Table A3.
The estimated correlations for each set of simulations: median (standard deviation). The number label of each line corresponds to the shape and scale parameters in Appendix A Table A1 or Appendix A Table A2, and the letter label of each line corresponds to the zero inflation parameters in Table 1 or Table 2.
| 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) |