# Multiple imputation for proteomics

#### Marie Chion, Université de Strasbourg et CNRS, IRMA, labex IRMIA, LSMBO, IPHC, marie.chion@protonmail.fr

#### Christine Carapito, Université de Strasbourg et CNRS, LSMBO, IPHC, ccarapito@unistra.fr

#### Frédéric Bertrand, Université de Strasbourg et CNRS, IRMA, labex IRMIA, Université de technologie de Troyes, LIST3N, frederic.bertrand@lecnam.net

#### 2025-09-20

# mi4p: multiple imputation for proteomics

This repository contains the R code and package for the mi4p methodology (Multiple Imputation for Proteomics), proposed by Marie Chion, Christine Carapito and Frédéric Bertrand (2021) in Accounting for multiple imputation-induced variability for differential analysis in mass spectrometry-based label-free quantitative proteomics, https://arxiv.org/abs/2108.07086.

The following material is available on the Github repository of the package https://github.com/mariechion/mi4p/.

1. The `Functions` folder contains all the functions used for the workflow.

2. The `Simulation-1`, `Simulation-2` and `Simulation-3` folders contain all the R scripts and data used to conduct simulated experiments and evaluate our methodology.

3. The `Arabidopsis_UPS` and `Yeast_UPS` folders contain all the R scripts and data used to challenge our methodology on real proteomics datasets. Raw experimental data were deposited with the ProteomeXchange Consortium via the PRIDE partner repository with the dataset identifiers PXD003841 and PXD027800.

This website and these examples were created by M. Chion, C. Carapito and F. Bertrand.

## Installation

You can install the released version of mi4p from CRAN with:

    install.packages("mi4p")

You can install the development version of mi4p from github with:

    devtools::install_github("mariechion/mi4p")

## Examples

### First section

    library(mi4p)

    set.seed(4619)
    datasim <- protdatasim()
    str(datasim)
    #> 'data.frame':    200 obs. of  11 variables:
    #>  $ id.obs: int  1 2 3 4 5 6 7 8 9 10 ...
    #>  $ X1    : num  99.6 99.9 100.2 99.8 100.4 ...
    #>  $ X2    : num  97.4 101.3 100.3 100.2 101.7 ...
    #>  $ X3    : num  100.3 100.9 99.1 101.2 100.6 ...
    #>  $ X4    : num  99.4 99.2 98.5 99.1 99.5 ...
    #>  $ X5    : num  98.5 99.7 100 100.2 100.7 ...
    #>  $ X6    : num  200 199 199 200 199 ...
    #>  $ X7    : num  200 200 202 199 199 ...
    #>  $ X8    : num  202 199 200 199 201 ...
    #>  $ X9    : num  200 200 199 201 200 ...
    #>  $ X10   : num  200 198 200 201 199 ...
    #>  - attr(*, "metadata")='data.frame': 10 obs. of  3 variables:
    #>   ..$ Sample.name: chr [1:10] "X1" "X2" "X3" "X4" ...
    #>   ..$ Condition  : Factor w/ 2 levels "A","B": 1 1 1 1 1 2 2 2 2 2
    #>   ..$ Bio.Rep    : int [1:10] 1 2 3 4 5 6 7 8 9 10

    attr(datasim, "metadata")
    #>    Sample.name Condition Bio.Rep
    #> 1           X1         A       1
    #> 2           X2         A       2
    #> 3           X3         A       3
    #> 4           X4         A       4
    #> 5           X5         A       5
    #> 6           X6         B       6
    #> 7           X7         B       7
    #> 8           X8         B       8
    #> 9           X9         B       9
    #> 10         X10         B      10

## AMPUTATION

    MV1pct.NA.data <- MVgen(dataset = datasim[,-1], prop_NA = 0.01)
    MV1pct.NA.data

## IMPUTATION

    MV1pct.impMLE <- multi.impute(data = MV1pct.NA.data, conditions = attr(datasim,"metadata")$Condition, method = "MLE", parallel = FALSE)

## ESTIMATION

    print(paste(Sys.time(), "Dataset", 1, "out of", 1))
    MV1pct.impMLE.VarRubin.Mat <- rubin2.all(data = MV1pct.impMLE, metacond = attr(datasim, "metadata")$Condition)

## PROJECTION

    print(paste("Dataset", 1, "out of",1, Sys.time()))
    MV1pct.impMLE.VarRubin.S2 <- as.numeric(lapply(MV1pct.impMLE.VarRubin.Mat, function(aaa){
        DesMat = mi4p::make.design(attr(datasim, "metadata"))
        return(max(diag(aaa)%*%t(DesMat)%*%DesMat))
      }))

## MODERATED T-TEST

    MV1pct.impMLE.mi4limma.res <- mi4limma(qData = apply(MV1pct.impMLE,1:2,mean),
                     sTab = attr(datasim, "metadata"),
                     VarRubin = sqrt(MV1pct.impMLE.VarRubin.S2))
    MV1pct.impMLE.mi4limma.res
    (simplify2array(MV1pct.impMLE.mi4limma.res)$P_Value.A_vs_B_pval)[1:10]

    (simplify2array(MV1pct.impMLE.mi4limma.res)$P_Value.A_vs_B_pval)[11:200]<=0.05

True positive rate

    sum((simplify2array(MV1pct.impMLE.mi4limma.res)$P_Value.A_vs_B_pval)[1:10]<=0.05)/10

False positive rate

    sum((simplify2array(MV1pct.impMLE.mi4limma.res)$P_Value.A_vs_B_pval)[11:200]<=0.05)/190

    MV1pct.impMLE.dapar.res <-limmaCompleteTest.mod(qData = apply(MV1pct.impMLE,1:2,mean), sTab = attr(datasim, "metadata"))
    MV1pct.impMLE.dapar.res

Simulate a list of 100 datasets.

    set.seed(4619)
    norm.200.m100.sd1.vs.m200.sd1.list <- lapply(1:100, protdatasim)
    metadata <- attr(norm.200.m100.sd1.vs.m200.sd1.list[[1]],"metadata")

100 datasets with parallel comuting support. Quite long to run even with parallel computing support.

    library(foreach)
    doParallel::registerDoParallel(cores=NULL)
    requireNamespace("foreach",quietly = TRUE)

## AMPUTATION

    MV1pct.NA.data <- foreach::foreach(iforeach =  norm.200.m100.sd1.vs.m200.sd1.list,
                              .errorhandling = 'stop', .verbose = T) %dopar%
      MVgen(dataset = iforeach[,-1], prop_NA = 0.01)

## IMPUTATION

    MV1pct.impMLE <- foreach::foreach(iforeach =  MV1pct.NA.data,
                             .errorhandling = 'stop', .verbose = F) %dopar%
      multi.impute(data = iforeach, conditions = metadata$Condition,
                   method = "MLE", parallel  = F)

## ESTIMATION

    MV1pct.impMLE.VarRubin.Mat <- lapply(1:length(MV1pct.impMLE), function(index){
      print(paste(Sys.time(), "Dataset", index, "out of", length(MV1pct.impMLE)))
      rubin2.all(data = MV1pct.impMLE[[index]], metacond = metadata$Condition)
    })

## PROJECTION

    MV1pct.impMLE.VarRubin.S2 <- lapply(1:length(MV1pct.impMLE.VarRubin.Mat), function(id.dataset){
      print(paste("Dataset", id.dataset, "out of",length(MV1pct.impMLE.VarRubin.Mat), Sys.time()))
      as.numeric(lapply(MV1pct.impMLE.VarRubin.Mat[[id.dataset]], function(aaa){
        DesMat = mi4p::make.design(metadata)
        return(max(diag(aaa)%*%t(DesMat)%*%DesMat))
      }))
    })

## MODERATED T-TEST

    MV1pct.impMLE.mi4limma.res <- foreach(iforeach =  1:100,  .errorhandling = 'stop', .verbose = T) %dopar%
      mi4limma(qData = apply(MV1pct.impMLE[[iforeach]],1:2,mean),
                     sTab = metadata,
                     VarRubin = sqrt(MV1pct.impMLE.VarRubin.S2[[iforeach]]))

    MV1pct.impMLE.dapar.res <- foreach(iforeach =  1:100,  .errorhandling = 'stop', .verbose = T) %dopar%
      limmaCompleteTest.mod(qData = apply(MV1pct.impMLE[[iforeach]],1:2,mean),
                            sTab = metadata)