BZINB Model-Based Pathway Analysis and Module Identification Facilitates Integration of Microbiome and Metabolome Data
Abstract
:1. Introduction
2. Materials and Methods
2.1. Description of BZINB Model
2.1.1. ZINB Model
2.1.2. BNB Model
2.1.3. BZINB Model and BZINB-Based Correlation
2.2. Existing Correlation Calculation Methods for Network/Pathway Analysis
2.3. Description of Microbiome and Metabolome Data from the ZOE 2.0 Study
2.4. Simulation Study
2.4.1. Lognormal Based Simulation
2.4.2. BZINB-Based Simulation
2.5. Spectral Clustering for Module Identification
2.5.1. Approach for BZINB Application in Spectral Clustering
2.5.2. Evaluation of Cut-Based Spectral Clustering Using Crafted Semi-Parametric Simulation
- If the most common predicted cluster for an assigned cluster is the same as the most common assigned cluster for that predicted cluster, those clusters are matched.
- Then, the overall proportion of accurate predicted cluster assignments is calculated for each possible combination of the remaining clusters.
- The remaining clusters are matched with the combination that maximizes the proportion of accurate predicted cluster assignments.
2.6. Network Visualization
3. Results
3.1. BZINB Model Is a Good Fit for the ZOE 2.0 Microbiome and Metabolome Data
3.2. Estimation Accuracy of Underlying Correlation in Simulated Correlated Pairs of Count Data Vectors
3.3. Accuracy Evaluation of Identified Species Modules Using Semi-Parametric Simulation
3.4. Application in the ZOE 2.0 Study
Interactions among Commensal Species and among ECC-Associated Species
3.5. Species Modules Identified Using BZINB-Based Correlation and Spectral Clustering
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ZINB | Zero-inflated negative binomial |
BNB | Bivariate negative binomial |
BZINB | Bivariate zero-inflated negative binomial |
MI | Mutual Information |
ECC | Early childhood caries |
Appendix A
1 | 0.2 | 0.1 | 0.3 | 20 | 40 | 0.498 |
2 | 0.3 | 0.5 | 0.8 | 12 | 21 | 0.300 |
3 | 0.15 | 1.1 | 1.5 | 20 | 30 | 0.100 |
4 | 0.05 | 0.85 | 1 | 30 | 50 | 0.050 |
1 | 0.3 | 0.3 | 0.3 | 30 | 40 | 0.486 |
2 | 0.35 | 0.7 | 0.8 | 20 | 30 | 0.306 |
3 | 0.1 | 0.75 | 1 | 30 | 30 | 0.100 |
4 | 0.05 | 0.9 | 1 | 50 | 50 | 0.049 |
Theoretical | Spearman | Pearson | BNB | BZINB | ||
---|---|---|---|---|---|---|
lognormal (metabolome– microbiome) | 1a | 0.5 | 0.273 (0.056) | 0.374 (0.115) | 0.383 (0.047) | 0.524 (0.058) |
1b | −0.011 (0.06) | 0.075 (0.122) | 0.112 (0.054) | 0.153 (0.21) | ||
1c | 0.058 (0.058) | 0.213 (0.118) | 0.188 (0.049) | 0.339 (0.18) | ||
1d | −0.064 (0.06) | 0.131 (0.123) | 0.181 (0.07) | 0.435 (0.205) | ||
2a | 0.3 | 0.181 (0.058) | 0.223 (0.096) | 0.241 (0.058) | 0.313 (0.08) | |
2b | −0.007 (0.058) | 0.046 (0.099) | 0.081 (0.048) | 0.064 (0.127) | ||
2c | 0.038 (0.06) | 0.13 (0.101) | 0.124 (0.06) | 0.146 (0.144) | ||
2d | −0.043 (0.062) | 0.08 (0.093) | 0.106 (0.064) | 0.215 (0.171) | ||
3a | 0.1 | 0.071 (0.058) | 0.076 (0.071) | 0.08 (0.061) | 0.077 (0.068) | |
3b | −0.002 (0.058) | 0.019 (0.071) | 0.053 (0.041) | 0.019 (0.05) | ||
3c | 0.015 (0.059) | 0.042 (0.071) | 0.052 (0.053) | 0.027 (0.053) | ||
3d | −0.019 (0.059) | 0.029 (0.07) | 0.049 (0.046) | 0.045 (0.07) | ||
4a | 0.05 | 0.039 (0.059) | 0.042 (0.065) | 0.05 (0.052) | 0.042 (0.048) | |
4b | 0 (0.058) | 0.007 (0.063) | 0.045 (0.036) | 0.014 (0.042) | ||
4c | 0.009 (0.056) | 0.023 (0.061) | 0.036 (0.042) | 0.016 (0.034) | ||
4d | −0.01 (0.059) | 0.012 (0.065) | 0.04 (0.042) | 0.025 (0.045) | ||
lognormal (within microbiome) | 1a | 0.5 | 0.25 (0.058) | 0.367 (0.11) | 0.351 (0.047) | 0.52 (0.065) |
1b | 0.011 (0.061) | 0.121 (0.13) | 0.102 (0.046) | 0.228 (0.242) | ||
1c | 0.052 (0.06) | 0.203 (0.123) | 0.173 (0.051) | 0.356 (0.191) | ||
2a | 0.3 | 0.167 (0.06) | 0.223 (0.102) | 0.226 (0.056) | 0.319 (0.083) | |
2b | 0.01 (0.057) | 0.077 (0.107) | 0.073 (0.041) | 0.089 (0.151) | ||
2c | 0.032 (0.059) | 0.124 (0.099) | 0.114 (0.054) | 0.156 (0.154) | ||
3a | 0.1 | 0.064 (0.059) | 0.075 (0.072) | 0.082 (0.061) | 0.078 (0.073) | |
3b | 0.006 (0.06) | 0.027 (0.077) | 0.048 (0.037) | 0.022 (0.055) | ||
3c | 0.014 (0.057) | 0.042 (0.073) | 0.055 (0.046) | 0.028 (0.055) | ||
4a | 0.05 | 0.034 (0.059) | 0.04 (0.064) | 0.052 (0.051) | 0.041 (0.05) | |
4b | 0.002 (0.061) | 0.013 (0.063) | 0.043 (0.035) | 0.014 (0.041) | ||
4c | 0.006 (0.059) | 0.022 (0.067) | 0.039 (0.04) | 0.016 (0.034) | ||
BZINB (metabolome– microbiome) | 1a | 0.4978 | 0.329 (0.056) | 0.416 (0.113) | 0.409 (0.047) | 0.48 (0.07) |
1b | 0.177 (0.069) | 0.192 (0.146) | 0.184 (0.067) | 0.274 (0.224) | ||
1c | 0.064 (0.063) | 0.18 (0.128) | 0.135 (0.056) | 0.321 (0.2) | ||
1d | 0.09 (0.058) | 0.185 (0.118) | 0.162 (0.056) | 0.318 (0.203) | ||
2a | 0.300 | 0.228 (0.061) | 0.257 (0.083) | 0.279 (0.055) | 0.275 (0.074) | |
2b | 0.195 (0.065) | 0.156 (0.103) | 0.166 (0.056) | 0.132 (0.164) | ||
2c | 0.016 (0.057) | 0.086 (0.082) | 0.071 (0.047) | 0.118 (0.151) | ||
2d | 0.026 (0.058) | 0.09 (0.085) | 0.086 (0.053) | 0.131 (0.164) | ||
3a | 0.100 | 0.135 (0.059) | 0.114 (0.067) | 0.202 (0.068) | 0.094 (0.061) | |
3b | 0.209 (0.063) | 0.129 (0.076) | 0.151 (0.047) | 0.046 (0.082) | ||
3c | 0.005 (0.057) | 0.026 (0.066) | 0.053 (0.04) | 0.019 (0.046) | ||
3d | 0.008 (0.058) | 0.028 (0.065) | 0.066 (0.047) | 0.021 (0.052) | ||
4a | 0.050 | 0.11 (0.06) | 0.065 (0.065) | 0.125 (0.067) | 0.054 (0.047) | |
4b | 0.205 (0.064) | 0.105 (0.076) | 0.122 (0.049) | 0.032 (0.062) | ||
4c | 0.002 (0.057) | 0.013 (0.063) | 0.039 (0.034) | 0.013 (0.027) | ||
4d | 0.001 (0.058) | 0.014 (0.063) | 0.04 (0.036) | 0.015 (0.038) | ||
BZINB (within microbiome) | 1a | 0.486 | 0.334 (0.057) | 0.412 (0.094) | 0.407 (0.044) | 0.461 (0.061) |
1b | 0.2 (0.066) | 0.198 (0.13) | 0.187 (0.059) | 0.27 (0.22) | ||
1c | 0.046 (0.058) | 0.17 (0.108) | 0.131 (0.047) | 0.287 (0.191) | ||
1d | 0.051 (0.06) | 0.163 (0.105) | 0.131 (0.047) | 0.332 (0.194) | ||
2a | 0.306 | 0.239 (0.058) | 0.264 (0.081) | 0.303 (0.05) | 0.282 (0.071) | |
2b | 0.207 (0.061) | 0.161 (0.093) | 0.167 (0.051) | 0.123 (0.157) | ||
2c | 0.017 (0.059) | 0.088 (0.083) | 0.079 (0.047) | 0.109 (0.139) | ||
2d | 0.019 (0.061) | 0.09 (0.082) | 0.089 (0.047) | 0.126 (0.151) | ||
3a | 0.100 | 0.132 (0.059) | 0.104 (0.069) | 0.156 (0.061) | 0.088 (0.058) | |
3b | 0.204 (0.064) | 0.113 (0.077) | 0.132 (0.05) | 0.045 (0.081) | ||
3c | 0.006 (0.058) | 0.03 (0.068) | 0.045 (0.038) | 0.025 (0.056) | ||
3d | 0.005 (0.058) | 0.028 (0.069) | 0.044 (0.039) | 0.026 (0.058) | ||
4a | 0.049 | 0.109 (0.06) | 0.066 (0.066) | 0.135 (0.066) | 0.055 (0.047) | |
4b | 0.208 (0.062) | 0.107 (0.07) | 0.12 (0.046) | 0.03 (0.058) | ||
4c | 0.004 (0.056) | 0.014 (0.06) | 0.043 (0.034) | 0.011 (0.017) | ||
4d | 0.005 (0.056) | 0.014 (0.06) | 0.04 (0.035) | 0.012 (0.022) |
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Relationship | Zero Inflation | Number of Zeros | Means | |
---|---|---|---|---|
Metabolite–Species | a | Balanced, low | 30, 60 | 14, 11 |
b | Balanced, high | 150, 200 | 12, 9 | |
c | 30, 200 | 14, 9 | ||
d | 150, 60 | 12, 11 | ||
Species–Species | a | Balanced, low | 60, 60 | 11, 11 |
b | Balanced, high | 200, 200 | 9, 9 | |
c | 60, 200 | 11, 9 |
Zero Inflation | Expected Zeros | |||||
---|---|---|---|---|---|---|
a | Balanced, low | 30, 60 | 0.75 | 0.15 | 0.05 | 0.05 |
b | Balanced, high | 210, 240 | 0.1 | 0.2 | 0.1 | 0.6 |
c | 60, 225 | 0.2 | 0.6 | 0.05 | 0.15 | |
d | 225, 60 | 0.2 | 0.05 | 0.6 | 0.15 |
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Lin, B.M.; Cho, H.; Liu, C.; Roach, J.; Ribeiro, A.A.; Divaris, K.; Wu, D. BZINB Model-Based Pathway Analysis and Module Identification Facilitates Integration of Microbiome and Metabolome Data. Microorganisms 2023, 11, 766. https://doi.org/10.3390/microorganisms11030766
Lin BM, Cho H, Liu C, Roach J, Ribeiro AA, Divaris K, Wu D. BZINB Model-Based Pathway Analysis and Module Identification Facilitates Integration of Microbiome and Metabolome Data. Microorganisms. 2023; 11(3):766. https://doi.org/10.3390/microorganisms11030766
Chicago/Turabian StyleLin, Bridget M., Hunyong Cho, Chuwen Liu, Jeff Roach, Apoena Aguiar Ribeiro, Kimon Divaris, and Di Wu. 2023. "BZINB Model-Based Pathway Analysis and Module Identification Facilitates Integration of Microbiome and Metabolome Data" Microorganisms 11, no. 3: 766. https://doi.org/10.3390/microorganisms11030766
APA StyleLin, B. M., Cho, H., Liu, C., Roach, J., Ribeiro, A. A., Divaris, K., & Wu, D. (2023). BZINB Model-Based Pathway Analysis and Module Identification Facilitates Integration of Microbiome and Metabolome Data. Microorganisms, 11(3), 766. https://doi.org/10.3390/microorganisms11030766