imputation: Quantitative mass spectrometry data imputation
In MsCoreUtils: Core Utils for Mass Spectrometry Data

Description Usage Arguments Details Author(s) References Examples

The impute_matrix function performs data imputation on matrix objects instance using a variety of methods (see below).

Users should proceed with care when imputing data and take precautions to assure that the imputation produce valid results, in particular with naive imputations such as replacing missing values with 0.

impute_matrix(x, method, ...)

imputeMethods()

impute_neighbour_average(x, k = min(x, na.rm = TRUE))

impute_knn(x, ...)

impute_mle(x, ...)

impute_bpca(x, ...)

impute_mixed(x, randna, mar, mnar, ...)

impute_min(x)

`x`	A matrix with missing values to be imputed.
`method`	`character(1)` defining the imputation method. See `imputeMethods()` for available ones.
`...`	Additional parameters passed to the inner imputation function.
`k`	`numeric(1)` providing the imputation value used for the first and last samples if they contain an `NA`. The default is to use the smallest value in the data.
`randna`	`logical` of length equal to `nrow(object)` defining which rows are missing at random. The other ones are considered missing not at random. Only relevant when `methods` is `mixed`.
`mar`	Imputation method for values missing at random. See `method` above.
`mnar`	Imputation method for values missing not at random. See `method` above.

There are two types of mechanisms resulting in missing values in LC/MSMS experiments.

Missing values resulting from absence of detection of a feature, despite ions being present at detectable concentrations. For example in the case of ion suppression or as a result from the stochastic, data-dependent nature of the MS acquisition method. These missing value are expected to be randomly distributed in the data and are defined as missing at random (MAR) or missing completely at random (MCAR).
Biologically relevant missing values resulting from the absence of the low abundance of ions (below the limit of detection of the instrument). These missing values are not expected to be randomly distributed in the data and are defined as missing not at random (MNAR).

MNAR features should ideally be imputed with a left-censor method, such as QRILC below. Conversely, it is recommended to use host deck methods such nearest neighbours, Bayesian missing value imputation or maximum likelihood methods when values are missing at random.

Currently, the following imputation methods are available.

MLE: Maximum likelihood-based imputation method using the EM algorithm. Implemented in the norm::imp.norm(). function. See norm::imp.norm() for details and additional parameters. Note that here, ... are passed to the [norm::em.norm()function, rather to the actual imputation functionimp.norm'.
bpca: Bayesian missing value imputation are available, as implemented in the pcaMethods::pca() function. See pcaMethods::pca() for details and additional parameters.
knn: Nearest neighbour averaging, as implemented in the impute::impute.knn function. See impute::impute.knn()] for details and additional parameters.
QRILC: A missing data imputation method that performs the imputation of left-censored missing data using random draws from a truncated distribution with parameters estimated using quantile regression. Implemented in the imputeLCMD::impute.QRILC function. imputeLCMD::impute.QRILC() for details and additional parameters.
MinDet: Performs the imputation of left-censored missing data using a deterministic minimal value approach. Considering a expression data with n samples and p features, for each sample, the missing entries are replaced with a minimal value observed in that sample. The minimal value observed is estimated as being the q-th quantile (default q = 0.01) of the observed values in that sample. Implemented in the imputeLCMD::impute.MinDet function. See imputeLCMD::impute.MinDet() for details and additional parameters.
MinProb: Performs the imputation of left-censored missing data by random draws from a Gaussian distribution centred to a minimal value. Considering an expression data matrix with n samples and p features, for each sample, the mean value of the Gaussian distribution is set to a minimal observed value in that sample. The minimal value observed is estimated as being the q-th quantile (default q = 0.01) of the observed values in that sample. The standard deviation is estimated as the median of the feature standard deviations. Note that when estimating the standard deviation of the Gaussian distribution, only the peptides/proteins which present more than 50\ are considered. Implemented in the imputeLCMD::impute.MinProb function. See imputeLCMD::impute.MinProb() for details and additional parameters.
min: Replaces the missing values with the smallest non-missing value in the data.
zero: Replaces the missing values with 0.
mixed: A mixed imputation applying two methods (to be defined by the user as mar for values missing at random and mnar for values missing not at random, see example) on two MCAR/MNAR subsets of the data (as defined by the user by a randna logical, of length equal to nrow(object)).
nbavg: Average neighbour imputation for fractions collected along a fractionation/separation gradient, such as sub-cellular fractions. The method assumes that the fraction are ordered along the gradient and is invalid otherwise.

Continuous sets NA value at the beginning and the end of the quantitation vectors are set to the lowest observed value in the data or to a user defined value passed as argument k. Then, when a missing value is flanked by two non-missing neighbouring values, it is imputed by the mean of its direct neighbours.
with: Replaces all missing values with a user-provided value.
none: No imputation is performed and the missing values are left untouched. Implemented in case one wants to only impute value missing at random or not at random with the mixed method.

The imputeMethods() function returns a vector with valid imputation method arguments.

Laurent Gatto

Olga Troyanskaya, Michael Cantor, Gavin Sherlock, Pat Brown, Trevor Hastie, Robert Tibshirani, David Botstein and Russ B. Altman, Missing value estimation methods for DNA microarrays Bioinformatics (2001) 17 (6): 520-525.

Oba et al., A Bayesian missing value estimation method for gene expression profile data, Bioinformatics (2003) 19 (16): 2088-2096.

Cosmin Lazar (2015). imputeLCMD: A collection of methods for left-censored missing data imputation. R package version 2.0. http://CRAN.R-project.org/package=imputeLCMD.

Lazar C, Gatto L, Ferro M, Bruley C, Burger T. Accounting for the Multiple Natures of Missing Values in Label-Free Quantitative Proteomics Data Sets to Compare Imputation Strategies. J Proteome Res. 2016 Apr 1;15(4):1116-25. doi: 10.1021/acs.jproteome.5b00981. PubMed PMID:26906401.

## test data
set.seed(42)
m <- matrix(rlnorm(60), 10)
dimnames(m) <- list(letters[1:10], LETTERS[1:6])
m[sample(60, 10)] <- NA

## available methods
imputeMethods()

impute_matrix(m, method = "zero")

impute_matrix(m, method = "min")

impute_matrix(m, method = "knn")

## same as impute_zero
impute_matrix(m, method = "with", val = 0)

## impute with half of the smalles value
impute_matrix(m, method = "with",
              val = min(m, na.rm = TRUE) * 0.5)

## all but third and fourth features' missing values
## are the result of random missing values
randna <- rep(TRUE, 10)
randna[c(3, 9)] <- FALSE

impute_matrix(m, method = "mixed",
              randna = randna,
              mar = "knn",
              mnar = "min")