Optimal transport for automatic alignment of untargeted metabolomic data
- Nutrition and Metabolism Branch, International Agency for Research on Cancer, France
- Massachusetts Institute of Technology, Department of Mathematics, United States
Figures
Figure 1
An optimal transport approach for combining untargeted metabolomics datasets (GromovMatcher).
(a) Inputs are two LC-MS datasets of unlabeled metabolic features (rows) identified by their , RT, and feature intensities across biospecimen samples. Both studies can have differing numbers of …
Figure 2
Simulated data for testing untargeted metabolomics alignment methods.
(a) Initial LC-MS dataset taken from the EXPOsOMICS project with , RT, and feature intensities of metabolites identified in cord blood across newborns. (b) Newborns (rows) are split into two …
Figure 3 with 2 supplements
Comparison of MetabCombiner, M2S, and GromovMatcher on simulated data.
(a) Ground-truth matchings, and matchings inferred by metabCombiner, M2S, GM, and GMT. Pairs of datasets are generated for three levels of overlap (low, medium and high), with a medium noise level …
Figure 3—figure supplement 1
Average precision and recall obtained on simulated data, with fixed overlap .
The noise level corresponds to different values of and . High, medium, and low noise level correspond to and (1, 1) respectively. We run 20 simulations for each setting.
Figure 3—figure supplement 2
Performance on centered and scaled data.
The feature intensities of both datasets are centered and scaled to have means of 0 and standard deviations of 1. The average precision and recall of the three methods are computed on 20 randomly …
Figure 4 with 3 supplements
Application of GromovMatcher and comparison to existing methods on EPIC dataset.
(a) Dimensions of the three EPIC studies used. For each ionization mode, the cross-sectional (CS) study is aligned successively with the hepatocellular carcinoma (HCC) study and the pancreatic …
Figure 4—figure supplement 1
Consistency of the mean feature intensities (FI) in EPIC.
Each scatter plot represents the mean feature intensities of manually matched features from the validation subset. Each dot represents a pair of manually matched features. The axis represent the …
Figure 4—figure supplement 2
Overlap between the matching results obtained by metabCombiner, M2S and GromovMatcher in EPIC.
Venn diagrams are not up to scale.
Figure 4—figure supplement 3
Estimated RT drift between the EPIC studies aligned in the main experiment.
Each dot correspond to a candidate matched pair after the first step of GM ( constrained GW matching), before the RT drift estimation and RT-based filtering.
Figure 5
Comparison of GromovMatcher and Loftfield et al., 2021 analysis for alcohol biomarker discovery on EPIC data.
(a) Loftfield study implemented a discovery step, examining the relationship between alcohol intake and metabolic features in the CS study. The significant features in CS were manually matched to …
Appendix 2—figure 1
Performance of metabCombiner with the different parameter settings.
The first setting, labelled ‘Scores’ correspond to the design of our main analysis, where 100 randomly selected true pairs are supplied to metabCombiner to set the scoring weights automatically, but …
Appendix 3—figure 1
Sensitivity of thresholded GromovMatcher (GMT) to feature overlap fraction , feature imbalance fraction , and sample imbalance fraction between two datasets being matched.
Appendix 3—figure 2
Sensitivity of M2S to feature overlap fraction , feature imbalance fraction , and sample imbalance fraction between two datasets being matched.
Appendix 3—figure 3
Sensitivity of metabCombiner (mC) to feature overlap fraction , feature imbalance fraction , and sample imbalance fraction between two datasets being matched.
Appendix 5—figure 1
Overlap between the 706 features common to the HCC and PC studies found via reference matching, and the 938 features common to HCC and PC found by direct matching.
Appendix 5—figure 2
Overlap between the features identified as common to the three EPIC studies using either the CS study or the HCC study as a reference.
Tables
Table 1
Results from the manual matching conducted for Loftfield et al., 2021.
Features from the CS study (163 features in positive mode, 42 features in negative mode) were manually investigated for matches in the HCC and PC studies.
| Study | Manual matches found in positive mode | Manual matches found in negative mode |
|---|---|---|
| Hepatocellular carcinoma (HCC) | 90 | 19 |
| Pancreatic cancer (PC) | 66 | 28 |
Table 2
Precision and recall on the EPIC validation subset in positive mode.
95% confidence intervals were computed using modified Wilson score intervals (Brown et al., 2001; Agresti and Coull, 1998).
| Method | Precision | Recall | Precision | Recall |
| GromovMatcher | 0.989 (0.939, 0.999) | 0.978 (0.923, 0.996) | 0.903 (0.813, 0.952) | 0.985 (0.919, 0.999) |
| M2S | 0.967 (0.908, 0.991) | 0.978 (0.923, 0.996) | 0.855 (0.759, 0.917) | 0.985 (0.919, 0.999) |
| metabCombiner | 0.961 (0.868, 0.993) | 0.544 (0.442, 0.643) | 0.967 (0.833, 0.998) | 0.439 (0.326, 0.559) |
Table 3
Precision and recall on the EPIC validation subset in negative mode.
95% confidence intervals were computed using modified Wilson score intervals (Brown et al., 2001; Agresti and Coull, 1998).
| Method | Precision | Recall | Precision | Recall |
| GromovMatcher | 0.950 (0.764, 0.997) | 1.000 (0.832, 1.000) | 0.929 (0.774, 0.987) | 0.929 (0.774, 0.987) |
| M2S | 1.000 (0.824, 1.000) | 0.947 (0.754, 0.997) | 0.931 (0.780, 0.988) | 0.964 (0.823, 0.998) |
| metabCombiner | 0.875 (0.529, 0.993) | 0.368 (0.191, 0.590) | 1.000 (0.845, 1.000) | 0.750 (0.566, 0.873) |
Appendix 2—table 1
Performance of M2S in a setting where the RT drift between studies is linear.
| Metric | Low overlap | Medium overlap | High overlap |
|---|---|---|---|
| Precision | 0.831 | 0.917 | 0.947 |
| Recall | 0.934 | 0.933 | 0.939 |
Appendix 4—table 1
Precision and recall on the EPIC validation subset for unnormalized data in (a) positive mode, and (b) negative mode.
95% confidence intervals were computed using modified Wilson score intervals Brown et al., 2001; Agresti and Coull, 1998.
| Method | Precision | Recall | Precision | Recall |
| GromovMatcher | 0.988 (0.937, 0.999) | 0.944 (0.876, 0.997) | 0.873 (0.776, 0.932) | 0.939 (0.854, 0.976) |
| M2S | 0.967 (0.908, 0.991) | 0.978 (0.923, 0.996) | 0.855 (0.759, 0.917) | 0.985 (0.919, 0.999) |
| metabCombiner | 0.979 (0.889, 0.999) | 0.511 (0.410, 0.612) | 0.926 (0.766, 0.987) | 0.379 (0.271, 0.499) |
| (a) Positive mode | ||||
| Method | Precision | Recall | Precision | Recall |
| GromovMatcher | 0.950 (0.764, 0.997) | 1.000 (0.832, 1.000) | 0.964 (0.823, 0.998) | 0.964 (0.823, 0.998) |
| M2S | 1.000 (0.824, 1.000) | 0.947 (0.754, 0.997) | 0.931 (0.780, 0.988) | 0.964 (0.823, 0.998) |
| metabCombiner | 1.000 (0.566, 1.000) | 0.263 (0.118, 0.488) | 1.000 (0.785, 1.000) | 0.500 (0.326, 0.674) |
| (b) Negative mode | ||||
