BayesMetab: treatment of missing values in metabolomic studies using a Bayesian modeling approach

Jeremy Gaskins,Guy N. Brock,Jasmit Shah

doi:10.1186/s12859-019-3250-2

Abstract

BackgroundWith the rise of metabolomics, the development of methods to address analytical challenges in the analysis of metabolomics data is of great importance. Missing values (MVs) are pervasive, yet the treatment of MVs can have a substantial impact on downstream statistical analyses. The MVs problem in metabolomics is quite challenging and can arise because the metabolite is not biologically present in the sample, or is present in the sample but at a concentration below the lower limit of detection (LOD), or is present in the sample but undetected due to technical issues related to sample pre-processing steps. The former is considered missing not at random (MNAR) while the latter is an example of missing at random (MAR). Typically, such MVs are substituted by a minimum value, which may lead to severely biased results in downstream analyses.ResultsWe develop a Bayesian model, called BayesMetab, that systematically accounts for missing values based on a Markov chain Monte Carlo (MCMC) algorithm that incorporates data augmentation by allowing MVs to be due to either truncation below the LOD or other technical reasons unrelated to its abundance. Based on a variety of performance metrics (power for detecting differential abundance, area under the curve, bias and MSE for parameter estimates), our simulation results indicate that BayesMetab outperformed other imputation algorithms when there is a mixture of missingness due to MAR and MNAR. Further, our approach was competitive with other methods tailored specifically to MNAR in situations where missing data were completely MNAR. Applying our approach to an analysis of metabolomics data from a mouse myocardial infarction revealed several statistically significant metabolites not previously identified that were of direct biological relevance to the study.ConclusionsOur findings demonstrate that BayesMetab has improved performance in imputing the missing values and performing statistical inference compared to other current methods when missing values are due to a mixture of MNAR and MAR. Analysis of real metabolomics data strongly suggests this mixture is likely to occur in practice, and thus, it is important to consider an imputation model that accounts for a mixture of missing data types.

Highlights

With the rise of metabolomics, the development of methods to address analytical challenges in the analysis of metabolomics data is of great importance
While the bias for estimating the beta coefficients is relatively similar between the two approaches (Fig. 2), our BayesImp method has a smaller mean squared error (MSE) than GSimp as the percent missing increases (Fig. 3)
In the scenario where all missingness is due to intensities below the limit of detection (LOD) (MNAR only), all the methods demonstrate comparable power, type I error, and area under the ROC curve (AUC) (Fig. 4), as well as similar bias (Fig. 5) and MSE (Fig. 6) for estimating the beta coefficients

Summary

Introduction

The MVs problem in metabolomics is quite challenging and can arise because the metabolite is not biologically present in the sample, or is present in the sample but at a concentration below the lower limit of detection (LOD), or is present in the sample but undetected due to technical issues related to sample pre-processing steps. The former is considered missing not at random (MNAR) while the latter is an example of missing at random (MAR). By incorporating the prior distributions in model building, one can utilize the initial (un)certainty about a parameter [4]

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