The quantile–quantile plots of p-values showed that false positive rates were well calibrated by LMM, whereas other methods not accounting for sample-specific mixed effects led to serious inflation. LMM identified 37 potentially significant genes with differential expression in DLPFC for at least one of the AD traits, 17 of which were replicated in the additional RNA-Seq data of DLPFC, supplemental motor area, spinal cord, and muscle tissues. This application study showed not only well calibrated DGE results by LMM, but also possibly shared gene regulatory mechanisms of AD traits across different relevant tissues.Differential gene expression (DGE) analysis has been widely employed to identify genes expressed differentially with respect to a trait of interest using RNA sequencing (RNA-Seq) data. Recent RNA-Seq data with large samples pose challenges to existing DGE methods, which were mainly developed for dichotomous traits and small sample sizes. Especially, existing DGE methods are likely to result in inflated false positive rates. To address this gap, we employed a linear mixed model (LMM) that has been widely used in genetic association studies for DGE analysis of quantitative traits. We first applied the LMM method to the discovery RNA-Seq data of dorsolateral prefrontal cortex (DLPFC) tissue ( RNA sequencing (RNA-Seq) technology has been widely used to profile transcriptome-wide gene expression levels and has revolutionized transcriptome analyses3. Differential gene expression (DGE) analysis is one approach for studying RNA-Seq data to identify genes expressed differentially with respect to a trait of interest5. Due to the cost of RNA-Seq studies and the difficulty in obtaining large numbers of relevant tissue samples from individuals, most existing DGE methods have been developed to handle small sample sizes and dichotomous traits, e.g., DESeq26, edgeR8, Limma9, Voom10, and MACAU11. However, with the recently reduced cost of RNA-Seq technology, RNA-Seq data from hundreds of samples have been generated for studying both dichotomous and continuous quantitative traits.Next-generation sequencing technology has been widely used in genetics and genomics studies to elucidate the biology underlying complex human diseases and traits11. As a result, information could be lost, and power could be reduced by not characterizing the continuous characteristics of phenotypes. This loss of information by dichotomizing a continuous biologic process  may homogenize individuals together who often, in fact, lie on a continuum of disease, especially for chronic conditions of aging. For example, the cognitive manifestation of AD related dementia unfolds over years to decades12. Further, in older persons, AD dementia is often due to a combination of mixed pathologies and resilience14, which is better characterized by continuous cognitive traits and neuropathologic traits. During the prolonged course of this chronic disease, individuals who initially show no cognitive impairment (NCI) may manifest mild cognitive impairment (MCI) for years before they finally develop Alzheimer’s dementia as a late final manifestation  project V8 profiled hundreds of samples per tissue for 53 human tissues (up to n = 803 for muscle tissue)19; the CommonMind Consortium sequenced RNA from dorsolateral prefrontal cortex (DLPFC) of people with schizophrenia (n = 258) and control subjects (n = 279) for studying schizophrenia and other psychological diseases20; the prospective cohort studies of Religious Orders Study (ROS) and the Rush Memory and Aging Project (MAP) sequenced RNA from DLPFC of ~ 1200 participants for study AD traits including the continuous cognitive decline and continuous markers of AD neuropathologic changes (AD-NC), i.e., neurofibrillary tangles (NFTs) and beta amyloid (Aβ))17. Enabling DGE of continuous quantitative traits (such as cognitive decline and AD-NC traits) with hundreds of sample sizes is crucial to advance our understanding and the development of targeted treatments for complex diseases.The decreasing cost of RNA-Seq technology and the recognition of the importance of RNA-seq data have led to the recent availability of much larger RNA-Seq sample sizes from individuals with both dichotomous and quantitative phenotypes21 and robust regression21 were proposed for DGE analysis of quantitative traits, which takes the quantitative trait as the response variable and the log2 transformed RNA-Seq read counts per gene as the test covariate21 (see Methods). However, the methods based on standard linear regression and robust regression models often lead to inflated false positive rates by failing to account for unknown confounders23. To improve on existing DGE methods, we apply the linear mixed model (LMM) based method as implemented by the Genome-wide Efficient Mixed Model Association (GEMMA) tool22 to conduct DGE of quantitative traits. The LMM based method can account for shared confounding factors among test samples through the sample-specific mixed effect term, which has been widely used in large-scale genetic association testing to achieve calibrated false positive rates24. The Linear Mixed Model (LMM) implemented by GEMMA employs the full-rank sample-sample correlation matrix  to model the sample-specific random effects (see Methods), which models unknown confounding factors and thus corrects the inflated false positives that occur in linear regression models without mixed effect terms22. To demonstrate the feasibility of this approach, we developed an analytic LMM pipeline to conduct DGE, and applied the pipeline to study four cognitive and pathologic AD traits—the rate of cognitive decline and three AD-NC traits .Recently, methods based on the standard linear regressionn = 632) with respect to cognitive decline and each of the AD-NC traits. Several previous studies have shown that Alzheimer Disease affects not only cognition but also non-cognitive traits such as motor functions that may be affected by the accumulation of AD-NC in tissues outside the brain25. Thus, to validate our findings with the discovery RNA-Seq data of DLPFC, we then conducted DGE analysis on the same continuous cognitive decline and AD-NC traits using additional RNA-Seq datasets from DLPFC brain tissue (n = 588) and three tissues relevant to motor functions a) supplementary motor area (SMA) within the brain (n = 234), (b) lumbar spinal cord (n = 232) neural tissues within the central nervous system (CNS) but outside the brain, and (c) muscle (n = 268), the final effector of all volitional movement, composted of non-neural tissue and located in the periphery outside the CNS. We showed that false positive rates were well calibrated by the LMM based method, compared to serious inflation of the DGE results by using the standard linear regression21, robust regression21, and Voom10. As a result, our DGE analyses by LMM identified 37 genes differentially expressed for either cognitive decline or at least one of the AD-NC traits, with 17 of those genes replicated in the additional RNA-Seq data from DLPFC, SMA, spinal cord, and muscle tissues.We first used the LMM pipeline to conduct DGE analysis using discovery RNA-Seq data of DLPFC brain tissue . Our DGE analyses adjusted for various covariates, including sex, age, postmortem interval  and study group (ROS or MAP) in both models Table . We consmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimp-values < 0.0001 for at least one trait) by the LMM-based test method, including 2 for cognitive decline, 4 for –6  and gene NPNT  have previously identified as differentially expressed genes in the context of AD in earlier studies28. Likewise, Gene DDAH2  has been linked to increased levels of oxidative stress in AD brains29. Furthermore, mutations in the ALDH family genes such as ALDH6A1  were identified as significant risk variants for AD30. Additionally, PLCD3  is a notable protein that is cross-correlated with β-amyloid and Tau proteins in AD brains31. These results indicated the effectiveness of LMM based test for conducting DGE analyses of quantitative traits with well calibrated false positive rates. These intriguing results further underscore the efficacy of the LMM-based approach in facilitating DGE analyses involving quantitative traits, while concurrently maintaining well-calibrated false positive rates.Importantly, many of the potential significant genes associated with cognitive decline and AD-NC traits identified by the LMM method have been reported in prior studies. This confluence of findings bolsters the credibility of our outcomes. Notably, for example, gene NPNT, ALDH6A1, DDAH2, PLCD3, MEIS3) were also reported in previous studies30. Interestingly, both NPNT and MEIS3 showed significant differential expression in cognitive decline and tangle density. We also found that 3 of these 37 genes had significant differential expression in cognitive decline and at least one of the AD pathology traits, suggesting a shared gene regulatory mechanism between cognition and AD pathology.In summary, 8 of these 37 genes had significant LMM P-values with Bonferroni correction, and 5 of these , SMA n = 234), spinal cord (n = 232), and muscle (n = 268) tissues  to identify replicated genes. As a result, for the replicated differentially expressed genes in the CNS tissues, we found 8 in SMA with 5 overlapped in DLPFC, 2 in spinal cord, 3 in muscle with one overlapped in spinal cord, and one overlapped in SMA  have sample sizes of only ~ 100 . For each replicated gene, we calculated the average gene expression level of the discovery DLPFC and replication tissues, for samples in each decile of the discovery and replicated traits. Then we calculated the correlations between these two vectors of average gene expression. Heatmaps of these correlations  with Bonferroni corrected significant p-values in the discovery data were replicated in the validation data of DLPFC tissue. Furthermore, we validated a total of 17 unique genes across the validation RNA-Seq data of DLPFC and three motor function related tissues, including 10 in DLPFC, 8 in SMA, 2 in spinal cord, and 3 in muscle. The identification of shared differentially expressed genes in two different tissue types, such as DLPFC and SMA, DLPFC and non-neural muscle, as well as spinal cord and non-neural muscle outside the brain, suggests a possible shared molecular mechanism between motor and cognition functions.In conclusion, our analysis revealed that all 5 differentially expressed genes  has been associated with aging and neurodegenerative diseases, such as Alzheimer's disease and Parkinson's disease38. Similarly, the 5HT2 type receptor mediated signaling pathway (FDR = 4.37 × 10–2) could influence the behavioral and psychological symptoms of dementia (BPSD) in Alzheimer's disease (AD)39. The Oxytocin receptor medicated signaling pathway (FDR = 4.37 × 10–2) was suggested to be a novel protective target for vascular dementia and mixed dementias40. The toll-like receptor (TLR) signaling pathway (FDR = 1.42 × 10–2) may be involved in clearance of amyloid β-protein (Aβ) in the brain making it a potential therapeutic target for AD41. The Renin-Anigotensin System (RAS) and tumorigenesis pathway (FDR = 1.52 × 10–2) is known to play a key role in interacting with pathophysiological mechanisms of AD42. Several evidences suggest that enhancing Wnt pathway (FDR = 1.88 × 10–2) can boost synaptic function during aging, and ameliorate synaptic pathology in AD which could be novel therapeutic for restoration in the brain43. The Epidermal growth factor receptor (EGFR1) pathway (FDR = 2.01 × 10–2), a preferred target for treating memory loss induced by amyloid-beta (Aβ)44, is also enriched in β-amyloid.For example, for the pathways significantly enriched with top 100 differentially expressed genes of cognitive decline Fig. A, the Th–3) that plays a critical role in deregulation in AD thus manipulating DAPK1 activity and/or expression could be a promising drug target in AD45. The additional protective mechanism of AndrogenReceptor (FDR = 3.92 × 10–2) might enhance neural health and deter the progression of AD46.Also, for the pathways significantly enriched with top 100 differentially expressed genes of tangle density Fig. B, Death-11 are developed for dichotomous traits with small sample sizes. However, with increased sample sizes in RNA-Seq datasets, there is a huge demand for methods for studying quantitative traits in population-based RNA-Seq studies. As shown by the MACAU11 method paper, incorporating a mixed term into DGE analysis can help to control for false positive rates in RNA-Seq studies. In this study, we develop an analytic pipeline for implementing the GEMMA tool22, enabling the DGE analysis of quantitative traits by LMM, and apply to real ROS/MAP RNA-Seq datasets of DLPFC, SMA, spinal cord, and muscle tissues for studying continuous cognitive decline and AD-NC traits. The pipeline is freely available from https://github.com/tangjiji199645/LMM_DGE_Pipeline.Most existing DGE analysis methodsOur application studies found that DGE analyses results obtained by LMM-based tests were all well calibrated for false positive rate, especially in our discovery RNA-Seq data of DLPFC, while the DGE results obtained by the alternative standard linear regression, robust regression, and Voom methods all have inflated false positive rates. A list of 37 potential differentially expressed genes were identified by LMM in the discovery data, and 17 of these were replicated in the additional RNA-seq data of DLPFC, SMA, spinal cord, and muscle tissues. AD relevant biological pathways were also found to be enriched with top differentially expressed genes of cognitive decline and tangle density.47, which could lead to a biased estimation of effect sizes. One might apply both the MACAU (mixed Poisson model-based test that is suitable for modeling RNA-Seq read counts) and our LMM analytic pipeline for DGE analysis and examine the results by QQ-plots. Second, the effect of the gene expression on the quantitative trait of interest may be heterogeneous, with effect sizes varying across the quantiles of the quantitative trait. The LMM-based method only tests the association between gene expression and quantitative trait of interest in expectation, ignoring the possible heterogeneous effects on different quantiles of the quantitative trait48. Therefore, further studies are needed to develop a DGE method based on quantile regression with a mixed effect term to account for the possible heterogeneous effect of gene expression across all the quantiles of the quantitative trait of interest, while controlling for false positive rates.However, the LMM-based test still has several limitations for studying RNA-Seq data. First, the LMM assumes normal distributions for both the response variable and covariates, while the raw RNA-Seq data are read counts per gene. Even after log2 transformation for the raw RNA-Seq read counts, the transformed quantitative gene expression level per gene may not be normally distributedOverall, we provide a useful LMM pipeline for conducting DGE analysis with quantitative traits and large sample sizes, which is shown well calibrating for false positive rates in real studies. Our real application studies not only demonstrated the effectiveness of the LMM approach for DGE analysis, but also identified a list of differentially expressed genes for cognitive decline and AD-NC traits in DLPFC that were validated in DLPFC, SMA, spinal cord, and muscle tissues. Our findings have important implications for understanding the underlying biological mechanisms of the continuous AD traits of cognitive decline and neuropathologic changes, and may provide insights into the development of new therapeutic approaches for AD.6 to normalize raw RNA-Seq data.Preprocessing and normalization of raw read counts is a critical step in DGE analysis. Generally, samples with total mapped reads < 10 million are suggested to be excluded, and genes with expression levels < 0.1 transcript per million (TPM) in > 20% samples are also suggested to be excluded. We use DESeq2j and sample i, following a negative binomial distribution with mean Let 50:The normalization factor Normalized read counts 21, testing if gene  is differentially expressed with respect to a quantitative trait n is the number of test samples; j; and As proposed by previous study21 assumes the same model as the standard linear regression model (4), yet it furnishes robust coefficient estimates when the test samples contain influential outliers that could heavily impact standard linear regression estimates. Different from the standard linear regression method where each sample contributes equally to the ordinary least squared estimation of regression coefficients, robust regression incorporates Huber’s M-estimation51 that is obtained by minimizing the following objection function through a numerical method called iteratively reweighted least squares (IRLS):Robust regression21, the R packages of “rlm” and “sfsmisc” can be used to conduct the statistical test of As described in the previous study that proposed using the robust regression for DGE analysis10 is developed for detecting differentially expressed genes between two or more conditions, the quantitative trait  is differentially expressed. Generally, the quantitative trait is dichotomized to j representing log2-fold-changes between two conditions of the dichotomous trait. The same hypothesis with 10.Since the Voom method  is differentially expressed with respect to a quantitative trait j; Z is a u is a 0 and variance–covariance matrix To test if gene 22 is a C++ programed software that can be used to conduct tens of thousands of Wald test for GEMMA tool17. Our analyses were conducted in two steps. First, we normalized raw RNA-Seq data using DESeq26. Second, we tested DGE using the LMM method as implemented in the GEMMA tool22.We demonstrate the feasibility and effectiveness of conducting DGE analyses using the LMM method through application studies with the ROS/MAP data52. All ROSMAP participants agree to structured annual clinical testing and autopsy and brain donation upon their death. RNA-Seq data  and AD pathologies were profiled from decedents. Both studies were approved by the Institutional Review Board of Rush University Medical Center, and all participants signed informed and repository consents and an Anatomic Gift Act.The Religious Order Study (ROS) and the Rush Memory and Aging Project (MAP) are two prospective community-based harmonized cohort studies of aging, which recruit senior individuals without known dementia at study entryβ-amyloid, tangle density, and global AD pathology burden. The cognitive decline  is the estimated person-specific rate of change in the global cognition variable over all follow-ups generated by a mixed effects model54. The AD-NC trait of tangle density was quantified using molecularly specific immunohistochemistry. It was profiled as the average PHFtau tangle density within two or more 20 µm sections from eight brain regions—hippocampus, entorhinal cortex, midfrontal cortex, inferior temporal, angular gyrus, calcarine cortex, anterior cingulate cortex, and superior frontal cortex. These two are identified by molecularly specific immunohistochemistry. Trait β-Amyloid quantifies the average percent area of cortex occupied by β-Amyloid protein in adjacent sections from the same eight brain regions. The global AD pathology burden is a quantitative summary of AD pathology derived from counts of three AD pathologies: neuritic plaques, diffuse plaques, and neurofibrillary tangles with 5 brain regions midfrontal cortex, midtemporal cortex, inferior parietal cortex, entorhinal cortex, and hippocampus . To improve normality, these three quantitative AD pathology traits were transformed by taking the square root. Futher details have been previously reported56.Our study focused on cognitive decline and three AD-NC traits, including n = 1220, n = 632 as discovery data Table n = 588 as validation data; Supplemental Table n = 234), contralateral ventral horn in the lumbar spinal cord , and non-neural quadriceps muscle ipsilateral to the ventral horn . The raw RNA-Seq fastq data were first aligned to the reference human genome and then quantified by the number of reads mapped to gene regions. Raw read counts were first normalized and log2 transformed by DESeq2, and then used as the test gene expression covariates in the LMM model. The ROS/MAP RNA-Seq data of DLPFC (n = 632) were analyzed as discovery data, while RNA-Seq datasets another 588 DLPFC samples, and samples of SMA, spinal cord, and muscle tissues were analyzed as validation data. Participants are not overlapped between the DLPFC samples and samples of SMA, spinal cord, and muscle tissues, while participants of RNA-Seq data of SMA, spinal cord, and muscle tissues are largely overlapped. Technical details of RNA-Seq data profiling can be found in the Supplemental Text.RNA-Seq data were profiled from deceased ROS/MAP participants for DLPFC tissue within the brain (The Religious Order Study (ROS) and the Rush Memory and Aging Project (MAP) were approved by the Institutional Review Board of Rush University Medical Center, and all participants signed informed and repository consents and an Anatomic Gift Act. All data analyzed in this study were de-identified which are not considered as human data according to NIH protocols. We confirm that all analytical methods were performed in accordance with the relevant guidelines and regulations.Supplementary Information.


ABCF1, SART3, APC5, NONO, KAT7, ZPR1, RABGAP1, SLC7A8, SPAG9, and KAT6A were found to have a differential expression between NAFLD and healthy individuals. Based on validation results and ROC analysis, NR4A2 and IGFBP1b were identified as diagnostic markers. These key genes may be predictive markers for the development of fatty liver. It is recommended that these key genes are assessed further as possible predictive markers during the development of fatty liver.Non-alcoholic fatty liver disease (NAFLD) comprises a range of chronic liver diseases that result from the accumulation of excess triglycerides in the liver, and which, in its early phases, is categorized NAFLD, or hepato-steatosis with pure fatty liver. The mortality rate of non-alcoholic steatohepatitis (NASH) is more than NAFLD; therefore, diagnosing the disease in its early stages may decrease liver damage and increase the survival rate. In the current study, we screened the gene expression data of NAFLD patients and control samples from the public dataset GEO to detect DEGs. Then, the correlation betweenbetween the top selected DEGs and clinical data was evaluated. In the present study, two GEO datasets  were downloaded. The dysregulated expressed genes (DEGs) were identified by machine learning methods . Then, the shared DEGs between the two training datasets were validated using validation datasets. ROC-curve analysis was used to identify diagnostic markers. R software analyzed the interactions between DEGs, clinical data, and fatty liver. Ten novel genes, including  NAFLD affects about 25–30% of the population globally and is associated with an increased risk of other diseases, including type 2 diabetes mellitus, atherosclerotic cardiovascular disease, and chronic kidney disease (CKD)5. The frequency of NAFLD is anticipated to increase from 83 million in 2015 to 100 million by 20306. The main reasons are an unhealthy diet and a sedentary lifestyle7. The advanced type of fatty liver disease is non-alcoholic steatohepatitis8, with features that include: fibrosis, necrotic inflammation leading to cirrhosis, and hepatocellular carcinoma10. The morbidity and mortality rates of cirrhosis and hepatocellular carcinoma are much greater than NAFLD11. Therefore, diagnosing and treating disease in the early stages might reduce the risk of liver damage and increase the survival rate13.Non-alcoholic fatty liver disease (NAFLD) is a range of chronic liver diseases resulting from the accumulation of excess triglycerides in the liver14. The other diagnostic tools ,resonance imaging15, and computed tomography (CT) whichare high-cost and time-consuming methods that burden the healthcare system financially17. Additionally, recognizing the higher level of lipid content and inflammatory factors such as C-reactive protein (CRP), IL-6, IL-18, IL-1b, IL-8, and TNF-a signify chronic inflammation in NASH development19. Therefore low-cost, reliable, and non-invasive methods are required to identify specific diagnostic biomarkers in the early stage of NAFLD.The gold standard for detecting NASH is liver biopsy, an invasive approach22. ML has various advantages, including automation, Handling multi-dimensional data, nonlinearity, low fault, and wide applications24.In the progression of NAFLD, the molecular pathways are altered, leading to differential expression genes (DEGs). In the new era of technology, Machine learning (ML) is a novel artificial intelligence that has been widely performed to screen DEGs in different diseases and discover new diagnostic and prognostic biomarkers. Artificial intelligence enables processing data sets using programmed algorithms in logical models for performance tasksIn the current investigation, we screened the gene expression data of NAFLD patients and control samples from the public dataset GEO (Gene Expression Omnibus) to detect DEGs. Then, the correlation between the top selected DEGs and clinical data was evaluated.The RNASeq data of fatty liver patients and clinical features were downloaded from the GEO dataset (GSE126848 and GSE48452). Filtering and normalization were performed as preprocessing, and the data quality was controlled using Principal Component Analysis (PCA). Before classification, feature selection was implemented using Relief-based algorithms to calculate the higher score for each feature. Then Penalize machine learning technique was used to detect the most important biomarkers. Eventually, the candidate genes were validated by other datasets.https://www.ncbi.nlm.nih.gov/geo/geo2r/?acc=GSE48452 and https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE126848, respectively. The two datasets also have clinical and demographic variables considered in the analysis.In the present study, two datasets from GEO were downloaded. The first dataset included 33,297 array-based expression profiling of 73 samples which were grouped into C (control = 14), O (obese = 27), S (steatosis = 14), and N (NASH = 18), and the second dataset consisted of 19786 gene expression from normal individuals (n = 14), obese (n = 12), NAFLD (n = 15) and NASH (n = 16) patients. The two datasets were extracted from Gene expression data were screened by filtering, and the zero expressions were eliminated; then, data were normalized with limma in R 4.1 software. The adjusted p < 0.05 and − 1.5 <|Log2FC (fold change) |< 1.5 were identified for subsequent analysis as significant genes. After that, Principal Component Analysis (PCA) which is a statistical procedure for visualizing whether the sample groups (control and patients) were separable and correlated was applied..The effect coefficient of all factors on the fatty liver was calculated using Regularization regressions  models. These models will be described as follows. Before the modeling, Relief-based feature selection was implemented. Weight by Relief is applied to calculate the weights of the attributes in the polynomial dataset. Chi-square and One way-ANOVA also were used to evaluate the relationship between clinical variables and disease, and Kolmogorov–Smirnov was used for normality test distribution. The binary correlation of some variables was examined using a correlation matrix. R4.1.and EVIEWS12 software was utilized for analysis.In statistics and machine learning, Regularization regression is a type of regression analysis for variable selection and is used when train and test data are varying. To better manage many parameters or Multicollinearity between variables and reduce complexity, a “penalty” is added to cost function (Regularization) for the best fitting of training data. This reduce the variance of the test data, prevent over-fitting and enhance the prediction accuracy. Here are briefly introduced three Regularization regressions methods.The term Lasso stands for “least absolute shrinkage and selection operator”. Lasso uses shrinkage by shrinking data values to a central point such as mean. In this model, the regularization method is based on the absolute value of loss function. As a result, the target function in "Lasso Regression" is written as followsIn the Ridge regression, the Quadratic Loss Function is used. In such way, the amount of penalty is determined as the sum of squares of coefficients.Thus, if we consider the regression model as follows:The Ridge regression model is performed by minimizing the following function.Note that argmin refers to values of ββ that minimize the desired function.To estimate the regression parameters in the Ridge method, there is a constraint on the parameters which is written as follows.This constraint specifies that the sum of the squares of the parameters must be less than a constant or threshold value. In this way, the method of estimating the parameters will be as follows. It is clear that a balance is established between the existence of ββ parameters and their zeroing in the constraint section, and the num ber of related parameters and variables is optimized.The λλ parameter here is called the Penalty Regulation (Regularization Parameter).Note that regularization is done only for parameters β1β1 to βnβn, and intercept of β0β0 is an exception in this regard. Estimation of the parameters of the Ridge regression model according to the mentioned constraint will be as follows.Elastic Net Regression, by combining lasso regression and Ridge regression, overcomes their disadvantages and is a reliable alternative to them. Thus, if you are faced with a model whose descriptive variables are correlated with each other, it is better to use Elastic Net regression. In this method, Loss Function and Quadratic Loss Function are applied to the model simultaneously. As a result, the target function in the elastic network regression will be written as follows.Considering the multiple linear regression model, it can also be written as follows.26.Note that, like the lasso regression and the Ridge regression, in the Elastic Net regression there is no assumption that the residual is normal. Also, the intercept is not involved in the regularizationhttps://www.string-db.org/) was performed to analyze DEGs’ protein–protein interaction with a score of 0.4. Moreover, all the networks were depicted using R software.The online string tool  dataset (GSE89632 and GSE63067). The validation datasets consisted of data from patients with fatty liver, which were downloaded from this web tool, and the pre-processing was performed.The receiver operating characteristic (ROC) curve was performed to evaluate the efficacy of the diagnostic model. Specificity, sensitivity, area under the ROC curve, positive predictive value, negative predictive value, and cut-off value were assessed for each gene and their combination. All the procedures were analyzed by package combioROC in R.Figure The weight of the variables of the two datasets can be seen in Fig. 2 = 0.999 and alpha = 0.5, l1 Norm = 1.31). The area under the curve was approximately 0.99 with a confidence interval . The Elastic Net is an extension of the lasso robust to extreme correlations among the predictors. The results of Elastic Net method for identifying important factors can be seen in Table Three methods of Regularization regression, including LASSO, Ridge, and Elastic Net, were candidate to identify the effect coefficient of variables on fatty liver. Each of the color lines belongs to the coefficient of one variable, which with increasing Lambda parameter, the number of non-zero coefficients decreases, and the size of the coefficients becomes smaller and approaches zero. After fitting the model, with five k-fold cross-validation, the optimal value of the Lambda parameter was determined, and the results of the final model were reported. The model’s cross-validation results were plotted in a graph containing different values of Lambda versus Train/Test error, which shows the Train/Test Error related fitted models in different Lambda sizes Fig. . Among t2 = 0.999 and alpha = 0.5, l1 Norm = 213.66). The area under the curve was approximately 0.99 with a confidence interval . The Elastic Net is an extension of the lasso robust to extreme correlations among the predictors. The results of Elastic Net method for identifying important factors can be seen in Table The three methods of Regularization regression were used to identify candidate genes that may be used to identify the effect coefficient of variables on fatty liver. Each of the colored lines represents the coefficient of one variable, which with increasing Lambda parameter, the number of non-zero coefficients decreases, and the size of the coefficients becomes smaller and approaches zero. After fitting the model, with five k-fold cross-validation, the optimal value of Lambda parameter was gained, and the results of the final model were reported. The results of cross-validation of the model were plotted in a graph containing different values of Lambda versus Train/Test error, which shows the Train/Test Error related fitted models in different Lambda sizes Fig. . Among t2 = 0.999 and alpha = 1, L1 Norm = 15.96) Fig. . For GSE96) Fig. .The GSE48452 chip contained 14 NAFLD, 18 NASH, and 27 obese samples, among which 15,000 genes and 1400 DEGs were identified. Moreover, the GSE126848 chip had 15 NAFLD, 16 NASH, and 12 obese 9540 genes, and 843 DEGs were found in this dataset based on specific criteria , and also, its combination with ZEB2  had the highest rank of ROC analysis and can be considered as diagnostic markers , and its combination with AKR1B10, DHRS2, IGFBP1, and UGT2B17 with AUC of 0.96, 95% CI with a sensitivity of 0.94 and specificity of 0.95, also had the highest rank , which transport different molecules, including carbohydrates, amino acids, and ions. Furthermore, ABCF1 is critical in regulating innate immune and inflammatory responses28. This protein is considered an oncofetal protein significantly expressed in the fetal liver, not healthy adult cells. Fung et al. showed that the expression of ABCF1 was increased in hepatocellular carcinoma (HCC), and was associated with chemoresistance29. Cheung et al. demonstrated that upregulated ABCF1 gene is associated with poor recurrence-free survival (RFS) in liver cancer30. A significant association between other members of the ABC family and NAFLD has been proven in previous studies. ABCB1 plays a crucial role in transporting phospholipids and cholesterol into the liver cells. An animal study exhibited that the level of transporter proteins such as ABCB1, ABCC1-6, and ABCG2 increased during the progression of NASH31. The ABCB1 is overexpressed in liver diseases such as cholestatic, biliary cirrhosis, and obstructive jaundice34. The SART3 and RNPS1 are the genes with the highest score in the advanced stage of NAFLD; moreover, the result of PPI revealed that there is a strong correlation between SART3 and RNPS1, both of them are members of the post-splicing complex. SART3 is known as tumor-associated antigens detected in HCC and makes hepatocytes sensitive to immunotherapy35. A previous study used two datasets of GEO (GSE33814 and GSE89632) and showed that RNPS1 is one of the top genes overexpressed in NAFLD cells compared to the control group. RNPS1 is a member of the post-splicing complex role in RNA processing and apoptosis36. One of the other key genes detected in our investigation was APC5, a subunit of the anaphase-promoting complex (APC). Zhang et al. showed APC5 plays a critical role in activating the cell cycle during adipose tissue proliferation37. A study showed that after feeding, the expression of NONO gene significantly increased to uptake glucose. Furthermore, the results revealed that the deficient-NONO gene in mice reduces triglyceride storage and increases hepatocyte lipid catabolism38. In a current study, Wu et al. indicated that the expression of NONO gene was highly elevated in NAFLD mice39. our result indicates that CNTNAP1 is upregulated in NAFLD, which agrees with the previous study. CNTNAP1 has a positive role in triglyceride metabolism40. KAT7 gene, also known as HBO1, belongs to the lysine acetyltransferase family, which is a key factor in forming a replication complex, regulating the immune system and developing embryonic development. Information confirmed that the expression of KAT7 in mRNA and protein levels elevated in HCC cells leads to the proliferation and invasion of tumor cells. Zhong et al. reported that silencing the KAT7 gene using short hairpin RNA (shRNA) and CRISPR/Cas9 in the xenograft HCC model inhibited tumorigenesis41. ZPR1 is a zinc finger family member, and Wo et al. showed patients with severe NAFLD had ZPR1 rs964184 polymorphism. we hypothesized that this polymorphism could be associated with high expression of ZPR1 in patients42.RABGAP1 gene is associated with NAFLD. The previous studies showed Rabgap1 expression raised in perirenal fat and brown fat in Gpr21 knockout mice when fed with a high-fat diet43. Rabgap1 GTPase Activating protein which transited the cells from metaphase to anaphase. SLC7A8 and SPAG9 are two novel DEGs identified in our study. SLC7A8, the light-chain subunit solute carrier family 7, member 8, is a vital gene in inducing hypertrophy in adipose tissue and inflammation. Pitere et al. reported that the SLC7A8 deficiency in mice with diet-induced obesity decreases lipid accumulation in the liver44. SPAG9 is expressed explicitly in the testis and has a vital role in fertility. A study on chicken illustrated that the samples that overexpressed the SPAG9 gene have more fat content on the abdominal and liver tissues45. Furthermore, SPAG9 increases the proliferation of HCC cells through the interaction with MAPK/Jun pathway45. KAT6A is another member of the lysine acetyltransferase family, which epigenetically regulates the transcription of different genes involved in DNA repairing systems, cell cycle, metabolism, and autophagy. Many studies confirmed the overexpression of KAT6A related to HCC progression and chemoresistance47.The analysis of the GSE126848 dataset revealed that the expression of 48. BMI measurement is a helpful and non-invasive marker for predicting fatty liver. They suggested triple approaches comprising examining the lipid panel, BMI measurement, and radiological techniques50. Inflammation and fibrosis are the major pathological consequences of NAFLD. Fibrogenesis is stimulated by the activation of hepatic stellate cells and Kupffer cells, resulting from high plasma levels of glucose and lipids51. The activated hepatic stellate cells express different myogenic and pro-inflammatory markers such as myocyte enhancer factor-2 (Mef2), c-myb, and TGF-β. Moreover, inflammation results from increasing the level of reactive oxygen species (ROS) and cytokines in liver tissue53. The result of a meta-analysis revealed that the fibrosis stage significantly correlates with the risk of mortality in NAFLD54.Our result revealed a significant relationship between clinical and demographic data, including fat, fibrosis, body mass index (BMI), inflammation, and fatty liver. In many studies, BMI is announced as a critical index for increasing the risk of fatty liver. The BMI score of patients is a 4 to 14-fold change higher than healthy individuals. Fan et al. reported that 73% of patients with NAFLD were obese and overweight55. NR4A2 is a transcription factor that plays a pivotal role in regulating fatty acid beta-oxidation. Therefore, the dysregulation of NR4A2 causes fat accumulation in the liver56. Chen et al. showed that NR4A2 overexpression prevents Hepatic stellate cell (HSCs) proliferation which plays a key role in liver fibrogenesis57.We reported NR4A2 and IGFBP1b as novel diagnostic biomarkers in fatty liver. Insulin-like growth factor binding protein (IGFBP) binds to insulin-like growth factors (IGFs) and regulates cellular metabolism. Hepatocytes largely produce IGFBP and secrete it into the serum. Previous studies are in line with our results, Pan et al. reported a high expression of IGFBP in NAFLD patients, L02 cells, and also in mice models of NAFLD58. The result of a cross-sectional investigation showed that machine learning is a predictive model of NAFLD. They revealed that this method enhances clinical decisions and reduces end-stage disease59. Furthermore, previous studies used machine learning methods for identifying novel biomarkers in various conditions, such as cancer62, cardiovascular diseases64, pulmonary diseases66, and neurological disorders68.Previous evidence confirmed that novel approaches, including machine learning, are promising strategies for diagnosing, preventing, and managing diseases. Wu et al. compared four machine learning algorithms in predicting fatty liver disease, and they showed that the random forest model has a higher performance in the early diagnosis of fatty liverIn conclusion, using a bioinformatic approach; twelve key genes were detected that are significantly related to the fatty liver. It is recommended that these key genes are assessed further as possible predictive markers during the development of the fatty liver.Supplementary Information.


Clustering is a critical component of single-cell RNA sequencing (scRNA-seq) data analysis and can help reveal cell types and infer cell lineages. Despite considerable successes, there are few methods tailored to investigating cluster-specific genes contributing to cell heterogeneity, which can promote biological understanding of cell heterogeneity. In this study, we propose a zero-inflated negative binomial mixture model (ZINBMM) that simultaneously achieves effective scRNA-seq data clustering and gene selection. ZINBMM conducts a systemic analysis on raw counts, accommodating both batch effects and dropout events. Simulations and the analysis of five scRNA-seq datasets demonstrate the practical applicability of ZINBMM.The online version contains supplementary material available at 10.1186/s13059-023-03046-0. Single-cell RNA sequencing (scRNA-seq) has been widely conducted to determine heterogeneity and diversity of cell populations. It helps determine cellular differences with high specificity and provide a deeper understanding of complex biological variations at the individual cell level . Most scAlthough scRNA-seq data clustering analysis is very promising owing to its extensive applications, several challenges exist because of technical and biological reasons, such as batch effects and dropout events. Systematic differences in gene expressions between batches caused by data generated at different times are known as batch effects. Several batch effect correction methods have been developed for scRNA-seq data, such as mutual nearest neighbours (MNN)  and canoAnother challenge is the high dimensionality of scRNA-seq data. This usually produces extensive noises, resulting in poor clustering accuracy and significantly adding to computation time. Dimension reduction is commonly conducted in scRNA-seq as a preliminary step prior to clustering. This step projects high-dimensional gene expression data into a lower dimension space and helps focus on relevant low-dimensional signals for better clustering . ExampleFeature selection can be used as an alternative to dimension reduction. It has attracted attention in recently published studies on scRNA-seq clustering and can output a subset of the original genes without transforming them. Because the majority of the genes are not differentially expressed among various cell types, feature selection can enhance signal-to-noise ratios and subsequently improve cell clustering by reducing the number of genes under consideration , 20. MorIn this study, we propose a zero-inflated negative binomial mixture model (ZINBMM) for scRNA-seq data clustering that can comprehensively account for the unique problems of batch effects, dropout events, and high dimensionality. The model directly applies to the raw counts without any transformation to avoid a potential loss of information. The mixture model with biological effects of genes being modelled using cell type-specific mean parameters is developed to accommodate heterogeneity, which achieves soft clustering and has the advantage of more meaningful probabilistic interpretations. In addition to dealing with high sparsity owing to dropouts, our method can also accommodate zero-expressed gene counts and correct the confounding batch effects by introducing corresponding parameterisation into the ZINB mixture model. ZINBMM innovatively performs feature selection by imposing penalisation on the differences between cluster-specific and global mean values. Thus, the informative genes can be identified automatically in the clustering process, which cannot be achieved in most of the existing scRNA-seq data clustering studies, such as . We demoZINBMM is a systemic model for the analysis of high-dimensional scRNA-seq data that have potential dropout events and batch heterogeneity. It can simultaneously identify cell types and cell type-specific genes. Herein, we briefly introduce the method. The technical details are provided in the “n single cells and J genes, and denote K being the number of mixture components (clusters) and Consider  methods , 13, 17,To further control various technical batch effects, we propose a decomposition of To evaluate the performance of ZINBMM in clustering and feature selection, we conduct extensive simulation studies. In brief, we consider three clusters and generate data from the ZINB mixture model using the baseline expression parameters obtained from the Zeisel dataset . DropoutIn addition to the proposed ZINBMM, we conduct analysis using nine competing clustering methods: CIDR , SC3 [3]P-values computed from the Wilcoxon test for the proposed method and each alternative, are summarised. The median values of ARI and F1 are shown in Fig. A hundred replicates are simulated under each setting, and medians and median absolute deviations (MADs), as well as P-values computed from the Wilcoxon test are mostly p-value 0.00027) is mainly due to the biological cluster difference, which is not covered by the limited number of zeros  as shown in Fig. Sp value 0.0071 in Fig. Sp value of 0.65) across clusters are weak, leading to slightly worse clustering performance. Similar statements that dropouts can be informative have also been presented in [As shown in Fig. entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaented in  and 31]P-values In addition to the above analyses, we consider another setting, under which dropout rate is independent of cell types and thus dropouts are non-informative for cell clustering (see Methods), and observe that ARI values decrease as dropout rate increases  with more unknown parameters and the sample size of each cluster is limited, clustering performance of the proposed method is slightly worse than SC3. However, such performance can be easily enhanced by a larger sample size. The current simulation studies show that 150 samples per cluster can already provide satisfactory results, which can be easily satisfied with practical data.We also perform simulations with various values of entclass1pt{minimaOverall, the proposed method can achieve superior performance in both clustering and gene selection, and the significance of improvement is supported by statistical testing. SC3 achieves the second best clustering accuracy. Under some settings with low levels of dropouts, SC3 behaves slightly better than the proposed, perhaps because of the combined clustering strategy. However, it gets less effective when there are higher levels of dropouts. RZiMM achieves the second best gene selection accuracy, since it also accommodates dropouts, batch effects, and cell heterogeneity. The superiority of the proposed method over CIDR, Seurat, snbClust, and sparseKmeans directly supports the zero-inflation-based strategy for accommodating for dropout events. Improved performance over RZiMM and scDeepCluster suggests the effectiveness of the proposed penalisation scheme. Moreover, the proposed method performs much better than two MNN-based methods, partially suggesting the potential loss of information and bias introduction through multi-staged processing. Without an effective accommodation of cell heterogeneity, the two dropout-based gene selection methods M3Drop and NBDrop have unsatisfactory selection performance.P-value computed from the Wilcoxon test being 0.946. However, the proposed method still outperforms the other competing ones. The majority of the alternatives behave poorly under the RZiMM setting, probably due to the presence of multiple batch effects. On the other hand, under the CIDR setting, the inverse relationship between dropouts and expression levels enhances the differences among differentially expressed genes, leading to satisfactory clustering accuracy for most of the methods.We further evaluate stability of the proposed method and examine whether it can maintain its superiority when the data generation model is misspecified. In particular, we consider three types of models: (a) the negative binomial mixture model considered in snbClust  without To get more intuitive insight into the impact of batch effects and better appreciate the operating characteristics of the proposed method, we additionally conduct batch correction for SC3 and Seurat using the Harmony approach , under tFinally, we examine computational efficiency of the proposed method under the above simulation settings with various numbers of cells, genes, and clusters. All analysis is conducted using a computer with an Intel Core i5 processor and 16 GB RAM, and the average computer time with fixed tuning parameters is provided in Table S20  , human lTo obtain deeper insights into batch characteristics, we further provide a visualized illustration of these datasets in Fig. For each dataset, in principle, the proposed method can be directly applied. However, considering that only a small number of genes are potentially associated with the formation of cell types, we conduct a pre-screening by selecting the top 1,000 highly variable genes (HVGs) with the largest standard deviations for downstream analysis. As stated in , this scWe consider the following candidate sequence: for CIDR , random for CIDR , elbow-mfor CIDR , modularfor CIDR , modifiefor CIDR , and Gapfor CIDR .K as the true number of cell types for all methods in the following analysis, which is a common practice in recent clustering analysis of scRNA-seq data [The results are presented in Table seq data , 22.TabWe conduct analysis using the proposed method as well as the nine alternatives and present the ARI values in Fig. Besides cell types, the proposed method also identifies 33, 24, 51, 55, and 80 important cell type-associated genes for the mouse embryonic stem cell, human lung cancer cell, mouse uterus cell, mouse liver cell, and mouse mammary gland datasets, respectively. We also conduct gene selection using RZiMM, snbClust, sparseKmeans, M3Drop, and NBDrop. The summary results are shown in Additional file To obtain insights into the selected genes using the proposed method, we present an expression heatmap based on the ground true cell types in Fig. Literature search suggests that many of the identified genes have strong biological implications for cell types. For example, for the mouse embryonic stem cell dataset, the high expression of gene Krt18 has been found to contribute to the formation of a minor formative-state pluripotent population . Gene GJTo provide an additional indicator for the quality of gene selection, we further analyse biological relevance of the selected genes by conducting gene ontology (GO) enrichment analysis. The analysis is conducted to evaluate molecular functions, cellular components, and biological processes of the selected genes. The results are shown in Fig. Advances in single-cell technologies have enabled the measurement of gene expressions in massive individual cells, providing opportunities for a better understanding cellular heterogeneity. However, scRNA-seq experiments suffer from severe batch effects and dropout events, making read count data noisy and sparse. Furthermore, these experiments are characterised as high dimensional, because they typically measure the expressions of tens of thousands of genes. Even after pre-processing, the remaining genes may still contain redundant information. These factors call for the development of effective statistical models that can account for high-dimensional scRNA-seq data clustering with batch effects and zero inflation.We have developed ZINBMM, incorporating a penalisation technique that simultaneously achieves clustering and gene selection. ZINBMM directly models raw count data without transformation. The mixture model can naturally describe batch effects and dropout events, facilitating a biologically interpretable clustering analysis. Furthermore, with penalisation on the differences between global and cluster-specific means, ZINBMM can conduct cluster-discriminatory gene selection, improving clustering accuracy and biological understanding. Comprehensive evaluations and comparisons with state-of-the-art methods on both simulation and real data applications have been conducted. ZINBMM has demonstrated stable and superior results over the alternatives.We have developed a two-layer mixture model, where the first and second layers have been proposed to accommodate cell heterogeneity and zero-inflated values. The identifiability of mixture distributions is unfortunately still a wide-open problem . In publWe have conducted analysis with 1000 HVGs to improve performance and reduce computational cost. Additionally, we have also examined the results with 2000 HVGs. The comparison is provided in Additional file In this work, we have developed a novel statistical method ZINBMM to conduct simultaneous clustering and cluster-specific gene identification for scRNA-seq data, specifically to address the challenges of batch effects and dropout events. Experiment results on both simulation and five real datasets have demonstrated that the proposed method significantly improves clustering and gene selection performance compared to the alternatives. Motivated by the importance of clustering analysis for high-dimensional scRNA-seq data, ZINBMM is a valuable tool for elucidating cellular heterogeneity and providing biological insights into the underlying mechanism.K is the number of cell types (mixture components), S being the number of batches known in advance, and Let j that has all For regularised estimation and gene selection, we propose the following penalised objective function:We adopt an expectation-maximisation (EM) algorithm for the maximisation of . First, entclass1pt{minimaWith  and a fiFor Initialise Initialise Set Update Compute Compute Compute Optimise Optimise Optimise Optimise q is the number of We iterate the  studies , 57. We  studies . Such a entclass1pt{minimaedgeR package following [CIDR, SC3, and Seurat, respectively. For the two MNN-based methods, fastMNN in R package batchlor is first conducted to adjust for batch effects, and graph-based and K-means clustering are then conducted using R package igraph and stats, respectively. scDeepCluster, RZiMM, and snbClust are implemented using codes from https://github.com/ttgump/scDeepCluster, https://github.com/SkadiEye/RZiMM and https://github.com/YujiaLi1994/snbClust, respectively. SparseKmeans is implemented using R package sparcl. M3Drop and NBDrop are conducted with the functions M3DropFeatureSelection and NBumiFeatureSelectionCombinedDrop in R package M3Drop, respectively. For each competing method, we adopt the running settings and convergence criterion suggested by the corresponding package or code.CIDR, SC3, Seurat, scDeepCluster, MNN-Graph, MNN-Kmeans, RZiMM, snbClust, sparseKmeans, M3Drop, and NBDrop are considered as competing methods. Among these, CIDR  is an imollowing , and gloollowing . CIDR, SJ values from the MLEs. (c) Three settings of dropout levels are considered, where the dropout rates U, U, and U, resulting in low (about 5%), medium (about 45%), and high (about 75%) level of dropout rates, respectively. Here, for each j, we sample K different k of each cell following a multinomial distribution with probability k and We consider the following settings. (a) Sample size filed by , genes wn and K. Specifically, we consider Beyond the above scenarios with U, respectively.In the above simulations, we assume that the dropout rate For data with known cell-type labels, we use ARI to compare clustering performance of different algorithms. Specifically, for the true and estimated cluster assignment For simulated data with known significant genes, to evaluate gene selection performance, we adopt In the mouse embryonic stem cell dataset, the transcriptome of 704 mouse embryonic stem cells was sequenced across three culture conditions , using the Fluidigm C1 microfluidics cell capture platform followed by illumina sequencing . FollowiThe human lung cell dataset was collected from three lung adenocarcinoma cell lines HCC827, H1975, and H2228 on three different platforms with CELseq2, 10x Chromium, and Drop-seq protocols , respectThe mouse uterus, mouse liver, and mouse mammary gland datasets were processed on the Microwell-seq platform from the Mouse Cell Atlas project . We consAdditional file 1:Supplementary Figs S1-S13.Additional file 2:Supplementary Tables S1-S26.Additional file 3. Supplementary Note. IRLS Algorithm for Additional file 4. Review history.


Mass spectrometry technology can realize dynamic detection of many complex matrix samples in a simple, rapid, compassionate, precise, and high-throughput manner and has become an indispensable tool in accurate diagnosis. The mass spectrometry data analysis is mainly to analyze all metabolites in the organism quantitatively and to find the relative relationship between metabolites and physiological and pathological changes. A feature construction of mass spectrometry data (MSFS) method is proposed to construct the features of the original mass spectrometry data, so as to reduce the noise in the mass spectrometry data, reduce the redundancy of the original data and improve the information content of the data. Chi-square test is used to select the optimal non-redundant feature subset from high-dimensional features. And the optimal feature subset is visually analyzed and corresponds to the original mass spectrum interval. Training in 10 kinds of supervised learning models, and evaluating the classification effect of the models through various evaluation indexes. Taking two public mass spectrometry datasets as examples, the feasibility of the method proposed in this paper is verified. In the coronary heart disease dataset, during the identification process of mixed batch samples, the classification accuracy on the test set reached 1.000; During the recognition process, the classification accuracy on the test set advanced to 0.979. On the colorectal liver metastases data set, the classification accuracy on the test set reached 1.000. This paper attempts to use a new raw mass spectrometry data preprocessing method to realize the alignment operation of the raw mass spectrometry data, which significantly improves the classification accuracy and provides another new idea for mass spectrometry data analysis. Compared with MetaboAnalyst software and existing experimental results, the method proposed in this paper has obtained better classification results. Compared with upstream genomics, transcriptomics, and proteomics research, metabolomics can expand from the field of genes to the area of small molecules, realize the integration of small molecules into bioinformatics, and combine other omics technologies to discover systematic biomedicine research in the field. Nowadays, as one of the most widely used platforms of metabolites, mass spectrometry can repeatedly detect thousands of metabolites from cells6, tissues, and biological fluids, assist biomedical research in detecting multiple feature subsets, and is of great significance in promoting biomarker screening9, pathological research12, and drug development15. In metabolomics, researchers used mass spectrometry to analyze changes in the levels of metabolites in organisms to study the dynamic development of organism physiology. Although histopathology is still the gold standard for modern disease diagnosis, proteomics and metabolomics studies based on mass spectrometry technology have been widely used in the diagnosis of various diseases, which can Achieve early and accurate diagnosis of clinical-level diseases16. Exploring the metabolite molecules corresponding to biomarkers in the metabolic process of conditions will help elucidate the mechanism of disease in the disease process and find marker molecules that play an essential role in the occurrence and development of diseases17.Metabolomics plays a crucial role in biological systems and aims to investigate the development of biology and disease by studying all metabolites in biological samples18. Therefore, there is an urgent need to find an efficient data processing method to extract and analyze large-scale multidimensional raw spectral data, especially raw Mass spectral data generated from clinical samples.Due to the difference in sample sampling time, the sample length is different. At the same time, mass spectrometry data has a high feature dimension, which contains much biological information and a large amount of redundant information and noise. How to remove noise and errors from such high-dimensional features and extract useful biological information has become one of the leading research points of bioinformatics22. These machine learning methods are suitable for preprocessed mass spectrometry data, but differences in preprocessing pose a significant challenge for any comparative analysis. As a critical step in sample classification, data preprocessing is used to align mass spectrometry sample data and eliminate noise errors and redundant information from original mass spectrometry data. However, taking inappropriate preprocessing operations will result in the loss of useful information in the data. Therefore, proper preprocessing methods should be used when performing data preprocessing23.At present, many machine learning (ML) models have been widely used for accurate diagnosis of diseases and biomarker mining under mass spectrometry data, such as support vector machine (SVM), random forest (RF), Bayesian neural network (NB), and Linear discriminant analysis (LDA) has achieved good resultsThis paper mainly aims at the uneven raw data containing noise and uses two-dimensional mass spectrometry data to achieve accurate diagnosis of diseases and mining of biomarkers. The features of mass spectrometry data are constructed by the data preprocessing method, and the feature selection is carried out by the chi-square test method. In training ten supervised learning models, the model's classification effect is evaluated through various evaluation indicators.A step-by-step overview of the data processing in this paper is shown in Fig. The datasets used in this experiment mainly include the colorectal and liver datasets from Proteome Xchange and the coronary heart disease datasets provided by Thermo Fisher Scientific. Table 24. The plasma data is divided into two batches, in which 1-Batch contains 21P samples and 20N samples, and 2-Batch contains 38P samples and 23N samples. The pathogenesis of coronary heart disease is studied by identifying new biomarkers in plasma (Dataset connection: https://datadryad.org/stash/dataset/doi:10.5061%2Fdryad.s8k81).The first dataset was provided by Thermo Fisher Scientific in Massachusetts and included plasma and urine samples from 59 coronary heart disease (CHD) patients and 43 healthy controls (Control)25. The liver metastases of the same colorectal liver metastases and their adjacent tissue samples have certain similarities in the related proteins. Still, they have significant differences in the number of distributions, and the liver metastases are much more extensive in some essential proteins. Therefore, try to use the critical information of its high-precision mass spectrometry samples to distinguish the two samples through machine learning algorithms. .The second dataset is from the Proteome Xchange platform, including 30 colorectal liver metastasis (CRLM) samples from the same patient with colorectal liver metastasis and 30 adjacent normal tissue samples (Control)In the process of mass spectrometry data collection, the collection length of each sample is inconsistent, and the collected data is relatively sparse, so it is necessary to find a way to align the mass spectrometry data. In addition, there is external interference in the process of mass spectrometry data acquisition, and the collected data will contain a lot of noise. This feature construction method can align samples with different lengths, reduce the noise in mass spectrometry data and reduce the redundancy of original data. Figure 26.Data feature selection is widely used in extensive data mining, analysis, and machine learning. Especially in high-dimensional mass spectrometry data, selecting important data features is a critical factor in identifying disease biomarkers. The chi-square test is a conventional feature selection algorithm used for feature selection in different research worksThe Chi-square test is a statistical analysis method specially used for counting data in statistical analysis. Using the 2, the stronger their correlation. Get a sorted list of features according to the χ2 value, then select features according to the list. The chi-square test is used for feature selection, and the chi-square value estimates the importance of high-dimensional data features. This method can quickly find the relevant information in the data features and select the feature subset with the most significant correlation and the least redundancy27.Among them, F is the feature; 28 fits the relatively linear data with less loss and enables the fitted model to better predict the data. A Support Vector Machine (SVM)29 defines a linear classifier with the most significant margin in the feature space, capable of separating samples from two different classes. When predicting a new sample, K-Nearest Neighbor (KNN)30 judges which category the sample belongs to according to which type the K samples closest to the sample belong. The decision tree (DT)31 obtains the final result through the decision-making process and discrimination of the problem by the tree. Random Forest (RF)32 is a method that uses multiple decision trees to train, classify and predict sample data. Lightweight Gradient Boosting Machine (LightGBM)33 is a fast, distributed, high-performance decision tree-based gradient boosting algorithm that starts with weak models and trains models iteratively, each model adding to the predictions of previous models to produce a reliable Overall forecast. Naive Bayes (NB)34 estimates the conditional probability of each category by calculating the frequency of occurrence of each type in the training samples and dividing each feature attribute, and records the results, and finally outputs the classification of the samples. Bagging35 estimates a sample by averaging the posterior probabilities of the non-uncounted nodes it falls into. Reinforcement learning (Adaboost)36 trains different classifiers on the data set and then combines these weak classifiers to form a more robust final classifier. The classification effect is better than the conventional weak classifier. Classifier model effect. The deep learning model is a multilayer perceptron (MLP)37 or a multilayer perceptron. This forward-structured artificial neural network maps a set of input vectors to a group of output vectors and is used to fit complex functions or solve problems—classification problem.In order to verify the original mass spectrum, Table 38.To evaluate the prediction model, this paper uses seven evaluation indicators widely used in the medical field to assess the classification effect of ten models, including Precision, Specificity, Sensitivity, Matthew Coefficient (MCC), Accuracy, F1-score, and Area under roc curve (AUC)To evaluate the feasibility of the method proposed in the paper, the precision rate, sensitivity, specificity, Matthew coefficient, and accuracy rate were evaluated, respectively. The calculation formula is as follows:Among them, true negatives (TN) are the number of predicted healthy labels that match the true healthy labels; true positives (TP) are the number of predicted disease labels that match the actual disease labels; false negatives (FN) refer to the number of patients with disease The number of sick labels that are misidentified as healthy; false positives (FP) are the number of healthy labels that are predicted to be diseased.F1-score is the harmonic mean of precision rate and recall rate. The F1 score is calculated to measure the classification performance of samples of different categories. The calculation formula is:39. Calculated as follows:AUC refers to the area covered by the ROC (receiver operating character) curve. Since it is difficult for ROC to reflect the difference between models, AUC can remember the difference between models as a numerical value. The closer the AUC is to 1, the better the performance of the modelAmong them, positive class indicates that the category is a positive example, Considering that the original mass spectrometry data set is too large and inconvenient for analysis, it is necessary to use open sources of mass spectrometry software such as MZmine2.53, Raw Converter, and MSConver for sampling to extract detailed key data information in mass spectrometry. The main steps of sampling through MZmine2.53 mass spectrometry software in this paper are: (1) Input the original Raw file into MZmine2.53 software and save important mass information through mass detection; (2) Set the mass detector to exact Mass for sampling, set the noise level to 0, and finally, generate chromatographic column information through ADAP Chromatogram builder, to ensure that all data are complete; (3) Export all mass spectrometry information related to this experiment from the generated feature lists, and the exported CSV file contains 24 columns Mass spectral information, where important information includes Mass, retention-time, peak-height, and peak-area. These raw data are sequentially transformed into regular feature matrices through a series of subsequent preprocessing methods for subsequent supervised learning models.In the process of data collection, the length of each sample is different because of the different sampling time. In order to maintain the consistency of each sample in the M/Z dimension and construct suitable data for the machine learning model, it is necessary to use feature engineering method to construct and align the original data. Due to the difference of sampling time in the public coronary heart disease data set, the data set is divided into two batches. In this part of the experiment, the difference between the two batches was ignored and the samples of the two batches were mixed. The peak area and peak height of M/Z dimension are constructed by MSFS method, and the M/Z values in all samples are traversed, and the minimum and maximum M/Z values of 54 and 1223 are obtained. The minimum value and the maximum value are taken as the start value and the end value of the sliding window. Then, by setting the sliding window step size, the average of peak area and peak height in each sample window is taken as the feature value after feature construction.Taking two mixed coronary heart disease data sets as the research objects, the training set and the test set are divided according to the ratio of 2:1, the step size of the sliding window is 0.1, and the feature construction is carried out on the original data. The chi-square test is used to screen the minimum non-redundant feature combination. Training is performed on ten supervised learning models, and the classification results are evaluated by various evaluation metrics Table . The optThe 1.20.3 version of Numpy and the 1.3.4 version of Pandas were used to process the data, using the CH2 feature screening algorithm provided in the 0.24.2 version of Sklearn and ten kinds of Supervised learning algorithms .Under different window steps, the data exhibits different distributions, which provide different degrees of information for the machine learning model. This part compares the feature information extracted from five sliding windows with different step size parameters and finally determines the optimal sliding window step size parameters through the classification results on ten supervised learning models. Table To explore the effect of different sliding window step sizes on sample prediction, the same data preprocessing, feature screening, and model validation methods are used throughout the experiment, under the condition that only the window step size is changed. The influence of five different window steps on the classification results was verified on the coronary heart disease data set to determine the optimal window parameters. Through Table As shown in Fig. 40. Table This part of the experiment uses the widely used mass spectrometry software MetaboAnalyst 5.0 version to analyze the public coronary heart disease data set. The results are compared with the method proposed in this paper41, and verify the classification results under the optimal window step size. When there are two features on peak area and peak height, on the bagging model, the AUC is 1.000. The AUC of the comparison paper is 0.999 when there are eight features. Compared with the results of the comparison paper, the method proposed in this paper uses fewer features to achieve the same results as the comparison paper, proving the feasibility of the method proposed. The experimental results show that the method proposed in this paper has superior performance in distinguishing coronary heart disease and normal samples.Divide the coronary heart disease data set according to the ratio of the comparison papers With a sliding window of 1 as the step size, using the chi-square test, Peak-area and Peak-height screen out the two feature combinations with the most considerable chi-square value on the data of two batches mixed and two batches of mutual verification, respectively. Using visualization, use these feature combinations to draw scatter plots and further verify the classification effect between coronary heart disease samples and healthy samples. At the same time, it is confirmed that batch differences between batches 1 and 2 due to differences in collection time are generated on the coronary heart disease data set. Figure From Fig. From Fig. By visualizing the results in the previous summary, it can be found that there is a significant difference between different batches in the coronary heart disease dataset. To verify the influence of the differences between the two batches of samples on the experimental results, this part of the experiment uses different batches of samples to test each other to verify the classification effect of the model. The coronary heart disease data set contains two batches of samples. This part of the experiment considers the differences between the two batches of samples. Based on the optimal parameters of the previous model, one batch of samples is used as the training and verification sets. One batch of samples is left as the test set to verify the classification effect of the model further.The results in Table The significantly different mass-to-charge ratio intervals found by the method proposed in this paper have biological significance. By measuring the proteome expression profile and phosphorylated proteome profile of coronary heart disease and normal samples, it is possible to discover the precise treatment of coronary heart disease—potential biomarkers. Taking the feature subset corresponding to the optimal classification result in the mixed dataset when the sliding window step size is one as an example, two different features are found on Peak-area and Peak-height, Peak-area and Peak-height. The intersection is the F_59 difference feature. Using the feature to construct the index can determine the original cytoplasmic ratio interval and the biomarker of coronary heart disease. Formula 3.1 calculates the original feature interval through the feature through the sliding window calculation method. The calculation formula is as follows:Among them, The original quality interval can be calculated by formula  by usingOn the Peak-area and Peak-height, aiming at the remarkable feature F_59 corresponding to the original Mass interval 113–114, we traverse the common Mass values of all samples in the interval, and find that the mass value of 113.02 is the remarkable marker of healthy samples and sick samples, and the corresponding biological compounds can be obtained by combining metabolomics to compare the database in the later stage, thus revealing the pathogenesis of coronary heart disease.This part of the experiment uses the public colorectal liver metastases dataset to verify the classification results of the proposed method on other mass spectrometry datasets. In this part of the experiment, the training set and the test set are randomly divided according to the ratio of 7:3. By traversing the M/Z values in all colorectal liver metastases samples, the minimum and maximum M/Z values were 400 and 1600, which were used as the starting and ending values of the sliding window, respectively. Since the original data sparsity of the colorectal liver metastases is different from that of the coronary heart disease dataset, it is found that setting the sliding window step size parameter to 0.1 can effectively extract the effective original information of the colorectal liver dataset. Finally, the chi-square test is used for feature screening, model training is carried out on ten supervised learning models, and the classification effect is evaluated through various evaluation indicators.The results in Table In this study, MSFS method is used to construct the features of the original mass spectrometry data, so as to realize the alignment operation of the original mass spectrometry data and reduce the redundant information and noise in the data. Chi-square test is used to select the least non-redundant feature combination, and the classification effect is verified on 10 models, and the feasibility of this method is verified on two public data sets. Different batches of sample mixtures were tested and verified internally on the coronary heart disease data set. When there are two features, the classification accuracy of peak area and peak height can reach 1.000, and the classification result is better than MetaboAnalyst software and the current experimental results. At the same time, chi-square test was used to find out two significantly different chi-square characteristics corresponding to two batches of samples in coronary heart disease data set, and visual analysis was made. It is found that the two batches of samples are quite different. External verification is carried out on different batches to verify the classification effect of the method proposed in this paper on samples with significant batch differences. The results show that the classification accuracy is as high as 0.950 when there are four features in the peak area, which verifies the method proposed in this paper. Feasibility. At the same time, the approximate interval of biomarkers of coronary heart disease can be further determined by mapping the two groups of features with the best classification results back to the original M/Z interval. Finally, the method proposed in this paper is verified on the data set of liver metastasis of colorectal cancer. When there are 20 features in the peak area, the classification accuracy can reach 1.000, which shows that the method proposed in this paper is feasible in mass spectrometry data sets (Supplementary Information Supplementary Information.