostic subgroups of luminal-A breast cancer. Hence, we clustered 679 METABRIC samples using the latent features generated from the deep autoencoders and unsupervised learning. We used K-means clustering for unsupervised learning. Then, we performed the Kaplan-Meier survival analysis to compare prognosis between the subgroups and the significance was evaluated by log-rank test.As a result, the prognostic differences between the subgroups were stably significant  when the samples were divided into two subgroups regardless of the dimensional size of latent features , but theGiven these results, we concluded that the prognostic differences were the most distinct when 679 METABRIC samples were divided into the two subgroups using the 64-dimensional latent features . In the To validate the prognostic differences between the BPS-LumA and the WPS-LumA, we applied our stratification method to an independent dataset. We used the 415 TCGA luminal-A breast cancer samples for validation. We generated the 64-dimensional latent features of each TCGA sample using the deep autoencoder trained with METABRIC dataset in the previous section, and each sample was assigned to the closer subgroup based on the distance between the sample and the centroid of the BPS-LumA and the WPS-LumA in the latent space . Among 4Interestingly, even though the two datasets used the different expression profiling platforms , we proved that our method is applicable in the both datasets. To further explore these results, we measured the Spearman’s rank correlation coefficient (SRCC) between the mean expression levels of individual genes in the both datasets and we observed that they are highly correlated  and 2-  dimensional space using PCA , respectively. As a result, we observed that none of them successfully discovered the distinct prognostic subgroups .From these results, we confirmed that only the latent features were able to identify the prognostic subgroups p-value = 5.82E-05; Next, we tried to figure out which biological functions potentially makes the prognostic differences between the BPS-LumA and WPS-LumA. To this end, among top 5,000 genes with the highest variability, we found the 548 differentially expressed genes (DEGs) between BSP-LumA and WPS-LumA in the both METABRIC and TCGA datasets through limma  adjuste Tables. As a result, we observed that “lightcyan” co-expressed module includes the significantly large number of DEGs 11.6%, . We explWe found that there are many literature evidences that report the associations between the ribosomal proteins (RPs) and cancer . For exaAdditionally, we wanted to see how much our method coincides with previous luminal-A breast cancer stratification methods: Netanely’s method  and PoudFor example, our method was significantly concordant with the Netanely’s method .Consequently, the remaining challenge is to develop more effective therapeutic strategies for each subgroup, especially for the patients who belongs to the worse prognostic subgroup. The stratification method can further maximize its power when there is an appropriate treatment for each subgroup. For example, patients with hormone receptor-positive breast cancer  receive an endocrine therapy as a first-line treatment. On the other hand, dual HER2 blockade (e.g. Trastuzumab and Pertuzumab) is recommended to hormone receptor-negative and human epidermal growth factor 2-positive breast cancer (e.g. HER2-enriched) . Like thIn addition to the DEG analysis, there are recently lots of efforts to develop explainable and interpretable deep leaning models to overcome “black-box” problem , 34, espLastly, we showed that our and the previous methods are significantly coincident and they could complement each other for a more precise stratification through further study. For example, in the Poudel’s method, the samples belonged to goblet-like subgroups are regarded as intermediate prognosis, which are ambiguous than the other subgroups. Interestingly, we discovered that 41.18% and 58.82% of them are belonged to the BPS-LumA and WPS-LumA in our method. This result indicates that even though the samples show similar goblet cell-like signatures, they could show different characteristics in other biological pathways, such as ribosome-related pathways that we discovered with the DEG analysis. In this perspective, comprehensively considering the results of our and the previous methods can be helpful to more precisely define the disease states of the patients.To sum up, we successfully developed the precise stratification method of luminal-A breast cancer which is able to predict the prognosis. Given that luminal-A breast cancer is the most frequently occurring breast cancer and the prognosis varies from patient to patient due to the endocrine resistance, our method could be helpful to stratify the patients and prepare alternative treatment options according to the predicted prognosis.Two breast cancer datasets, METABRIC  , 43 and ith gene expression value of the jth sample, ej,META(i), to be in the range between zero and one, and it could be calculated as:ej,META(i)) and max ) is the minimum and maximum expression value of ith gene across the 679 METABRIC samples.Among 2,509 samples in the METABRIC dataset and 817 samples in the TCGA dataset, we picked out 679 and 415 luminal-A breast cancer samples from each dataset based on the PAM50 subtype data. We also selected 17,202 genes of which expression values are available in the all 679 METABRIC samples and 415 TCGA samples. Then, we chose the top 5,000 genes with the highest variability based on the median absolute deviations of each gene. Next, we renormalized the normalized gene expression profiles (median Z-scores) of the 679 METABRIC samples such that each Similarly, we renormalized the normalized gene expression profiles of the 415 TCGA samples using the minimum and maximum expression value of each gene in the METABRIC dataset, and it could be calculated as:We used python machine learning library Scikit-learn (version 0.23.2) to renormalize the gene expression profiles.jth sample generated in the kth layer of the deep autoencoders of which the hidden layer size is dim could be calculated as:We constructed deep autoencoders which are composed of five layers: input layer, three hidden layers, and output layer. As shown in encoders . We usedfk is the activation function in the kth layer. Wk,dim and bk,dim are weight matrix and bias in the kth layer of the deep autoencoders of which the hidden layer size is dim. For example, jth sample in the METABRIC dataset, which is generated in the second hidden layer of deep autoencoder of which the hidden layer size is 64.In Eq , fk is tX1) and the reconstructed gene expression profiles of the output layer (X5), and the deep autoencoders were trained to minimize the MSE:We used the 679 METABRIC samples as a training set and the 415 TCGA samples as a validation set. We evaluated the performance of the deep autoencoders using mean squared error (MSE) which measures the differences between the renormalized gene expression profiles of the input layer . They were calculated as:As shown in In consequence, each sample had the four latent features of the different dimensional size according to the size of hidden layers. Then, we divided the samples into several subgroups using each latent features of the different dimensional size as input features of K-Means clustering. We set the number of clusters as from two to five. Python machine learning library Scikit-learn (version 0.23.2) was used for the unsupervised learning.We performed Kaplan-Meier survival analysis  to compaUsing the renormalized gene expression profiles of 415 TCGA samples Then, we assigned the each TCGA sample to the closest subgroup based on distance from the centroid of each subgroup in the latent space, which was identified using the samples in the METABRIC dataset. The Kaplan-Meier survival analysis was performed to compare prognosis between the samples belonging to each subgroup.We compared our stratification with the two previous studies: Netanely’s method  and PoudWe used the normalized gene expression profiles of METABRIC dataset and R package limma to find differentially expressed genes (DEGs) between the subgroups  . We perfWe constructed weighted co-expression network, which is able to represent normal breast tissue, and detected co-expressed modules using gene expression profiles obtained from GTEx (the Genotype-Tissue Expression)  and R paWe performed Enrichr  to find S1 Fig(DOCX)Click here for additional data file.S2 Fig(DOCX)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.S8 Table(XLSX)Click here for additional data file.S9 Table(XLSX)Click here for additional data file.S10 Table(XLSX)Click here for additional data file.S11 Table(XLSX)Click here for additional data file.S12 Table(XLSX)Click here for additional data file. 28 Feb 2023Dear Dr. Lee,Thank you very much for submitting your manuscript "Identifying prognostic subgroups of luminal-A breast cancer using deep autoencoders and gene expressions" for consideration at PLOS Computational Biology.As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.Both reviewers have serious concerns about the methods and results described in the paper.We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.When you are ready to resubmit, please upload the following:[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).Important additional instructions are given below your reviewer comments.Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.Sincerely,Mark Alber, Ph.D.Section EditorPLOS Computational BiologyMark AlberSection EditorPLOS Computational Biology***********************Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: The authors suggest an autoencoder model that stratifies subgroups of breast cancers that displays different prognostic outcomes. They built an autoencoder model that takes gene expression data of breast cancer samples for feature extraction, then performed k-means clustering to identify subgroups, which indeed show different survival profiles in independent TCGA data as well as the METABRIC training data. They also compared the stratification performance against conventional models that directly use gene expression profiles as input with a varying number of genes. Further, they sought to explain the prognostic outcomes by overlaying differentially expressed genes between groups onto the co-expression network constructed from independent gene expression data from healthy samples. Meanwhile, it is a novel approach to delineating complicated biological samples, this work requires technical clarification and analysis.Autoencoder is indeed widely used for feature extraction and is proven to be effective in many studies. However, the actual application here is with some concern. First, the authors used all detected genes as input. Authors argue that it minimizes manual filtering and intervention. But obviously, there should be many genes that display minimal variance, hence are uninformative. These genes will be more of noise rather than useful features. This issue is related to the way of re-normalization by min/max scaling. Even when a gene displays very minimal noisy variation, those variances will be amplified via min/max scaling and ultimately will have an equal contribution to the model as much as highly variable and informative genes, which will obscure successful learning of the model. Also related to this in Fig4, the p-value vividly decreases as the number of input genes decreases, which suggests a preliminary gene filtering can be beneficial. Therefore, I’d like to recommend trying a combined approach of preliminary gene filtering and autoencoder, i.e. low variance gene filtering followed by autoencoder training. Here, I’d recommend selecting highly variable genes after variance stabilization to avoid the preference of highly expressed genes. If successful, it will help us to achieve a more compact model.On a second note, it is somewhat surprising to see that an autoencoder model trained using array data successfully classifies RNA-seq data. Is it because of the min-max normalization and highly correlated array vs RNA-seq data? Please discuss.Also, the authors build a WGCNA model using seemingly all detected genes. Given the nature of WGCNA relying on correlation coefficient, it conveys a similar risk when involving low variance genes. How would the author justify this? What if similar preliminary gene filtering is applied?In Fig 6- Panel B and C are not quite informative. Rather I’d recommend putting 1) a bar plot module size, and 2) % of genes in each module overlapping with DEG- Panels seem to be mislabeled in the legend for B and C. A appears twice, B once, and no C.In line 413, the authors described that the hidden layer size is 2048. However, they tried all different numbers of hidden layers in the supplementary figures. Please correct if necessary.Reviewer #2: In this paper, the authors proposed a data-driven method for identifying prognostic markers that can differentiate between different groups of breast cancer patients with different prognosis.The main idea is to first train auto-encoders that can extract low-dimensional latent features that encode the gene expression data from breast cancer patients and then can be used to faithfully reconstruct the gene expression data.The extracted features are then used to cluster breast cancer patients using k-means algorithm, and the authors demonstrate that the identified subgroups show very different prognosis.While the proposed method and the presented results are reasonable, there are several major concerns in the manuscript that need to be addressed.These concerns are outlined below.1. While the use of autoencoder to extract potential latent features for stratifying breast cancer patients is reasonable, the proposed method lacks novelty.The authors mainly train a standard autoencoder with different latent dimensions using breast cancer gene expression data, which is technically not novel.Except for varying the dimension size, no other architecture/hyperparameter optimization is performed to customize the model for the task and enhance the stratification results.2. The authors show that using the latent dimension of 2048 led to the best (most significant results).But considering that this latent dimension size was the largest among the test dimension sizes, and as this dimension size is comparable to the dimension of the original gene space, it is highly likely that the model is overfitted to the data .3. The latent features do not seem to have any biological significance. For example, while there has been recent work on constraining the latent space based on pathway info - in which case the latent features may potentially reflect underlying pathway activities, in this current work it is difficult to see whether the 2,048 latent features meaningfully reflect the underlying biological processes/pathways that may be associated with different prognosis of subgroups.Although the authors perform some analysis by analyzing the differentially expressed genes between the subgroups that are identified by the proposed method, such analysis beats the purpose of using an auto-encoder for latent feature extraction in the first place.For example, we could have simply started with DEG analysis without using autoencoders to detect gene markers that can be used to stratify subgroups and then analysis the identified DEGs to understand what might be leading to this difference.Why should one first use autoencoders to extract latent features (that cannot be easily interpreted), and then resort to DEG analysis for interpretation?4. Figure 2 and Figure 3 show PCA plots for the latent feature vectors, but how does it compare to using PCA directly to gene expression data?Why not use PCA to extract important principal components that reflect the main gene expression patterns, use these principal components for clustering patients and stratifying them?Does the use of autoencoder significantly improve the results?Such comparison would be critical in demonstrating the effectiveness of the proposed scheme.5. Furthermore, there have been pathway based methods and network analysis based methods for extracting gene modules that may be used as diagnostic and/or prognostic markers.How does the use of autoencoder-based data driven scheme for extracting latent features compare with more traditional methods that define/predict modular markers based on pathways or network info?Is there a clear evidence that even without using such additional information , the autoencoder can extract better prognostic signatures thare are predictive of patients' survival?6. The authors claim that "our method and previous methods can be complementary to each other for a more precise stratification for luminal-A breast cancer". However, this conclusion is drawn simply based on the fact the difference/discrepancies between the different methods.To justify such statement, the authors should actually show "how" they could be combined to improve the stratification results.7. (minor comment) The literary presentation of the paper should be improved, as the current manuscript includes a large number of grammatical and typographical errors.8. (minor comment) in line 198, the author mention that "the two datasets used the different sequencing platform", but note that microarray is not a "sequencing platform".**********Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: Yes**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool, Data Requirements:http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: Reproducibility:https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocolsTo enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at  18 Apr 2023Attachmentresponse_letter.pdfSubmitted filename: Click here for additional data file. 30 Apr 2023Dear Dr. Lee,Thank you very much for submitting your manuscript "Identifying prognostic subgroups of luminal-A breast cancer using deep autoencoders and gene expressions" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.Please prepare and submit your revised manuscript within 30 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email.When you are ready to resubmit, please upload the following:[1] A letter containing a detailed list of your responses to all review comments, and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).Important additional instructions are given below your reviewer comments.Thank you again for your submission to our journal. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.Sincerely,Mark Alber, Ph.D.Section EditorPLOS Computational BiologyMark AlberSection EditorPLOS Computational Biology***********************ploscompbiol@plos.org immediately:A link appears below if there are any accompanying review attachments. If you believe any reviews to be missing, please contact Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: Authors addressed all the concerns.One minor comment:Authors changed the presentation of the dimension reduction in the main figures. What was the basis of this changeReviewer #2: I would like to thank the authors for their careful revision.Most of my concerns regarding the initial version of this manuscript have been sufficiently addressed in the revised version, and I believe the main advantages of the proposed approach are conveyed in a clearer and a more convincing manner.For example, the updated analysis based on a lower-dimensional latent representation addresses the concern regarding overfitting, and the updated analysis results and discussions are therefore more convincing.Direct comparison between the proposed autoencoder-based scheme and the traditional PCA based dimensionality reduction is also very helpful, and it clearly demonstrates how using deep network models for dimensionality reduction can identify useful latent features that can more accurately cluster and stratify different patient groups with different prognosis, which may be difficult based on traditional schemes like the PCA.Regarding my previous comment concerning the comparison against existing methods that used prior knowledge , while I understand the authors position I nevertheless think that it would be meaningful to include at least some discussion comparing the pros and cons of the respective approaches.Finally, the authors have revised a number of places in the manuscript to convey the novel contributions made in this work more clearly, these are spread over the paper and it may be a good idea to summarize the main novel contributions more clearly at the outset .For example, the authors may want to clearly mention that while they are not proposing a novel methodology, the application of an autoencoder to luminal-A breast cancer to extract biologically meaningful low-dimensional latent features is novel and it may detect features not possible using other traditional techniques.**********Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: Yes**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool, Data Requirements:http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: Reproducibility:https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocolsTo enhance the reproducibility of your results, we recommend that you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at References:Review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript.If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. 7 May 2023Attachmentresponse_letter.docxSubmitted filename: Click here for additional data file. 18 May 2023Dear Dr. Lee,We are pleased to inform you that your manuscript 'Identifying prognostic subgroups of luminal-A breast cancer using deep autoencoders and gene expressions' has been provisionally accepted for publication in PLOS Computational Biology.Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. Best regards,Mark Alber, Ph.D.Section EditorPLOS Computational BiologyMark AlberSection EditorPLOS Computational Biology***********************************************************Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: Acceptable for publication.Reviewer #2: Thank you for the revision.The previous revision was fairly comprehensive and it already addressed all major concerns I had regarding the original manuscript.The remaining concerns were mostly minor, and the current revision has addressed them in a satisfactory manner.I do not have any further suggestions.**********Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: None**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  1223-442824 | ploscompbiol.org | @PLOSCompBiolPLOS Computational Biology | Carlyle House, Carlyle Road, Cambridge CB4 3DN | United Kingdom