<i>Space-log</i>: a novel approach to inferring gene-gene net-works using SPACE model with log penalty

Qian (Vicky) Wu; Wei Sun; Li Hsu

doi:10.12688/f1000research.26128.2

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Method Article

Revised

Space-log: a novel approach to inferring gene-gene net-works using SPACE model with log penalty

[version 2; peer review: 2 approved, 1 approved with reservations]

Qian (Vicky) Wu ^1,2, Wei Sun², Li Hsu²

PUBLISHED 05 Jan 2022

Author details Author details

¹ Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, WA, 98109, USA
² Public Health Division, Fred Hutchinson Cancer Research Center, Seattle, WA, 98109, USA

Qian (Vicky) Wu
Roles: Conceptualization, Data Curation, Formal Analysis, Methodology, Software, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing

Wei Sun
Roles: Conceptualization, Data Curation, Methodology, Software, Writing – Review & Editing

Li Hsu
Roles: Conceptualization, Funding Acquisition, Methodology, Supervision, Writing – Review & Editing

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Abstract

Gene expression data have been used to infer gene-gene networks (GGN) where an edge between two genes implies the conditional dependence of these two genes given all the other genes. Such gene-gene networks are of-ten referred to as gene regulatory networks since it may reveal expression regulation. Most of existing methods for identifying GGN employ penalized regression with L1 (lasso), L2 (ridge), or elastic net penalty, which spans the range of L1 to L2 penalty. However, for high dimensional gene expression data, a penalty that spans the range of L0 and L1 penalty, such as the log penalty, is often needed for variable selection consistency. Thus, we develop a novel method that em-ploys log penalty within the framework of an earlier network identification method space (Sparse PArtial Correlation Estimation), and implement it into a R package space-log. We show that the space-log is computationally efficient (source code implemented in C), and has good performance comparing with other methods, particularly for networks with hubs.Space-log is open source and available at GitHub, https://github.com/wuqian77/SpaceLog

Keywords

Gene-gene network, gene regulation, penalized regression, log penalty, partial correlation, R package, algorithm

Corresponding authors: Qian (Vicky) Wu, Li Hsu

Competing interests: No competing interests were disclosed.

Grant information: This research is supported by National Institutes of Health grant R01 CA189532.

Copyright: © 2022 Wu Q( et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite: Wu Q(, Sun W and Hsu L. Space-log: a novel approach to inferring gene-gene net-works using SPACE model with log penalty [version 2; peer review: 2 approved, 1 approved with reservations]. F1000Research 2022, 9:1159 (https://doi.org/10.12688/f1000research.26128.2) First published: 21 Sep 2020, 9:1159 (https://doi.org/10.12688/f1000research.26128.1) Latest published: 05 Jan 2022, 9:1159 (https://doi.org/10.12688/f1000research.26128.2)

Revised Amendments from Version 1

Updated background, and added discussion on run-time with a new table.

See the authors' detailed response to the review by Jessie Jeng
See the authors' detailed response to the review by Yuying Xie and Yuning Hao

Introduction

Complex diseases, such as colorectal cancer (CRC), are caused by a combination of genetic, environmental and lifestyle factors, most of which have not yet been identified and explained. In the era of precision medicine, human genome project, especially breakthroughs in high throughput technologies, provides information based on patient’s genetic and genomic data and have changed how researchers explain complex disease through personalized profiles. There is an urgent need to develop efficient statistical and computational tools to integrating genetic and genomic data to identify their contributions to complex diseases, such as gene expression and genetic regulatory networks. Analysis of gene expression data has led to the identification of novel disease-causing gene networks¹, thus contributing important new insights into understanding of these complex diseases. The objective of this paper is to introduce a novel method that constructs gene-gene network (GGN) based on high dimensional gene expression data. Popular methods for GGN include neighborhood selection², graphical Lasso³, and space (Sparse PArtial Correlation Estimation)⁴. Neighborhood selection consistently estimates the non-zero entries of the partial correlation matrix, and provide an approximation of the maximum likelihood estimate of partial correlation matrix. Graphical Lasso improves on neighborhood selection by providing a maximum likelihood estimate of the partial correlation matrix. The space method exploits the symmetry of partial correlation matrix to improve the estimation accuracy. It also avoids potential conflicts in neighborhood selection, that is, Y_i is selected as a neighbor of Y_j but Y_j is not selected as a neighbor of Y_i, and one has to make a post-hoc decision for whether Y_i and Y_j are connected. Furthermore, those available methods employ L₁, L₂ or elastic net penalty. However, penalties in the range of L₀ to L₁ is often needed to improve the accuracy of variable selection for high-dimensional gene expression data⁵. In this paper, we propose a new statistical method to estimate GGN by implementing the log penalty for the space approach, which enhances sparsity by reweighted L₁ minimization, and we refer to our method as space-log.

We compared space-log with the space algorithm through extensive simulations, as well as the comparison with neighborhood selection methods using lasso or log penalty below. Peng et al. (2009)⁴ have compared the space approach with gLasso and showed space outperformed gLasso in different simulation settings, thus we didn’t include gLasso methods in our simulation studies here.

Methods

Suppose that we have data on n independent individuals and m genes. Assume the expression of m genes, after appropriate normalization, follow a multivariate Gaussian distribution N(0, ∑).

Neighborhood selection using lasso or log penalty: `NS-lasso, NS-log`

The neighborhood selection (NS) approach considers each gene separately. Let Y_i be the gene expression value for the ith gene and Y_−i = (Y₁, ..., Y_i−1, Y_i₊₁, Y_m)^T . For the NS approach, Y_i is regressed on Y_-i by a penalized regression:

\hat{β} = argmin {\frac{1}{2} {(Y_{i} - Y_{- i} β)}^{T} (Y_{i} - Y_{- i} β) + n \sum_{i \neq j} p (| β_{i, j} |; ω)} (1)

with penalty function $p (| β |; ω) .$ We will compare NS-lasso with lasso penalty $p (| β |; λ) = λ | β |$ ⁶ and NS-log with log penalty $p (| β |; λ, τ) = λ log (| β | + τ)$ ^7,8. Source codes of NS-lasso and NS-log are available at https://github.com/Sun-lab/penalized_estimation/.

Joint modeling `space` using lasso penalty: `space-lasso`

The joint modeling approach space³ is to estimate GGN, without the need to fit many (m) single gene regression models separately, but directly estimate partial correlation among all the genes. Denote the partial correlation between Y_i and Y_j by ρ_i,j. If we know the concentration matrix ∑⁻¹ = (σ^ij)_m×m, then $ρ_{i, j} = - \frac{σ^{i j}}{\sqrt{σ^{i i} σ^{j j}}} .$ Given $β_{i j} = - \frac{σ^{i j}}{σ^{i i}}$ , we can easily get that $ρ_{i, j} = sign (β_{i, j}) \sqrt{β_{i, j} β_{j, i}}$ . Thus, the problem is translated into partial correlation matrix estimation. Specifically⁴, proposed to minimize a penalized loss function

L_{n} (β, σ, Y) = \frac{1}{2} \sum_{i = 1}^{m} w_{i} {‖ Y_{i} - \sum_{j \neq i} β_{i j} Y_{j} ‖}^{2} + \sum_{i \neq j} p (| ρ_{i, j}; λ |) (2)

= \frac{1}{2} {\sum_{i = 1}^{m} w_{i} ‖ Y_{i} - \sum_{j \neq i} ρ_{i j} \sqrt{\frac{σ^{j j}}{σ^{i i}}} Y_{j} ‖}^{2} + \sum_{i \neq j} p (| ρ_{i, j}; λ |) (3)

where w_i ≥ 0 is the weight, e.g., uniform weights w_i = 1 for space-no, residual variance based weights w_i = σ_jj for space-res, and degree based weights w_i = number of genes that {j : ρ_i,j ≠ 0, j ≠ i} for space-df. In Peng et al. (2009)4, p(|ρ|; λ) = λ|ρ| and we call it as space-lasso.

New algorithm `space-log`: joint modeling space using log penalty

Inspired by Sun et al. (2010)⁷ and Ha et al. (2016)⁸, we extended the space approach with log penalty as space-log p(|ρ|; λ, τ) = λlog(|ρ| + τ) and used the active shooting algorithm⁴ to update the coefficient estimates iteratively in space-log (Supplementary Materials). We determined the tuning parameters by using extended BIC (extBIC)⁹.

Denote the target loss function as

\begin{array}{l} f (ρ; σ) = \frac{1}{2} \sum_{i = 1}^{m} w_{i} {‖ Y_{i} - \sum_{j \neq i} ρ_{i j} \sqrt{\frac{σ^{j j}}{σ^{i i}}} Y_{j} ‖}^{2} + \sum_{i \neq j} p (| ρ_{i, j} |; τ, λ) \\ = \frac{1}{2} \sum_{i = 1}^{m} w_{i} {‖ Y_{i} - \sum_{j \neq i} ρ_{i j} \sqrt{\frac{σ^{j j}}{σ^{i i}}} Y_{j} ‖}^{2} + λ \sum_{i \neq j} \log (| ρ_{i, j} | + τ) (4) \end{array}

The goal is to estimate $\hat{ρ}$ = argmin_ρf(ρ) for a given λ and τ. We implement the penalized estimation using space and Log penalties by Local Linear Approximation (LLA)¹⁰.

p (| ρ_{i, j}; λ, τ |) \approx p (| {\hat{ρ}}_{i, j}^{(k)} |; λ, τ) + p^{'} (| {\hat{ρ}}_{i, j}^{(k)} |; λ, τ) (| ρ_{i, j} | - | {\hat{ρ}}_{i, j}^{(k)} |) (5)

where $| {\hat{ρ}}_{i, j}^{(k)} |$ is the estimate of regression coefficient ρ_i,j at the k-th iteration. After applying LLA for the penalty part, we can minimize loss function at the (k + 1)-th step, while solving for ρ_i,j by

\begin{array}{l} f^{(k + 1)} (ρ_{i, j}) = \frac{1}{2} \sum_{i = 1}^{m} w_{i} {‖ Y_{i} - ρ_{i, j} \sqrt{\frac{σ^{j j}}{σ^{i i}}} Y_{j} - \sum_{l \neq i; l \neq j} {\hat{ρ}}_{i, l}^{(k)} \sqrt{\frac{{\hat{σ}}_{(k)}^{l l}}{{\hat{σ}}_{(k)}^{i i}}} Y_{l} ‖}^{2} \\ + \sum_{i \neq j} p^{'} (| {\hat{ρ}}_{i, j}^{(k)} |; λ, τ) | ρ_{i, j} | (6) \end{array}

By letting $\partial f^{(k + 1)} (ρ_{i, j}) / \partial ρ_{i, j} = 0,$ we can find the solution for ρ_i,j as follows:

{\hat{ρ}}_{i, j}^{(k + 1)} = {\begin{array}{l} 0 & if | z_{j}^{(k)} | \leq v_{j}^{- 1} p^{'} (| {\hat{ρ}}_{i, j}^{(k)} |; λ, τ) \\ s g n ({\hat{ρ}}_{i, j}^{(k)}) [| z_{j}^{(k)} | - v_{j}^{- 1} p^{'} (| {\hat{ρ}}_{i, j}^{(k)} |; λ, τ)] & if | z_{j}^{(k)} | > v_{j}^{- 1} p^{'} (| {\hat{ρ}}_{i, j}^{(k)} |; λ, τ) \end{array} (7)

where $z_{j}^{(k)} = Y_{j} (Y_{i} - \sum_{l \neq i; l \neq j} {\hat{ρ}}_{i, l}^{(k)} \sqrt{\frac{{\hat{σ}}_{(k)}^{l l}}{{\hat{σ}}_{(k)}^{i i}}} Y_{l}) / V_{j}, V_{j} = Y_{j}^{T} Y_{j},$ and $p^{'} (| {\hat{ρ}}_{i, j}^{(k)} |; λ, τ) = s g n ({\hat{ρ}}_{i, j}^{(k)}) \frac{λ}{| {\hat{ρ}}_{i, j}^{(k)} | + τ} .$

Active-shooting

We adapted the same idea active-shooting algorithm from 4 to update the coefficient estimation iteratively in space-log. Without loss of generality, we kept most notation from 4 but tailored with space-log. The details are included in the Supplementary Materials.

Simulation studies

In this section, we present Monte Carlo simulation to evaluate the performance of the space-log, space-lasso, NS-log, and NS-lasso. Following⁸, we studied two types of graphs: the traditional random graphs (ER model) where all the genes have the same expected number of neighbors^11,12, and hubs graphs where a few genes may have a large number of neighbors (BA model), and BA model is more frequently observed in gene networks¹³.

We simulated GGN of m genes under both the BA and ER models, respectively. The initial graph had one gene and no edge. In the (k+1)th step, we added e edges between a new gene and e old genes. Under the BA model, there is a greater probability for the new gene to connect to an existing hub gene that has larger number of edges with the probability $p_{E} = v_{i}^{(t)} / \sum_{j} v_{j}^{(t)},$ where $v_{i}^{(t)}$ number of edges connected with the ith gene at the tth step. For the ER model, each edge of any gene pair (G_i, G_j) was added randomly in the GGN with probability p_E independent from all other edges. After constructing the bone of GGN, we simulated gene expression based on multivariate Gaussian. Without loss of generality, we simulated data sets with n = 400 individuals, which is similar to the sample size in our real data examples. As shown in Table 1, we considered different number of genes m = 100, 200, 300 with various sparsity level determined by p_E = 1=m or 2=m for the ER model and e = 1 or e = 2 for the BA model.

Table 1. Simulation settings.

m	n	p_E (ER)	e (BA)
400	100	1/100, 2/100	1,2
400	200	1/200, 2/200	1,2
400	300	1/300, 2/300	1,2

We evaluated the performance of the methods by the following metrics: number of false positives (FP), false negatives (FN), FP+FN, F1 score, FDR, true positive rate (power). Note that there are three different weights used in joint modeling setting (space-log, space-lasso): (1) uniform weights; (2) residual variance based weights; and (3) degree freedom based weights. The corresponding methods are referred to as sp_no, sp_res, and sp_df with/without log respectively.

Under the BA model with m=100 and e=1 (Figure 1), we can see that space-log has smallest Errors (FP+FN), smallest FDR, and highest F1 score than other approaches, indicating that space-log controls overall false positive and false negative rates well. Under the ER model (Figure 2) with m=100 and e=1, space-log is slightly better than space, and NS-log shows lower Errors and higher F1 score than other approaches including space-log. Under both models, the log penalty has less false positives but slightly more false negatives compared to lasso penalty. We note that although log penalty performs well for both the ER and BA models, space-log is particularly powerful in identifying hub networks (such as BA models).

Figure 1. BA with 100 genes and e=1.

Figure 2. ER with 100 genes and e=1.

In the Extended data, Figures S3 and S4 show the results under the BA model for m=100,200,300 with low number of connections (e=1) and high number of connections (e=2), respectively. Figures S5 and S6 show the results under the ER model with low and high numbers of connections, respectively. Comparing with Figure 1, a similar pattern was noted with the increase of number of genes (m increases from 100, 200, to 300). In BA with low connections (Figure S3), space-log showed smallest FP+FN error and largest F1 score, which outperform all other methods. In BA with high connections (Figure S4), NS-log showed smallest FP+FN error and largest F1 score. For ER model with low and high connections, NS-log outperforms other methods in terms of FP+FN and F1 scores. It’s in line with our understanding that space-log is powerful at identifying hubs network, and NS-log is powerful at dealing with complex network with high number of gene-gene interactions and random networks.

We showed a simulated graph for the BA model with 400 subjects, 100 genes and each gene has only 1 connection (Figure 3). The GGN was estimated by 8 different approaches. In Figure 3, the true edges were indicated by black color, false positive (FP) edges by red color, and false negative (FN) edges by grey color. It’s clear that space-log identified far fewer false positive edges (red line) comparing with space-lasso and NS approaches, while clearly indicating the hub structures. We observed that the FP edges by two NS approaches were quite randomly identified, and the FP edges by two space approaches were mostly within a hub and not between hubs.

Figure 3. A simulated graph for the BA model with 100 genes (e=1) and multiple hubs.

A total of 400 subjects were generated. The GGN was estimated by 8 different approaches. Black is true edges, red is false positive edges, and grey is false negative edges.

We also compared the run-time under different simulation scenarios in Figure S7 and Table 2 under the BA model and low number of connections (e=1). Here the computing time for the space with no weight is presented. The computational time of the methods using log penalty is higher than that using lasso penalty, and the computational time for the space methods is much less than NS methods. Similar to what was observed in 8, the runtime increases approximately linearly with m. The difference of the run-time between the ER and BA model, the low and high numbers of connections or different weights of space methods are not significant (Figure S7).

Table 2. Computational time in minutes with median (range) under the BA model with e=1 and n=400.

Methods	m=100	m=200	m=300
NS-lasso	6 (0.04, 8)	13 (0.2, 19)	20 (0.6, 30)
NS-log	71 (0.6, 94)	142 (3, 190)	226 (8, 293)
space	0.81 (0.1, 2,2)	2 (0.5, 3.3)	3 (1.1, 9)
space-log	9 (0.7,18)	16 (2.4, 27)	23 (5, 45)

In summary, the log penalty generally has better performance than the lasso penalty, and both space-log and NS-log control false positive and false negative rate well. For random networks, i.e., no hub, NS-log performs better than other methods. space-log performs best for hub-like gene networks (Figure 1 and Figure 3) with higher F1 score and less false positive edges. Identifying hub networks is generally considered of great interest in the GGN analysis, because a few of hubs connecting with a large proportion of genes, and those hub genes are thought to be master regulators and play a critical role in a biological system¹⁴.

Application to GTEx and TCGA data

TCGA data

We applied both proposed space-log and existing methods (space-lasso, NS-log, and NS-lasso) to identify GGN using RNA-seq data from tumor tissue of 550 TCGA (The Cancer Genome Atlas) Colon Adenocarcinoma (TCGA-COAD) cancer patients¹⁵. The preprocessing steps of RNA-seq data included: (1) transforming the expression of each gene by log(total read count) = logTReC (2) removing the confounding effects by taking residuals of logTReC from a linear regression with the following covariates: 75% of logTReC per sample (which captures read depth), plate, institution, age, and six PCs from the corresponding germline genotype data. After removing genes with low expression across most samples, we had 18,238 genes and 450 samples.

We considered gene sets C6 curated oncogenic pathways by MSigDB from the Broad Institute and inferred the GGN within each gene set. There were 189 gene pathways with a total of 8,737 unique genes for which TCGA have expression data. The sizes of gene sets ranged from 9 to 338 genes. Since we don’t know the true GGN, we downloaded the common pathway version 10 from www.pathwaycommons.org to provide a partial "gold standard". The observed GGN by different methods were compared with the known edges from common pathway and calculated FP, FN, FP+FN, number of total discovery, F1 score, and true positive rate (Figure 4). The NS-based approach with both LASSO and log penalty discovered much more edges than space-based approach and space-log had fewer false positive (fewer FN+FP too) than space-lasso. There is almost no difference on number of false negative between different methods, as well as F1 score (Figure 4). Furthermore, in order to show the performance of these methods on the hub networks, we identified 17 pathways with hub-like genes (each hub gene set has < 50 genes and variance of the number of identified edges for each gene in the gene set > the first quartile of all 189 gene sets) and re-calculated the summary metrics in Figure 5. We noted that space-log approach has smallest Errors and slightly higher F1 than other approaches, which is in line with our finding in simulation that space-log is powerful in identifying hub networks, (such as BA models).

Figure 4. TCGA data analysis with ALL 189 Gene Sets.

Figure 5. TCGA data analysis with BA hub-type Gene Sets.

To further understand whether our proposed methods can better handle high dimensional data with larger number of genes, we generated k=71 larger network by combining gene sets with overlapping genes. The sizes of this new larger gene sets list ranged from 476 to 1253 genes, which is larger than the sample size n=450 (m > n). We applied space-log, space-lasso, NS-log, and NS-lasso approaches on this new larger list, and calculated similar metrics (FP, FN, FP+FN, etc in Figure S8). Comparing with TCGA data with smaller gene sets (Figure 4 and Figure 5), we observed that the NS-based approach with both lasso and log penalty discovered much more false positive edges than space-based approaches for this new larger gene sets setting, which is consistent with our finding in simulation that NS-based approach has more false positive in general.

GTEx data

The Genotype Tissue Expression (GTEx) project¹⁶ aims to study tissue-specific gene expression and regulation in normal individuals. In this paper, we used gene expression data (RNA-seq) from blood tissue of 451 patients to identify GGN. We pre-processed gene expression data using the same procedure as for TCGA data. We mapped genes to gene pathways by MSigDB (https://www.gsea-msigdb.org/gsea/msigdb/index.jsp). A total of 189 gene pathways were represented with a total of 8097 unique genes. The size of gene sets ranged from 8 to 306 genes.

Again, we applied space-log, space-lasso, NS-log, and NS-lasso approaches to identify GGN. Using the same common pathway file used for the TCGA analysis as gold standard, we calculated FP, FN, FP+FN, # of discovery, F1, TPR (Figure 6). We obtained very similar results to the TCGA data. The NS-based approach with both LASSO and log penalty discovered much more edges than the space-based approach and space-log has fewer false positive (fewer FN+FP too) than space-lasso. There is almost no difference in the number of false negative between different methods, as well as F1 score. A similar sensitivity analysis was conducted to a subset of hub-type genes (Figure 7), where 30 pathways were selected to be in the first quartile of the variance of the number of identified genes with < 50. It also showed the space-log approach has smallest Errors (F1 is similar to other approaches).

Figure 6. GTEx data analysis with ALL 189 Gene Sets.

Figure 7. GTEx data analysis with BA hub-type Gene Sets.

Conclusions

In this paper, we proposed a new joint modeling method with log penalty, space-log, to identify gene-gene network. An assumption of the GGN analysis is that most of gene pairs do not directly interact with each other, and there are a few of master genes (hubs) for network that connect with many other genes, which are thought to play a critical role in a biological system^1,14. Both simulation and real data analyses showed that space-log is particularly powerful in identifying hub networks and master genes, which is considered of great interest in gene-gene network analysis. In the Extended data, we compared several tuning parameter selection approaches, such as BIC Zou et al.¹⁷, extBIC^9,18, and oracle⁵, and showed that extBIC outperforms other methods in simulation. The R package "SpaceLog" on GitHub includes algorithms, simulation, and real data examples: https://github.com/wuqian77/SpaceLog.

Data availability

Underlying data

Simulation data. We used barabasi.game function from igraph R package to generate the skeleton of a BA model.

Source code, simulated data, and plots: https://github.com/wuqian77/SpaceLog/tree/master/Simulation.

TCGA data. The RNA-seq dataset from tumor tissue of 550 TCGA (The Cancer Genome Atlas) colon adenocarcinoma (TCGA-COAD) cancer patients¹⁵ can be downloaded from dbGap phs000178.v1.p1.: https://www.cancer.gov/about-nci/organization/ccg/research/structural-genomics/tcga.

Pre-processing and data analysis source code: https://github.com/wuqian77/SpaceLog/tree/ master/Analysis/TCGA.

GTex data. The RNA-seq dataset of blood tissue from the Genotype Tissue Expression (GTEx) project¹⁶ can be downloaded from dbGap Genotype-Tissue Expression Project and the study accession is phs000424.v7.p2.: https://www.gtexportal.org/home/datasets.

Pre-processing and data analysis source code: https://github.com/wuqian77/SpaceLog/tree/master/Analysis/GTex.

Extended data

Zenodo: SpaceLog: First release of spacelog, http://doi.org/10.5281/zenodo.4002931¹⁹.

This project contains the following extended data:

the detailed algorithm for active shooting;
simulation and figures on comparing methods to choose tuning parameters;
simulation and figures on comparing different GGN methods under various scenarios.

License: GPL-3

Software availability

Source code for space-log available from: https://github.com/wuqian77/SpaceLog

Archived source code as at time of publication: http://doi.org/10.5281/zenodo.4002931¹⁹.

License: GPL-3

Source code for NS-log and NS-lasso available from: https://github.com/Sun-lab/penalized_estimation

License: GPL-3

Existing methods space-lasso is available on R CRAN: https://cran.r-project.org/web/packages/space/index.html.

Faculty Opinions recommended

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Version 2

VERSION 2 PUBLISHED 21 Sep 2020

Author details Author details

¹ Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, WA, 98109, USA
² Public Health Division, Fred Hutchinson Cancer Research Center, Seattle, WA, 98109, USA

Qian (Vicky) Wu
Roles: Conceptualization, Data Curation, Formal Analysis, Methodology, Software, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing

Wei Sun
Roles: Conceptualization, Data Curation, Methodology, Software, Writing – Review & Editing

Li Hsu
Roles: Conceptualization, Funding Acquisition, Methodology, Supervision, Writing – Review & Editing

Competing interests

No competing interests were disclosed.

Grant information

This research is supported by National Institutes of Health grant R01 CA189532.

Article Versions (2)

version 2

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Published: 05 Jan 2022, 9:1159

https://doi.org/10.12688/f1000research.26128.2

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Wu Q(, Sun W and Hsu L. Space-log: a novel approach to inferring gene-gene net-works using SPACE model with log penalty [version 2; peer review: 2 approved, 1 approved with reservations]. F1000Research 2022, 9:1159 (https://doi.org/10.12688/f1000research.26128.2)

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Version 2

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PUBLISHED 05 Jan 2022

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Reviewer Report 20 Jan 2022

Jessie Jeng, Department of Statistics, North Carolina State University, Raleigh, NC, USA

Approved

https://doi.org/10.5256/f1000research.58701.r118658

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Reviewer Report 12 Jan 2022

Yuying Xie, Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA

Yuning Hao, Amazon, Seattle, WA, USA

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https://doi.org/10.5256/f1000research.58701.r118659

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Reviewer Report 21 Jun 2021

Jessie Jeng, Department of Statistics, North Carolina State University, Raleigh, NC, USA

Approved with Reservations

https://doi.org/10.5256/f1000research.28834.r86957

This paper considers the problem of identifying gene regulatory networks based on high-dimensional gene expression data. A new method, space-log, is introduced to perform penalized regression with a log penalty. The new method is compared with several existing methods in simulation and real applications using GTEx and TCGA data. The new method seems to outperform other methods in identifying networks with hubs and master genes.

The overall presentation is clear. However, several improvements can be made:

I think it would be important to explain why the proposed method has advantages in identifying networks with hubs. I would imagine that a network with hubs tends to have more diverse sparsity levels of association across different genes than a network without hubs. Is the proposed method with a log penalty more effective for such scenarios? Or there are other reasons?
The Introduction is a bit too short. I would suggest adding more biological background and a motivation from a real application point of view.
Some discussions on the computational complexity or a comparison of the computational times of different methods should be helpful.

Is the rationale for developing the new method (or application) clearly explained?

Partly
Is the description of the method technically sound?

Yes
Are sufficient details provided to allow replication of the method development and its use by others?

Yes
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?

Partly

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Statistics, Statistical Genomics

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

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Author Response 05 Jan 2022

Qian Wu, Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, 98109, USA

05 Jan 2022

Author Response

1. I think it would be important to explain why the proposed method has advantages in identifying networks with hubs. I would imagine that a network with hubs tends to have ... Continue reading 1. I think it would be important to explain why the proposed method has advantages in identifying networks with hubs. I would imagine that a network with hubs tends to have more diverse sparsity levels of association across different genes than a network without hubs. Is the proposed method with a log penalty more effective for such scenarios? Or there are other reasons?

We totally agree with the reviewer that hub type network has more diverse sparsity (BA type graph has a larger variation (number of edges per gene) than ER type graph) and one additional evidence that log penalty works better for diverse sparsity are the results of an earlier paper https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5628772/ e.g., the results in tables 1 and 2.

2. The Introduction is a bit too short. I would suggest adding more biological background and motivation from a real application point of view.

Good comment. We added biological background in the introduction section accordingly.

3. Some discussions on the computational complexity or a comparison of the computational times of different methods should be helpful.

We thank the reviewer for pointing out this. We have added the run-time discussion with a table in the online manuscript, and a figure in Supplementary Materials on Github. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf
1. I think it would be important to explain why the proposed method has advantages in identifying networks with hubs. I would imagine that a network with hubs tends to have more diverse sparsity levels of association across different genes than a network without hubs. Is the proposed method with a log penalty more effective for such scenarios? Or there are other reasons?

We totally agree with the reviewer that hub type network has more diverse sparsity (BA type graph has a larger variation (number of edges per gene) than ER type graph) and one additional evidence that log penalty works better for diverse sparsity are the results of an earlier paper https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5628772/ e.g., the results in tables 1 and 2.

2. The Introduction is a bit too short. I would suggest adding more biological background and motivation from a real application point of view.

Good comment. We added biological background in the introduction section accordingly.

3. Some discussions on the computational complexity or a comparison of the computational times of different methods should be helpful.

We thank the reviewer for pointing out this. We have added the run-time discussion with a table in the online manuscript, and a figure in Supplementary Materials on Github. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf
Competing Interests: NA Close
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COMMENTS ON THIS REPORT

Author Response 05 Jan 2022

Qian Wu, Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, 98109, USA

05 Jan 2022

Author Response

1. I think it would be important to explain why the proposed method has advantages in identifying networks with hubs. I would imagine that a network with hubs tends to have ... Continue reading 1. I think it would be important to explain why the proposed method has advantages in identifying networks with hubs. I would imagine that a network with hubs tends to have more diverse sparsity levels of association across different genes than a network without hubs. Is the proposed method with a log penalty more effective for such scenarios? Or there are other reasons?

We totally agree with the reviewer that hub type network has more diverse sparsity (BA type graph has a larger variation (number of edges per gene) than ER type graph) and one additional evidence that log penalty works better for diverse sparsity are the results of an earlier paper https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5628772/ e.g., the results in tables 1 and 2.

2. The Introduction is a bit too short. I would suggest adding more biological background and motivation from a real application point of view.

Good comment. We added biological background in the introduction section accordingly.

3. Some discussions on the computational complexity or a comparison of the computational times of different methods should be helpful.

We thank the reviewer for pointing out this. We have added the run-time discussion with a table in the online manuscript, and a figure in Supplementary Materials on Github. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf
1. I think it would be important to explain why the proposed method has advantages in identifying networks with hubs. I would imagine that a network with hubs tends to have more diverse sparsity levels of association across different genes than a network without hubs. Is the proposed method with a log penalty more effective for such scenarios? Or there are other reasons?

We totally agree with the reviewer that hub type network has more diverse sparsity (BA type graph has a larger variation (number of edges per gene) than ER type graph) and one additional evidence that log penalty works better for diverse sparsity are the results of an earlier paper https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5628772/ e.g., the results in tables 1 and 2.

2. The Introduction is a bit too short. I would suggest adding more biological background and motivation from a real application point of view.

Good comment. We added biological background in the introduction section accordingly.

3. Some discussions on the computational complexity or a comparison of the computational times of different methods should be helpful.

We thank the reviewer for pointing out this. We have added the run-time discussion with a table in the online manuscript, and a figure in Supplementary Materials on Github. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf
Competing Interests: NA Close
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Reviewer Report 19 Oct 2020

Chi Song, College of Public Health, Division of Biostatistics, The Ohio State University, Columbus, OH, USA

Approved with Reservations

https://doi.org/10.5256/f1000research.28834.r71864

In this paper, the authors developed “space-log”, a new method to infer gene-gene network (GGN), by incorporating log penalty into the “space” method. The authors compared their method to the original “space” with LASSO penalty and the neighborhood selection (NS) methods, using simulation and real data. In general, the description of the proposed method is clear, and the simulation and real application settings made sense. However, I believe this paper needs to be revised to (1) provide the rationale for choosing the combination of “space” and log penalty, (2) compare with more state-of-the-art methods, and (3) improve the presentation and writing. Here are some specific comments.

The authors need to discuss why they decided to combine “space” and log penalty for GGN detection. What is the benefit of using log penalty over other penalty choices, including concave penalties and other nonconcave penalties such as SCAD, MCP, and TLP? The introduction should be extended to include more state-of-the-art methods, such as adaptive LASSO or high-dimensional regression methods with sparse precision matrix estimation.
Although briefly mentioned gLasso in the introduction, the authors did not talk about this class of methods in the rest of the paper. I am curious to see how space-log compares to gLasso and its extensions with nonconcave penalties in simulation and real application (see Fan et al., 2009). ¹
Based on my understanding, the major benefit of using nonconcave penalties is to reduce the estimation bias of the correlation coefficients. I suggest the authors include comparisons based on the coefficient estimation. In addition, the authors should provide details about how the precision matrices are simulated. Currently, only the simulation methods for its bone structure are provided.
In conclusion/discussion, the authors should provide more insights or heuristics about why the proposed method performed better than other methods. What aspects of the data makes the proposed method favorable? Is there any limitation that the users should pay attention to when applying this method in application?

Minor comments:

The citations in this paper are apparently converted from an author-year citation format. The authors need to make changes to the writing to adapt to numbered citation format.
Presentation and writing issues, for example:

The authors need to decide if a comma is needed between two subscripts in the notation (e.g. \beta_{ij} or \beta_{i,j} on page 3 left column).
On page 4, left column, third paragraph, the sentence “The initial paragraph …” only applies to BA model, but not ER model.
Also, it should be “in the (t+1)th step” instead of “in the (k+1)th step”.
In the last sentence of this paragraph, it should be “1/m” and “2/m”.
This is not an exhaustive list of writing issues. I suggest the authors proofread carefully.

Is the rationale for developing the new method (or application) clearly explained?

Partly
Is the description of the method technically sound?

Yes
Are sufficient details provided to allow replication of the method development and its use by others?

Yes
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?

Partly

References

1. Fan J, Feng Y, Wu Y: Network exploration via the adaptive LASSO and SCAD penalties. The Annals of Applied Statistics. 2009; 3 (2): 521-541 Publisher Full Text
2. Mohsen Pourahmadi: Sparse Gaussian Graphical Models. 2013. 121-140 Publisher Full Text

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Biostatistics, Bioinformatics

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Reviewer Report 14 Oct 2020

Yuying Xie, Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA

Yuning Hao, Amazon, Seattle, WA, USA

Approved with Reservations

https://doi.org/10.5256/f1000research.28834.r71868

The paper introduces an extension of the SPACE (Sparse Partial Correlation Estimation) method, which is used to estimate a gene-gene network (GNN). The proposed framework, space-log, relies on the log penalty, which delivers better variable selection performance than LASSO, especially for GGN with hubs. The authors also have created a very efficient R package for the proposed method. The paper is clearly written, and the proposed method showed promising results for real data analyses. I list my questions below:

In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. Since log penalty can handle high dimension low sample size data, can you also include a real application with m larger than n?
The numerical results are all based on the tuned model using extended BIC, which is one-shot of the result. It is better to also include ROC curves reflecting the whole spectrum of the results for a range of tuning parameters.

Minor comments:

In formula (3), the ‘square root’ should not include Yj.
In t page 3 section ‘Joint modeling space using lasso penalty: space-lasso’, it is better to include the relationship between \beta_{ij} and \simga_{ij} before making the conclusion that \rho_{i,j} = sign(\beta_{i,j}) \sqrt{\beta{ij}\beta_{ji}}.
For the log penalty, please also cite ‘Enhancing sparsity by reweighted L1 minimization’.

Is the rationale for developing the new method (or application) clearly explained?

Yes
Is the description of the method technically sound?

Yes
Are sufficient details provided to allow replication of the method development and its use by others?

Yes
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?

Yes

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Statistics, Biostatistics, Genetics, Bioinformatics

We confirm that we have read this submission and believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however we have significant reservations, as outlined above.

CITE

Report a concern

Author Response 05 Jan 2022

Qian Wu, Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, 98109, USA

05 Jan 2022

Author Response
1. In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. Since log penalty can handle high dimension low sample size data, can
... Continue reading
In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. Since log penalty can handle high dimension low sample size data, can you also include a real application with m larger than n?

We thank the reviewer for pointing out this limitation. We “create” some larger network by combining some gene sets with overlapping genes (m > n). An updated “larger size network” graph is added in supplementary.
https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

The numerical results are all based on the tuned model using extended BIC, which is one-shot of the result. It is better to also include ROC curves reflecting the whole spectrum of the results for a range of tuning parameters.

Good comment. Cross-validation (CV) approach is commonly used to choose the tuning parameter but time-consuming, and recent literature (Wang et al., 2009) showed BIC-type approach has better performance than CV. Thus, we tried different tuning parameters and used grid search to generate an “Oracle” result (based on maximize F1 score or minimize FDR) in supplementary (section S2.3). It showed extBIC performs better than BIC and its performance is close to Oracle for space approach. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

Minor comments:

In formula (3), the ‘square root’ should not include Yj.

In t page 3 section ‘Joint modeling space using lasso penalty: space-lasso’, it is better to include the relationship between \beta_{ij} and \simga_{ij} before making the conclusion that \rho_{i,j} = sign(\beta_{i,j}) \sqrt{\beta{ij}\beta_{ji}}.

For the log penalty, please also cite ‘Enhancing sparsity by reweighted L1 minimization’.

We thank the reviewer for pointing out this oversight. We have updated the manuscript accordingly.
In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. Since log penalty can handle high dimension low sample size data, can you also include a real application with m larger than n?

We thank the reviewer for pointing out this limitation. We “create” some larger network by combining some gene sets with overlapping genes (m > n). An updated “larger size network” graph is added in supplementary.
https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

The numerical results are all based on the tuned model using extended BIC, which is one-shot of the result. It is better to also include ROC curves reflecting the whole spectrum of the results for a range of tuning parameters.

Good comment. Cross-validation (CV) approach is commonly used to choose the tuning parameter but time-consuming, and recent literature (Wang et al., 2009) showed BIC-type approach has better performance than CV. Thus, we tried different tuning parameters and used grid search to generate an “Oracle” result (based on maximize F1 score or minimize FDR) in supplementary (section S2.3). It showed extBIC performs better than BIC and its performance is close to Oracle for space approach. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

Minor comments:

In formula (3), the ‘square root’ should not include Yj.

In t page 3 section ‘Joint modeling space using lasso penalty: space-lasso’, it is better to include the relationship between \beta_{ij} and \simga_{ij} before making the conclusion that \rho_{i,j} = sign(\beta_{i,j}) \sqrt{\beta{ij}\beta_{ji}}.

For the log penalty, please also cite ‘Enhancing sparsity by reweighted L1 minimization’.

We thank the reviewer for pointing out this oversight. We have updated the manuscript accordingly.
Competing Interests: No competing interests were disclosed. Close
Report a concern
Respond or Comment

COMMENTS ON THIS REPORT

Author Response 05 Jan 2022

Qian Wu, Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, 98109, USA

05 Jan 2022

Author Response
1. In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. Since log penalty can handle high dimension low sample size data, can
... Continue reading
In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. Since log penalty can handle high dimension low sample size data, can you also include a real application with m larger than n?

We thank the reviewer for pointing out this limitation. We “create” some larger network by combining some gene sets with overlapping genes (m > n). An updated “larger size network” graph is added in supplementary.
https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

The numerical results are all based on the tuned model using extended BIC, which is one-shot of the result. It is better to also include ROC curves reflecting the whole spectrum of the results for a range of tuning parameters.

Good comment. Cross-validation (CV) approach is commonly used to choose the tuning parameter but time-consuming, and recent literature (Wang et al., 2009) showed BIC-type approach has better performance than CV. Thus, we tried different tuning parameters and used grid search to generate an “Oracle” result (based on maximize F1 score or minimize FDR) in supplementary (section S2.3). It showed extBIC performs better than BIC and its performance is close to Oracle for space approach. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

Minor comments:

In formula (3), the ‘square root’ should not include Yj.

In t page 3 section ‘Joint modeling space using lasso penalty: space-lasso’, it is better to include the relationship between \beta_{ij} and \simga_{ij} before making the conclusion that \rho_{i,j} = sign(\beta_{i,j}) \sqrt{\beta{ij}\beta_{ji}}.

For the log penalty, please also cite ‘Enhancing sparsity by reweighted L1 minimization’.

We thank the reviewer for pointing out this oversight. We have updated the manuscript accordingly.
In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. Since log penalty can handle high dimension low sample size data, can you also include a real application with m larger than n?

We thank the reviewer for pointing out this limitation. We “create” some larger network by combining some gene sets with overlapping genes (m > n). An updated “larger size network” graph is added in supplementary.
https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

The numerical results are all based on the tuned model using extended BIC, which is one-shot of the result. It is better to also include ROC curves reflecting the whole spectrum of the results for a range of tuning parameters.

Good comment. Cross-validation (CV) approach is commonly used to choose the tuning parameter but time-consuming, and recent literature (Wang et al., 2009) showed BIC-type approach has better performance than CV. Thus, we tried different tuning parameters and used grid search to generate an “Oracle” result (based on maximize F1 score or minimize FDR) in supplementary (section S2.3). It showed extBIC performs better than BIC and its performance is close to Oracle for space approach. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

Minor comments:

In formula (3), the ‘square root’ should not include Yj.

In t page 3 section ‘Joint modeling space using lasso penalty: space-lasso’, it is better to include the relationship between \beta_{ij} and \simga_{ij} before making the conclusion that \rho_{i,j} = sign(\beta_{i,j}) \sqrt{\beta{ij}\beta_{ji}}.

For the log penalty, please also cite ‘Enhancing sparsity by reweighted L1 minimization’.

We thank the reviewer for pointing out this oversight. We have updated the manuscript accordingly.
Competing Interests: No competing interests were disclosed. Close
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Yuying Xie, Michigan State University, East Lansing, USA

Yuning Hao, Amazon, Seattle, USA
Chi Song, The Ohio State University, Columbus, USA
Jessie Jeng, North Carolina State University, Raleigh, USA

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20 Jan 2022 | for Version 2

Jessie Jeng, Department of Statistics, North Carolina State University, Raleigh, NC, USA

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Approved

Revisions are sufficient.

Competing Interests

No competing interests were disclosed.

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12 Jan 2022 | for Version 2

Yuying Xie, Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA

Yuning Hao, Amazon, Seattle, WA, USA

13 Views Cite this report Responses(0)

Approved

The authors have answered all my concerns. Congratulations!

Competing Interests

No competing interests were disclosed.

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Statistics, Biostatistics, Genetics, Bioinformatics

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21 Jun 2021 | for Version 1

Jessie Jeng, Department of Statistics, North Carolina State University, Raleigh, NC, USA

20 Views Cite this report Responses(1)

Approved With Reservations

I think it would be important to explain why the proposed method has advantages in identifying networks with hubs. I would imagine that a network with hubs tends to have more diverse sparsity levels of association across different genes than a network without hubs. Is the proposed method with a log penalty more effective for such scenarios? Or there are other reasons?
The Introduction is a bit too short. I would suggest adding more biological background and a motivation from a real application point of view.
Some discussions on the computational complexity or a comparison of the computational times of different methods should be helpful.

Is the rationale for developing the new method (or application) clearly explained?

Partly
Is the description of the method technically sound?

Yes
Are sufficient details provided to allow replication of the method development and its use by others?

Yes
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?

Partly

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Statistics, Statistical Genomics

Respond to this report

Responses (1)

Author Response

05 Jan 2022

Qian Wu, Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, 98109, USA

1. I think it would be important to explain why the proposed method has advantages in identifying networks with hubs. I would imagine that a network with hubs tends to have more diverse sparsity levels of association across different genes than a network without hubs. Is the proposed method with a log penalty more effective for such scenarios? Or there are other reasons?

We totally agree with the reviewer that hub type network has more diverse sparsity (BA type graph has a larger variation (number of edges per gene) than ER type graph) and one additional evidence that log penalty works better for diverse sparsity are the results of an earlier paper https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5628772/ e.g., the results in tables 1 and 2.

2. The Introduction is a bit too short. I would suggest adding more biological background and motivation from a real application point of view.

Good comment. We added biological background in the introduction section accordingly.

3. Some discussions on the computational complexity or a comparison of the computational times of different methods should be helpful.

We thank the reviewer for pointing out this. We have added the run-time discussion with a table in the online manuscript, and a figure in Supplementary Materials on Github. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

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Reviewer Report

19 Views

19 Oct 2020 | for Version 1

Chi Song, College of Public Health, Division of Biostatistics, The Ohio State University, Columbus, OH, USA

19 Views Cite this report Responses(0)

Approved With Reservations

The authors need to discuss why they decided to combine “space” and log penalty for GGN detection. What is the benefit of using log penalty over other penalty choices, including concave penalties and other nonconcave penalties such as SCAD, MCP, and TLP? The introduction should be extended to include more state-of-the-art methods, such as adaptive LASSO or high-dimensional regression methods with sparse precision matrix estimation.
Although briefly mentioned gLasso in the introduction, the authors did not talk about this class of methods in the rest of the paper. I am curious to see how space-log compares to gLasso and its extensions with nonconcave penalties in simulation and real application (see Fan et al., 2009). ¹
Based on my understanding, the major benefit of using nonconcave penalties is to reduce the estimation bias of the correlation coefficients. I suggest the authors include comparisons based on the coefficient estimation. In addition, the authors should provide details about how the precision matrices are simulated. Currently, only the simulation methods for its bone structure are provided.
In conclusion/discussion, the authors should provide more insights or heuristics about why the proposed method performed better than other methods. What aspects of the data makes the proposed method favorable? Is there any limitation that the users should pay attention to when applying this method in application?

Minor comments:

The citations in this paper are apparently converted from an author-year citation format. The authors need to make changes to the writing to adapt to numbered citation format.
Presentation and writing issues, for example:

The authors need to decide if a comma is needed between two subscripts in the notation (e.g. \beta_{ij} or \beta_{i,j} on page 3 left column).
On page 4, left column, third paragraph, the sentence “The initial paragraph …” only applies to BA model, but not ER model.
Also, it should be “in the (t+1)th step” instead of “in the (k+1)th step”.
In the last sentence of this paragraph, it should be “1/m” and “2/m”.
This is not an exhaustive list of writing issues. I suggest the authors proofread carefully.

Is the rationale for developing the new method (or application) clearly explained?

Partly
Is the description of the method technically sound?

Yes
Are sufficient details provided to allow replication of the method development and its use by others?

Yes
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?

Partly

References

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Biostatistics, Bioinformatics

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Reviewer Report

25 Views

14 Oct 2020 | for Version 1

Yuying Xie, Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA

Yuning Hao, Amazon, Seattle, WA, USA

25 Views Cite this report Responses(1)

Approved With Reservations

In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. Since log penalty can handle high dimension low sample size data, can you also include a real application with m larger than n?
The numerical results are all based on the tuned model using extended BIC, which is one-shot of the result. It is better to also include ROC curves reflecting the whole spectrum of the results for a range of tuning parameters.

Minor comments:

In formula (3), the ‘square root’ should not include Yj.
In t page 3 section ‘Joint modeling space using lasso penalty: space-lasso’, it is better to include the relationship between \beta_{ij} and \simga_{ij} before making the conclusion that \rho_{i,j} = sign(\beta_{i,j}) \sqrt{\beta{ij}\beta_{ji}}.
For the log penalty, please also cite ‘Enhancing sparsity by reweighted L1 minimization’.

Is the rationale for developing the new method (or application) clearly explained?

Yes
Is the description of the method technically sound?

Yes
Are sufficient details provided to allow replication of the method development and its use by others?

Yes
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?

Yes

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Statistics, Biostatistics, Genetics, Bioinformatics

Respond to this report

Responses (1)

Author Response

05 Jan 2022

Qian Wu, Clinical Research Division, Fred Hutchinson Cancer Research Center, Seattle, 98109, USA

In both TCGA and GTEx analyses, the dimensions m is smaller than the sample size n. Since log penalty can handle high dimension low sample size data, can you also include a real application with m larger than n?

We thank the reviewer for pointing out this limitation. We “create” some larger network by combining some gene sets with overlapping genes (m > n). An updated “larger size network” graph is added in supplementary.
https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

The numerical results are all based on the tuned model using extended BIC, which is one-shot of the result. It is better to also include ROC curves reflecting the whole spectrum of the results for a range of tuning parameters.

Good comment. Cross-validation (CV) approach is commonly used to choose the tuning parameter but time-consuming, and recent literature (Wang et al., 2009) showed BIC-type approach has better performance than CV. Thus, we tried different tuning parameters and used grid search to generate an “Oracle” result (based on maximize F1 score or minimize FDR) in supplementary (section S2.3). It showed extBIC performs better than BIC and its performance is close to Oracle for space approach. https://github.com/wuqian77/SpaceLog/blob/master/Document/F1000Research_Journal_Article_Spacelog_Supplementary_Materials.pdf

Minor comments:

In formula (3), the ‘square root’ should not include Yj.
In t page 3 section ‘Joint modeling space using lasso penalty: space-lasso’, it is better to include the relationship between \beta_{ij} and \simga_{ij} before making the conclusion that \rho_{i,j} = sign(\beta_{i,j}) \sqrt{\beta{ij}\beta_{ji}}.
For the log penalty, please also cite ‘Enhancing sparsity by reweighted L1 minimization’.

We thank the reviewer for pointing out this oversight. We have updated the manuscript accordingly.

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Competing Interests

No competing interests were disclosed.

Alongside their report, reviewers assign a status to the article:

Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested

Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.

Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions

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Space-log: a novel approach to inferring gene-gene net-works using SPACE model with log penalty

Abstract

Keywords

Revised Amendments from Version 1

Introduction

Methods

Neighborhood selection using lasso or log penalty: NS-lasso, NS-log

Joint modeling space using lasso penalty: space-lasso

New algorithm space-log: joint modeling space using log penalty

Active-shooting

Simulation studies

Table 1. Simulation settings.

Figure 1. BA with 100 genes and e=1.

Figure 2. ER with 100 genes and e=1.

Figure 3. A simulated graph for the BA model with 100 genes (e=1) and multiple hubs.

Table 2. Computational time in minutes with median (range) under the BA model with e=1 and n=400.

Application to GTEx and TCGA data

TCGA data

Figure 4. TCGA data analysis with ALL 189 Gene Sets.

Figure 5. TCGA data analysis with BA hub-type Gene Sets.

GTEx data

Figure 6. GTEx data analysis with ALL 189 Gene Sets.

Figure 7. GTEx data analysis with BA hub-type Gene Sets.

Conclusions

Data availability

Underlying data

Extended data

Software availability

References

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Neighborhood selection using lasso or log penalty: `NS-lasso, NS-log`

Joint modeling `space` using lasso penalty: `space-lasso`

New algorithm `space-log`: joint modeling space using log penalty