title: Handling missing rows in multi-omics data integration: multiple imputation in multiple factor analysis framework.
abstract: BACKGROUND
  In omics data integration studies, it is common, for a variety of reasons, for some individuals to not be present in all data tables. Missing row values are challenging to deal with because most statistical methods cannot be directly applied to incomplete datasets. To overcome this issue, we propose a multiple imputation (MI) approach in a multivariate framework. In this study, we focus on multiple factor analysis (MFA) as a tool to compare and integrate multiple layers of information. MI involves filling the missing rows with plausible values, resulting in M completed datasets. MFA is then applied to each completed dataset to produce M different configurations (the matrices of coordinates of individuals). Finally, the M configurations are combined to yield a single consensus solution.
  
  
  RESULTS
  We assessed the performance of our method, named MI-MFA, on two real omics datasets. Incomplete artificial datasets with different patterns of missingness were created from these data. The MI-MFA results were compared with two other approaches i.e., regularized iterative MFA (RI-MFA) and mean variable imputation (MVI-MFA). For each configuration resulting from these three strategies, the suitability of the solution was determined against the true MFA configuration obtained from the original data and a comprehensive graphical comparison showing how the MI-, RI- or MVI-MFA configurations diverge from the true configuration was produced. Two approaches i.e., confidence ellipses and convex hulls, to visualize and assess the uncertainty due to missing values were also described. We showed how the areas of ellipses and convex hulls increased with the number of missing individuals. A free and easy-to-use code was proposed to implement the MI-MFA method in the R statistical environment.
  
  
  CONCLUSIONS
  We believe that MI-MFA provides a useful and attractive method for estimating the coordinates of individuals on the first MFA components despite missing rows. MI-MFA configurations were close to the true configuration even when many individuals were missing in several data tables. This method takes into account the uncertainty of MI-MFA configurations induced by the missing rows, thereby allowing the reliability of the results to be evaluated.
authors.affiliation: Université de Toulouse, INRA, INPT, INP-ENVT, UMR1388, GenPhySE, Castanet-Tolosan, F-31326, France.
authors.forename: Valentin
authors.initials: V
authors.lastname: Voillet
authors.affiliation: Université de Toulouse INSA, UMR5219 Institut de Mathématiques, Toulouse, F-31077, France.
authors.forename: Philippe
authors.initials: P
authors.lastname: Besse
authors.affiliation: Université de Toulouse, INRA, INPT, INP-ENVT, UMR1388, GenPhySE, Castanet-Tolosan, F-31326, France.
authors.forename: Laurence
authors.initials: L
authors.lastname: Liaubet
authors.affiliation: Université de Toulouse, INRA, INPT, INP-ENVT, UMR1388, GenPhySE, Castanet-Tolosan, F-31326, France.|Université de Toulouse INSA, UMR5219 Institut de Mathématiques, Toulouse, F-31077, France.
authors.forename: Magali
authors.initials: M
authors.lastname: San Cristobal
authors.affiliation: INRAUR875 Mathématiques et Informatiques Appliquées, F-31326, Castanet-Tolosan, France. Ignacio.Gonzalez@toulouse.inra.fr.
authors.forename: Ignacio
authors.identifier: http://orcid.org/0000-0003-3432-6909
authors.initials: I
authors.lastname: González
mesh_terms: D000082:Acetaminophen / Q000633:toxicity*; D018712:Analgesics, Non-Narcotic / Q000633:toxicity; D000818:Animals; D056486:Chemical and Drug Induced Liver Injury / Q000209:etiology* / Q000378:metabolism / Q000473:pathology; D003627:Data Interpretation, Statistical; D005163:Factor Analysis, Statistical; D005786:Gene Expression Regulation / Q000187:drug effects*; D023281:Genomics / Q000379:methods*; D006801:Humans; D008297:Male; D015999:Multivariate Analysis; D009369:Neoplasms / Q000235:genetics / Q000378:metabolism*; D040901:Proteomics / Q000379:methods*; D051381:Rats; D017208:Rats, Wistar; D015203:Reproducibility of Results; D014407:Tumor Cells, Cultured
chemical_list: D018712:Analgesics, Non-Narcotic; D000082:Acetaminophen
keywords: Hot-deck imputation; Missing individuals; Multiple imputation; Multiple omics data integration; Multivariate factor analysis