NetPRS: SNP interaction aware network-based polygenic risk score for Alzheimer’s disease

Authors: sunghong  park
doyoon  kim
hyun woong roh
dong-gi  lee
chang hyung hong
kanghee  park
juhyeon  kim
sang joon son
dokyoon  kim
hyunjung  shin
hyun  goo woo
Venue: IEEE_org_EMBS_BHI_2024_Conference
Published: 2024-05-31 06:42:34

Abstract: Alzheimer’s disease (AD) is underscored by its polygenic nature, attributable to variants across multiple genetic loci. This has led to the development of the polygenic risk score (PRS) model, which estimates individual risk by aggregating risk alleles weighted from their effect sizes. While early models were limited to utilizing only independent effects of single nucleotide polymorphisms (SNPs), recent models have been advanced to consider epistatic interactions between SNPs. However, SNPs interact through various channels, and typically, they are associated with each other through SNP-gene relations and gene-gene interactions. Moreover, SNPs interact synergetically, exhibiting diverse joint effects of genetic variations. Given these properties of SNP interactions, the PRS models need improvement to account for the interactive effects between SNPs in a polygenic manner, especially for genetically complex diseases such as AD. In this study, we propose a two-stage approach for AD risk assessment, called network-based PRS (NetPRS). First, the phenotypic and genomic interactions are quantified and integrated into networks. Second, the independent effects of SNPs are propagated on the integrated SNP networks using graph-based machine learning model. Through this procedure, NetPRS extracts the globally interactive effects between SNPs and integrates these effects to predict the risk of AD. The proposed method was applied to two cohort datasets: the Alzheimer's Disease Neuroimaging Initiative dataset with 1,175 participants, and a South Korean dataset with 724 participants. Experimental results showed that the integrated effects of NetPRS more clearly distinguished between AD and control groups, outperforming the six existing methods by 16.4% on average.

Main paper: 
 i. introduction: 
 Alzheimer's disease (AD) is one of the most common neurodegenerative disorders, particularly affecting elderly people over 65 years of age with about 10% prevalence [1] . With the rapid aging of the global population, AD is becoming more prevalent, and the number of patients is expected to increase from 50 million in 2015 to 130 million in 2050 [2] . As AD has recently emerged as a serious problem, numerous studies have been conducted to overcome AD, focusing on achieving accurate diagnosis and early prediction. A representative field is the study based on genetic data. Genetic factors play a key role in AD pathogenesis, highlighting the importance of using genetic data to predict AD risk [3] . Recent genome-wide association studies (GWAS) have revealed that multiple genetic loci contribute to AD pathogenesis [4, 5] , expanding genetic risk assessment for AD to polygenic methods that consider other genetic factors in addition to APOE, which is known to be the most important AD-related gene [6] . Therefore, polygenic score models that integrate the effects of multiple genetic variants identified through GWAS have emerged as a key method for effectively predicting AD risk [7] .The polygenic risk score (PRS) model is the most commonly used method, which is constructed by calculating the sum of risk allele dosages weighted by their GWASderived effect sizes [8] . This approach was applied to individual assessment of AD risk [9] and investigated with respect to the optimal strategy related to genetic data processing that can achieve the highest accuracy [10] . Although the PRS-based assessment is an appropriate method to reflect the polygenic nature of AD, the challenge remains that the PRS model is limited to the independent effects of SNPs without considering the interactive effects between SNPs [11] . The interactions between SNPs have a critical impact on disease onset and progression through various pathways of genetic variation. In AD pathogenesis, SNP interactions can promote or inhibit pathological processes such as amyloid beta protein accumulation in the brain or abnormal phosphorylation of tau protein [12, 13] . The fact that the SNP interactions play a key role in understanding the complex genetic basis of Alzheimer's disease and developing personalized prediction models suggests that the PRS model needs to be further sophisticated by reflecting the interactive effects between SNPs.The epistatic effect is the most representative SNP interaction, which indicates the impact on the traits of individuals caused by the interactive effects occurring at different genetic loci. As the interactions between SNPs by epistasis significantly contribute to determining phenotype [14] , the analysis of epistatic effects is important for understanding the mechanisms of disease pathogenesis [15] . The advantage of epistatic effect can be more beneficial for complex diseases such as AD. Several AD-specific key genes were identified by utilizing the epistasis-based SNP interactions [16] , and the accuracy of the PRS model for AD was improved by combining the independent effect with the interactive effect between SNPs by the epistasis [17] . As a result, the PRS model achieves a more in-depth understanding of AD pathogenesis and a more accurate AD risk assessment by considering SNP interaction effects by epistasis.In addition to the epistatic effect, SNPs also interact with the genome, and such interactions can act as a stronger risk factor for disease by working synergistically [18] . The SNP interactions based on the genome, such as enhancer-promoter Fig. 1 . Schematic description of the proposed method. The proposed method consists of two stages: SNP interaction network construction and network-based polygenic risk score (NetPRS). At first, the proposed method quantifies the phenotypic and genomic interactions between SNPs and represent them as networks. (a) Phenotypic SNP interactions are measured by the epistasis test. (b) Genomic SNP interactions are measured by applying SNP-gene relations to gene-gene interaction network. Next, NetPRS assesses individual AD risk by utilizing the independent effect and the constructed SNP interaction networks. (c) Network propagation extracts the phenotypic and genomic interactive effects between SNPs by diffusing the independent effect to each network. Smoothness is a trainable parameter that controls the intensity of diffusion. As its value decreases, interactions be-tween close SNPs are highlighted, and as its value increases, even interactions between distant SNPs are reflected. (d) Effect integration linearly combines the independent effect and the extracted two interactive effects into the integrated effect. Combining coefficients are set as trainable parameters indicating the ratio of each effect reflected in the integrated effect. (e) Risk prediction calculates individual AD risk by applying the integrated effect to the parameter representing the effect size of SNPs.interactions, are significantly related to disease risk by affecting the regulation of gene expression. [19] . Furthermore, the genomic SNP interactions occur not only within the same gene but also across different genes. Recent studies have shown that such interactions are considered important risk factors for various diseases [20, 21] . Especially, AD is a complex disease involving the interactions between various molecular pathways, regarding the effects of genomic interactions more important [22] . Consequently, the effectiveness of genomic interactions on disease onset and the complexity of AD pathogenesis highlights the need for the PRS model to consider the genomic interactions for the AD risk assessment.For the more comprehensive and sophisticated assessment of AD risk, the best strategy would be for the PRS model to consider both phenotypic and genomic SNP interactions. However, there are several challenges in implementing this strategy as follows. (i) Quantification of genomic SNP interactions: while there is abundant information on SNPgene relations, there is a lack of information on the interactive effects that SNPs exert through their related genes. (ii) Computation of exponentially increasing SNP interactions: when the PRS model considers SNP interactive effects as input data, the number of variables increases exponentially, resulting in enormous computational complexity. Moreover, SNP interactions extend to higher orders. Although utilizing the synergistic effects of more SNPs helps in the more precise AD risk assessment, calculating the effect size becomes more exponentially complex. (iii) Integration of multiple SNP effects: by including not only independent effects of SNPs but also phenotypic and genomic interactive effects in the PRS model, AD risk can be calculated from a comprehensive perspective. At this time, the impact of each effect on AD may not be the same. Therefore, when utilizing various effects in an integrated manner, it is necessary to assign different weights rather than simple merging, which suggests that the PRS model should derive optimized weights for each effect.To overcome the aforementioned challenges, we propose a novel method, SNP interaction aware network-based polygenic risk score, for AD risk assessment. As shown in Fig. 1 , the proposed method consists of two stages: SNP interaction network construction and network-based polygenic risk score (NetPRS). In the first stage, the proposed method quantifies not only the phenotypic interactions by the epistasis test as Fig. 1 (a) but also the genomic interactions between SNPs as Fig. 1(b) . By applying SNP-gene relations to gene-gene interactions (GGIs), we consider the indirect genomic interactions between SNPs that can occur through GGIs. This approach is not limited to simply counting the number of shared genes, but also quantifies the genomic SNP interactions that comprehensively reflect the properties of GGIs. The quantified SNP interactions are represented as individual networks. In the second step, NetPRS derives interactive effects between SNPs based on the constructed networks and integrates all effects to predict AD risk. To implement this process, NetPRS consists of network propagation, effect combination, and risk prediction, which execute sequentially. The first function, network propagation, extracts the phenotypic and genomic interactive effects based on the constructed two networks. Fig. 1(c ) shows that each interactive effect is obtained by diffusing the independent effect throughout each network, so that NetPRS involves the global interactions between SNPs. Additionally, the intensity of diffusion is controlled by the smoothness parameter, which is trainable. As the smoothness decreases, interactions between close SNPs are highlighted, and as the smoothness increases, even interactions between distant SNPs are reflected. Therefore, NetPRS can scale SNP interactions to infinite-order that are differentially reflected by order. Next, the second function, effect integration, combines three effects into the integrated effect, as shown in Fig. 1(d ). The integrated effect is represented by the linear combination of all effects. Combining coefficient for each effect indicates the ratio of each effect reflected in the integrated effect. The coefficients are optimized through model training, and three effects differently contribute to the best AD risk assessment. In Fig. 1 (e), the third function, risk prediction, receives the integrated effect as input data and calculates individual AD risk, as depicted. Finally, the proposed method is summarized as the individual AD risk assessment by utilizing the independent effect and the phenotypic and genomic interactive effects applying global interactions between SNPs.To quantify the phenotypic SNP interactions, we perform the epistasis test using a GWAS tool, PLINK [23] . The epistasis test involves applying a logistic regression model to categorize case and control groups according to allele dosage from two SNPs, denoted as and , in the following manner:EQUATIONwhere represents the control group if it takes the value of 0 and the case group if it takes 1. The interaction between and is calculated by the odds ratio, denoted as , which is derived from the coefficients of the model in (1) , and specifically, it focuses on the coefficient for the interaction. If the value of is 1, it indicates that there is no interaction between and . The further the value deviates from 1, the stronger the interaction between and . In alignment with this concept, is transformed by the function , which converts its value into a measure of similarity between SNPs, as below.( ) = | | + 1Then, the phenotypic interaction between and is calculated as = , and this procedure is applied to every pair of SNPs. At last, after thresholding the interactions according to their significance, the phenotypic interaction network × is constructed, where is the number of SNPs.The genomic interaction network, denoted as × , is constructed by combining the SNP-gene relation ( × ) with the GGI network ( × ), where is the number of genes. Denoting as the genomic interaction from to , indicates the effect for -related genes ( × ) on -related genes ( × ) through GGI.× for the effect of on GGI, the objective function for is defined by applying graph-based semi-supervised learning (GSSL) [24] as follows:EQUATIONwhere is the graph Laplacian matrix defined as = , = diag( ) and = , and is a hyperparameter. The solution of ( 2) is obtained in the closed form asEQUATION)Therefrom, is derived by = , and then, its value is transformed by the function with a scaling parameter as below.( ) = / Consequently, the genomic interaction from to is calculated as = , and this procedure is applied to every pair of SNPs. Finally, the genomic interaction network × is constructed by thresholding the interactions according to their values.NetPRS consists of three functions: network propagation, effect integration, and risk prediction. First, the network propagation extracts the SNP interactive effects by applying the independent effect to the phenotypic and genomic interaction networks. Second, the effect integration linearly combines the independent effect and the extracted phenotypic and genomic interactive effects into the integrated effect. Finally, the risk prediction calculates individual AD risk by applying parameters for SNP effect size to the integrated effect. As shown in Fig. 2 , NetPRS is an end-to-end model designed with a neural network structure.Let the data matrix of the SNP independent effect be denoted as × , indicating the genotype of subjects, where is the number of subjects. To extract the interactive effects based on the phenotypic and genomic interaction networks, which are denoted as and , respectively, GSSL is applied to propagate through each network.Similar to (2), the objective function for is defined as, follows:min ( ) ( ) +where is the graph Laplacian matrix from , and is the trainable smoothness parameter that trades off the loss (the first term) and the smoothness (the second term). In the same manner in (3), the phenotypic and genomic interactive effects between SNPs are obtained as below.EQUATIONThe SNP independent effect and the two extracted interactive effects are represented as the integrated effect through a linear combination. The combining coefficients for , , and are denoted as , , and , respectively. These coefficients are transformed into the combining ratio, represented as , , and , using the softmax function.This transformation aims to prevent the problem of combining coefficients turning from negative during the model training. Then, is derived by linearly combining each effect with its ratio by representing as same as .EQUATIONFinally, individual AD risk is calculated by applying the integrated effect to the coefficient vector, which is denoted as × , indicating the SNP effect size. Since PRS provides disease risk in the form of probability, NetPRS employs a logistic classifier to assess individual AD risk.= 1 1 + × D.As shown in Fig. 2 , NetPRS contains a total of six parameters: { , } for network propagation, { , , } for effect combination, and for risk prediction. By denoting the actual diagnosis as × indicating whether AD or not as 1 or 0, respectively, the parameters are trained to minimize the cross-entropy loss between and as below.= 1 ( log + ( ) log( ))Then, the objective function of NetPRS is defined as follows:EQUATIONwhere is the L2 regularizer with the coefficient . The objective function is optimized by the gradient descent method.Minimization over : the gradient with respect to is obtained by differentiating the objective function in (6) by .= 1 ( ) + 2Minimization over : to find the gradient of , the derivative of with respect to is firstly obtained according to the derivative of the softmax function as below: Fig. 2 . Schematic structure of NetPRS. Network propagation extracts the interactive effect between SNPs by diffusing the independent effect to the SNP interaction network. The intensity of diffusion is controlled by the smoothness parameter, which is denoted as and for the phenotypic and genetic interaction network, respectively. Effect integration linearly combines the independent effect and the two interactive effects into the integrated effect. Combining coefficients, denoted as , , and for each effect, are parameters of effect integration and are converted to probability form to determine the ratio of each effect in the integrated effect. Risk prediction calculates individual AD risk by applying the integrated effect to the SNP effect size parameter . The structure of NetPRS is an end-to-end neural network.= ( 1), , = ,where { , , } is equivalent to the permutation of { , , }. Then, by (7) , the derivative of with respect to is represented as follows.(1 ) = ( )Therefrom, the gradient of is derived by combining with (8).Minimization over : to find the gradient with respect to , the derivative of with respect to is firstly obtained as below:EQUATION)By replacing ( + ) with for the brief description, ( 9) is derived according to the derivative of an inverse matrix [25] as follows:EQUATION)Therefrom, the gradient of is obtained by combining with (10) .Tr ( ) + 2As delineated in Table I , three types of data were utilized in this study. We firstly collected two genotype datasets from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the Biobank Innovations for chronic Cerebrovascular disease With Alzheimer's disease Study (BICWALZS) at Ajou University Hospital (Suwon, Republic of Korea) [26] . A total of 1,175 participants were included in the ADNI dataset, with 669,629 SNPs genotyped using the Illumina Omni 2.5M BeadChip, while the BICWALZS dataset comprised 724 participants, with 827,783 SNPs genotyped using the KoreanChip, which was designed for genomic research within the Korean population [27] . We also collected the data of approximately 334 million SNP-gene relations and approximately 6 million GGIs from the dbSNP [28] and STRING [29] , respectively. In addition, we divided the participants of the two datasets into the discovery and validation cohorts for the independent validation of the proposed method. In the ADNI dataset, the discovery and validation cohorts consisted of 765 participants from ADNI 2 and 410 participants from ADNI 1/GO, respectively. In the BICWALZS dataset, 547 participants recruited between 2016 and 2019 were included in the discovery cohort comprised, and the validation cohort contained 177 participants recruited between 2020 and 2021. Table II provides the demographic characteristics of study participants by cohorts.We performed quality control (QC) according to the following criteria [30] : genotyping rate >0.99, Hardy-Weinberg Equilibrium P >1E 6, and minor allele frequency >5%. In addition, Linkage Disequilibrium pruning was performed with thresholds (window size: 50, step size: 5, and R 2 threshold: 0.3). There were 583,526 and 399,129 SNPs that passed QC for the ADNI and BICWALZS datasets, respectively. Subsequently, we evaluated the statistical significance of QC-passed SNPs through GWAS and divided SNPs into three levels according to their P values. In the ADNI dataset, 974 SNPs were screened at level 1, 130 SNPs at level 2, and 15 SNPs at level 3; in the BICWALZS dataset, 420, 63, and 13 SNPs were screened at levels 1, 2, and 3, respectively.Then, we constructed the phenotypic and genomic interaction networks for each level of SNPs, where the phenotypic interactions between SNPs were measured by the epistasis test and selected by P-value of 0.05, while the genomic interactions between SNPs were measured by (3) with the smoothness of 1 and selected by the elbow point of 5.35×10 -5 . Table III presents the summarized results for the constructed SNP interaction networks. The average density across all networks was 4.2%, with the phenotypic interaction network having an average density of 4.4%, which is 10.5% higher than that of the genomic interaction network of 3.9%. Comparing two types of networks, there were common edges in level 1 and level 2, and their correlation coefficients for edge weights indicated an average of 0.0962 for level 1 and 0.6755 for level 2, but the distributions of common edges were revealed to be statistically different by the Kolmogorov-Smirnov test, suggesting that the two types of networks represent distinct patterns of SNP interactions.The proposed method was applied to all levels of SNP datasets. and were initially set to 1 and 0, respectively. NetPRS was trained with a learning rate of 0.01 using ADAM optimizer [31] . By measuring the area under the receiving operating characteristic curve (AUC), the performance of NetPRS was compared with the six existing methods: wPRS [8], PRSice2 [32] , EBPRS [33] , ERS [17] , PRSi [34] , and hiPRS [35] , where the initial three methods employed the independent effects of SNPs, whereas the subsequent three methods utilized the epistatic SNP interaction, and the results are presented in Fig. 3 and the Appendix.Fig. 3 (a) compares the average of AUCs for AD prediction by applying each method on the ADNI and BICWALZS cohorts. The average of AUCs in all levels for NetPRS was 0.7272, which was an average of 16.4% higher than the comparison methods. NetPRS demonstrated the best performance at level 2, with levels 1 and 3 exhibiting comparatively lower performance. This pattern was also observed in methods based on the epistatic SNP interactions (ERS, PRSi, and hiPRS), while methods based on SNP independent effects (wPRS, PRSice2, and EBPRS) typically yielded the best performance at level 3, followed by levels 1 and 2. As a result, the independent effect-based PRS models demonstrated superior performance as more significant SNPs for AD were screened, while the interactive effect-based PRS models necessitated a data-specific threshold of significance level for the best outcomes; experimentally, the optimal performance was achieved using 0.02% of the number of QCpassed SNPs as the thresholding criteria.In addition, we conducted an ablation study to further investigate the contribution of the three effects included in the integrated effect on the performance of NetPRS. We designed six different models that train the combinatorically configured datasets for three effects: three models for the single effect ( , , and ) and other three models for the dual effects ( , , and). The experimental settings for those models were same as NetPRS (), and Fig. 3 (b) shows the results. The average of AUCs in all levels for NetPRS was the highest, followed by and with almost similar performance. The performance of was the lowest, but when combined with interactive effects ( and ), it improved by 3.4% on average. Among the interactive effects, outperformed , and when they were combined, derived 1.3% better prediction results than each. Overall, the performance was improved as the three effects were combined together. These results confirm that the interactions between SNPs are effective in predicting AD risk, and that it is more advantageous to consider not only the commonly used phenotypic interactive effects but also the newly proposed genomic interactive effect.To interpret the proposed method, we conducted the statistical and explanatory analyses on NetPRS in level 2, which was the most accurate. First, we compared the statistical significance of the independent effect ( ) and the combined effect ( ) for the AD-positive and AD-negative groups. Fig. 4 (a) represents the comparison results on P-values of and , denoted as PX and P Z , respectively. A point in the scatter plot above the diagonal line means that the SNP effect values on the vertical axis is more significant. As the plot illustrates, the majority of the dots are situated above the diagonal line, indicating that is more effective than in the assessment of AD risk, where was identified as a more significant than for 107 out of 130 SNPs in the ADNI dataset and 46 out of 63 SNPs in the BICWALZS dataset, representing 79.3% of the total. The results of the statistical analysis also presented that the combined effect of NetPRS demonstrated a 33.8% greater capacity to discriminate AD patients than the independent effect on average. Next, in the explanatory analysis, we identified the impact of SNPs in the combined effect by applying SHapley Additive exPlanations (SHAP) [36] . Fig. 4 (b) shows the group-wise comparison of SHAP values for the top-10 most significant SNPs, denoted as key SNPs, in the ADNI and BICWALZS datasets. The SNP with the highest impact on AD risk was rs429358, which is related to APOE, followed by rs78953543, which is associated with CDH2 that has been identified to -amyloid-triggered synapse damage [37] . Moreover, there were two common key SNPs, rs4420638 and rs2075650, that are associated with APOE-neighboring genes, APOC1 and TOMM40, respectively, which are significantly related to AD risk [38] . The key SNPs associated with ANKH, EPHB1, and NECTIN2 which are implicated in AD pathogenesis [39] [40] [41] , also showed high impacts on predicting AD risk by NetPRS.As a result, in AD risk assessment, the combined effect of SNPs by NetPRS was more effective than the independent effect of SNPs in distinguishing AD patients with greater clarity, with the impact of the identified key SNPs aligning with the previous clinical studies. Our findings suggest that the combined effect represents the collective influences of SNPs through their interactions, encompassing the comprehensive information on the phenotypic and genomic interactions.V. CONCLUSION In this study, we propose a novel method, NetPRS, for AD risk assessment by utilizing the interactive effects between SNPs. The pronouncing features of NetPRS are summarized in three points. First, NetPRS quantifies the interactions that SNPs can exert through their related genes and GGIs. These genomic interactions provide comprehensive information on the SNP interactions along with the existing epistatic effects. Second, NetPRS derives the global interactive effect from the SNP networks. By propagating the independent effect through the networks, NetPRS extracts the effects arising from infinite-order interactions. This approach significantly improves computational complexity compared to methods that use combinations of SNPs as variables. Third, NetPRS integrates various SNP effects to assess AD risk. In this process, the optimal integrating ratio of each effect is derived for the most accurate prediction. The proposed method provides an intuitive interpretation for output results by linearly combining each effect without non-linear transformation. Experimental results showed that learning both phenotypic and genomic interactive effects together with the independent effect yielded the most accurate AD risk assessment. Several analyses for the model interpretation confirmed that the advantage of NetPRS results from that the combined effect differentiates AD groups more clearly and reflects the genetic combinations significantly affecting AD pathogenesis.Here are some remarks on the proposed method. First, it is possible that a more optimized construction of SNP interaction network may improve the utility of NetPRS. The computational burden associated with fitting logistic models to every pair of SNPs becomes significantly more demanding as the number of SNPs increases. Although this issue was mitigated by a pre-filtering process that employed statistical significance testing of SNPs through GWAS, future work will concentrate on the optimization of NetPRS through the use of graphical models, as well as the identification of the optimal P-value threshold for SNPs during the training process, beyond the current empirical search. Second, the integration of biological domain knowledge has the potential to enhance the validity of NetPRS. Further validation across multiple databases, along with expansion to other channels such as DNA and RNA in addition to genes, will facilitate a more sophisticated representation of genomic interactions between SNPs. Therefrom, a follow-up model for NetPRS is currently under development, which applies the biologically-informed clustering, with the expectation of providing further clarification regarding the impact of SNPs and those interactions on the AD risk.  
 
 Appendix:  



Reviews: review: title: title: The novel method incorporates SNP interaction networks into polygenic risk scoring.
paper_summary: paper_summary: The study presented a novel approach named Network-based Polygenic Risk Score (NetPRS) for estimating Alzheimer's disease risk. Most of the existing PRS models are based on the main effects of SNPs, while NetPRS considers both phenotypic and genomic SNP interactions. The method first builds SNP interaction networks and then extracts independent effects across these networks by a graph-based machine-learning model. This allows NetPRS to obtain global interactive effects between SNPs, which is then added to independent effects to estimate AD risk. The findings demonstrate that NetPRS achieves superior accuracy in risk estimation compared to standard PRS models.
strength_weakness: strength_weakness: 1. The model is relatively complex, and the computational cost of constructing and propagating the network makes it difficult to extend the analysis to larger datasets. 
2. The values for the smoothness parameter, p-value thresholds, and the number of SNPs are determined too subjectively. A more scientific approach to deciding these values is required.
3. The paper only focuses on Korean data but does not extensively explore the performance of NetPRS on external datasets or other ethnic groups.
questions: questions: 1. For the two SNP interaction networks, Phenotypic Interaction Network and Genomic Interaction Network, how do you interpret the values for the edges? Are there any meaningful statistics (e.g., marginal/conditional correlation) for the edge in the network structure?
2. When constructing the Phenotypic Interaction Network, fitting logistic regression for each pair of SNPs individually can become computationally intensive as the number of SNPs increases. Is there any way to deal with this problem? 
Also, alternative methods, such as Gaussian graphical models or graphical lasso, may offer more efficient approaches for network construction.
3. Why do you need to use data from dbSNP and STRING for the real data analysis? What specific information do these two databases provide in your experiment?
4. For the comparative analysis, although Level 3 shows the best performance, it has only two edges in both networks. Does a network with just two edges truly capture significant information? 
5. Based on the experiment, we observed that SNP thresholding significantly impacts model performance. How can we determine the appropriate number of SNPs for the analysis?
6. When calculating the PRS, it is important to account for Linkage Disequilibrium. Have you considered this in your model, or is there any part already addressing it?
title: title: NetPRS: SNP interaction aware network-based polygenic risk score for Alzheimer’s disease
paper_summary: paper_summary: The manuscript presents NetPRS, a novel polygenic risk score model for Alzheimer’s Disease (AD) that incorporates both phenotypic and genomic interactions between SNPs. Unlike traditional models that focus solely on independent SNP effects, NetPRS uses a two-stage approach to construct SNP interaction networks and predict AD risk. When evaluated on a Korean cohort, NetPRS demonstrates significant improvements in prediction accuracy compared to a conventional weighted-PRS model, attributed to its ability to capture complex SNP interactions. The manuscript also includes an explanatory analysis that highlights the contributions of individual SNPs, enhancing the interpretability of the model.
strength_weakness: strength_weakness: While the results on the Korean cohort are promising, the paper does not sufficiently address the potential limitations in generalizability. Given the significant variation in genetic architecture across populations, it is crucial to explore how the model might perform in diverse cohorts, particularly since Alzheimer’s disease risk factors can differ globally. If obtaining SNP data from other populations is challenging, the authors are recommended to conduct resampling tests on their validation cohort or use K-fold cross-validation to demonstrate the robustness of their model. Additionally, although the authors acknowledge the challenges of computational complexity, particularly with higher-order SNP interactions, the paper lacks a thorough comparison and detailed discussion of this issue. Furthermore, while the paper compares NetPRS with a conventional weighted PRS model, it does not provide a comparison with other state-of-the-art approaches that also consider SNP interactions, such as the method referenced in their introduction (Reference 17, DOI: https://doi.org/10.1186/s13195-021-00794-8). Including such comparisons would strengthen the argument for NetPRS and provide a more comprehensive evaluation of its effectiveness.
questions: questions: 1. How do the authors anticipate NetPRS performing in populations with different genetic profiles? Have the authors considered applying the model to diverse cohorts, or are there specific reasons for focusing solely on the Korean cohort?
2. In the explanatory analysis, the authors conclude that SNPs with a high impact on NetPRS exert their influence collectively through interactions, yet the discussion primarily focuses on the roles of these key SNPs at an individual level. Are there any results from this study or previous findings that support the collective impact of these SNPs? Could the authors provide further clarification or evidence for this statement?
title: title: NetPRS: SNP interaction aware network-based polygenic risk score for Alzheimer’s disease
paper_summary: paper_summary: The study develops a machine learning model using the independent and interactive effects of SNPs to generate a risk score for Alzheimer disease.
strength_weakness: strength_weakness: Some abbreviations are left unexplained such as SHAP and gene names and snp names makes it difficult to read the results section. Please explain them for a general audience.
questions: questions: I do not have any questions. If there is a public data set than the one used in the study adding its results like Figure 4a will improve the credibility of the model.