# Optimization of Imputation Strategies for High-Resolution Gas Chromatography–Mass Spectrometry (HR GC–MS) Metabolomics Data

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## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. Missing Values Simulation and Imputation Evaluation Using HR GC–MS Metabolomics Data for Replicates of NIST Plasma

#### 2.2. Evaluation of RF, GRR, and BPCA Imputation Methods on NHP Plasma

^{−13}). Similarly, metabolite missingness demonstrated a significant positive association with RMSE (estimate = 0.44, 4.2 × 10

^{−15}).

#### 2.3. Evaluation of RF, GRR, and BPCA Imputation Methods Using Metabolomics Data from Baboon Liver Biopsy Samples

^{−8}). Similarly, metabolite missingness demonstrated a significant positive association with RMSE (estimate = 0.42, 2.7 × 10

^{−12}).

^{−9}, 0.96 for GRR, BPCA, RF, respectively). Random forest demonstrated the smallest shift in these p-value differences, but all of the methods had mean differences that were slightly below zero (Figure 7).

#### 2.4. In-Depth Evaluation of RF Imputation Accuracy at Wide Range of Missingness Using the Entire Baboon Liver HR GC–MS Metabolomics Dataset

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Chemicals and Reagents

#### 4.2. Sample Processing

^{−1}) in pyridine incubated at 55 °C for 60 min, followed by trimethylsilylation at 60 °C for 60 min after adding 80 μL MTBSTFA.

#### 4.3. GC-HR Orbitrap MS Data Acquisition and Preprocessing

_{10}transformation.

#### 4.4. Generation of Missing Values

#### 4.5. Evaluation of Imputation Methods

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Metabolomics imputation study workflow. Diagram detailing metabolomics sample analysis, evaluation of imputation methods in technical replicate dataset (NIST plasma), and further validation in real baboon plasma and liver metabolomics datasets.

**Figure 2.**Initial evaluations of imputation accuracy in the complete NIST plasma for a mixture of missingness types (MCAR–MAR–MNAR). Methods are listed across the x-axis, and RMSE is shown on the y-axis. The center line represents the median. The lower and upper box limits represent the 25% and 75% quantiles, respectively. The whiskers extend to the largest observation within the box limit ± 1.5 × interquartile range. Black dots represent single iterations of evaluating RMSE that are outliers. The number of observations for each method is 22,070.

**Figure 3.**Evaluations of imputation accuracy in the complete baboon plasma. Accuracy is evaluated for levels of missingness types (MCAR–MAR–MNAR). Methods are listed across the x-axis, and RMSE is shown on the y-axis. The top row compares accuracy across a range of missingness types. The bottom row compares accuracy across a range of coefficients of variance. The center line represents the median. The lower and upper box limits represent the 25% and 75% quantiles, respectively. The whiskers extend to the largest observation within the box limit ± 1.5 × interquartile range. Black dots represent single iterations of evaluating RMSE that are outliers. The p-values are based on pairwise testing with the Wilcoxon Rank Sum test (* corresponds to p ≤ 0.05; ** corresponds to p ≤ 0.01; *** corresponds to p ≤ 0.001; **** corresponds to p ≤ 0.0001).

**Figure 4.**Evaluations of Cronbach’s alpha. Methods are listed across the x-axis, and the difference between the Cronbach’s alphas computed on the complete data and the imputed data is shown on the y-axis. The top row demonstrates differences in Cronbach’s alpha evaluated in the baboon plasma samples for 10% and 20% of overall missingness. The bottom row shows the differences in Cronbach’s alpha evaluated in the baboon liver samples for 10% and 20% overall missingness. The center line represents the median. The lower and upper box limits represent the 25% and 75% quantiles, respectively. The whiskers extend to the largest observation within the box limit ± 1.5 × interquartile range. Black dots represent single iterations of evaluating Cronbach’s alpha that are outliers. The p-values are based on pairwise testing with the Wilcoxon Rank Sum test (* corresponds to p ≤ 0.05; ** corresponds to p ≤ 0.01; *** corresponds to p ≤ 0.001; **** corresponds to p ≤ 0.0001).

**Figure 5.**Evaluations of regression coefficient and regression p-value accuracy. Methods are listed across the x-axis. The differences between the regression coefficients (or p-values) computed on the complete data and the imputed data are shown on the y-axis. The top row demonstrates differences in regression coefficients evaluated in the baboon plasma samples for metabolites with <10%, 10–20%, and 20–30% missingness. The top row demonstrates differences in regression p-values evaluated in the baboon plasma samples for metabolites with <10%, 10–20%, and 20–30% missingness. The center line represents the median. The lower and upper box limits represent the 25% and 75% quantiles, respectively. The whiskers extend to the largest observation within the box limit ± 1.5 × interquartile range. Black dots represent single iterations of evaluating differences that are outliers. The p-values are based on pairwise testing with the Wilcoxon Rank Sum test (* corresponds to p ≤ 0.05).

**Figure 6.**Evaluations of imputation accuracy in the complete baboon liver. Accuracy is evaluated for a mixture of missingness types (MCAR–MAR–MNAR). Methods are listed across the x-axis, and RMSE is shown on the y-axis. The top row compares accuracy across a range of missingness types. The bottom row compares accuracy across a range of coefficients of variance. The center line represents the median. The lower and upper box limits represent the 25% and 75% quantiles, respectively. The whiskers extend to the largest observation within the box limit ± 1.5 × interquartile range. Black dots represent single iterations of evaluating RMSE that are outliers. The p-values are based on pairwise testing with the Wilcoxon Rank Sum test (* corresponds to p ≤ 0.05; ** corresponds to p ≤ 0.01; *** corresponds to p ≤ 0.001; **** corresponds to p ≤ 0.0001).

**Figure 7.**Evaluations of regression coefficient and regression p-value accuracy. Methods are listed across the x-axis. The differences between the regression coefficients (or p-values) computed on the complete data and the imputed data are shown on the y-axis. The top row demonstrates differences in regression coefficients evaluated in the baboon liver samples for metabolites with <10%, 10–20%, and 20–30% missingness. The top row demonstrates differences in regression p-values evaluated in the baboon liver samples for metabolites with <10%, 10–20%, and 20–30% missingness. The center line represents the median. The lower and upper box limits represent the 25% and 75% quantiles, respectively. The whiskers extend to the largest observation within the box limit ± 1.5 × interquartile range. Black dots represent single iterations of evaluating differences that are outliers. The p-values are based on pairwise testing with the Wilcoxon Rank Sum test.

**Figure 8.**In-depth evaluation of RF imputation. Percent bias (accuracy of imputation on raw data) is shown in the upper left for metabolites in bins of percent missingness between 2–51%. Differences in Cronbach’s alpha are shown in the upper left for a variety of proportions of overall missingness between 10–70%. The differences in regression coefficients are shown in the bottom left for a variety of proportions of overall missingness between 10–60%. The respective differences in p-values are shown in the bottom right. The center line represents the median. The lower and upper box limits represent the 25% and 75% quantiles, respectively. Black dots represent single iterations of evaluating differences that are outliers. The whiskers extend to the largest observation within the box limit ± 1.5 × interquartile range.

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**MDPI and ACS Style**

Ampong, I.; Zimmerman, K.D.; Nathanielsz, P.W.; Cox, L.A.; Olivier, M.
Optimization of Imputation Strategies for High-Resolution Gas Chromatography–Mass Spectrometry (HR GC–MS) Metabolomics Data. *Metabolites* **2022**, *12*, 429.
https://doi.org/10.3390/metabo12050429

**AMA Style**

Ampong I, Zimmerman KD, Nathanielsz PW, Cox LA, Olivier M.
Optimization of Imputation Strategies for High-Resolution Gas Chromatography–Mass Spectrometry (HR GC–MS) Metabolomics Data. *Metabolites*. 2022; 12(5):429.
https://doi.org/10.3390/metabo12050429

**Chicago/Turabian Style**

Ampong, Isaac, Kip D. Zimmerman, Peter W. Nathanielsz, Laura A. Cox, and Michael Olivier.
2022. "Optimization of Imputation Strategies for High-Resolution Gas Chromatography–Mass Spectrometry (HR GC–MS) Metabolomics Data" *Metabolites* 12, no. 5: 429.
https://doi.org/10.3390/metabo12050429