Bio Metabolomics Normalization Qc

Version Compatibility

Reference examples tested with: pmp 1.14+, statTarget 1.30+, imputeLCMD 2.1+, missForest 1.5+, sva 3.50+

Before using code patterns, verify installed versions match. If versions differ:

• R: packageVersion('<pkg>') then ?function_name to verify parameters

Valid drift correction requires QC injections that bracket the samples at both ends and sample the drift curve (~1 QC every 5-10 injections); conditioning injections must be excluded. Valid batch correction requires biological groups randomized across batches; a confounded design cannot be rescued by any algorithm.

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Metabolomics Normalization and QC

"Normalize my metabolomics data and correct for batch effects" -> Filter junk features by QC quality, correct within-batch drift against injection order, normalize per-sample dilution, and impute by missingness mechanism -- each step verified against held-out QCs, not just QC clustering.

• R drift correction: QCRSC() (pmp), shiftCor() (statTarget)
• R normalization: pqn_normalisation() (pmp)
• R imputation: mv_imputation() (pmp), impute.QRILC() (imputeLCMD), missForest() (missForest)

The Single Most Important Insight -- Normalization Is a Modeling Decision, Not a Cleanup Step

Every preprocessing step imposes an assumption about where the unwanted variance lives; if that assumption is wrong the result is not noisier, it is confidently wrong. Three corollaries reorganize the whole skill. (1) QC-based correction assumes the pooled QC's per-feature drift trajectory is the samples' trajectory -- false for subgroup-specific features (the pool dilutes them toward absence) and for features at different abundance in samples vs pool (suppression is concentration-dependent), so correcting them extrapolates from noise. (2) The order/batch/biology confound is information-theoretically unwinnable post hoc: if group is collinear with batch or injection order, no estimator can attribute the shared variance to one source -- it only redistributes it, wrongly. Randomization at the bench is the only real fix. (3) Over-correction is invisible to the metric everyone reports: "QC RSD dropped / QCs cluster tighter" is exactly what a too-flexible model games (a cubic spline threading every QC drives QC RSD to ~0% while raising biological-sample RSD). Validate on held-out QCs and dilution-QC linearity, never on the metric the model optimized.

The Four Orthogonal Operations (Do Not Conflate)

TIC normalization does not handle drift, and -- because of closure -- can spread one feature's change across all others. Keep the axes separate.

Pipeline Order (and Why Order Matters)

Detection-rate filtering must precede imputation: never impute a feature that is 90% missing, which would fabricate 90% of it.

Decision Tree -- Sample Normalization by Matrix

When >50% of features move coherently (potent drug, gross pathology), the PQN median-quotient measures the biology, not dilution, and subtracts it out -- switch to a measured external quantity and check whether the normalization factor correlates with the phenotype.

Decision Tree -- Drift Correction Method

Flexible ML methods (SERRF/RF/adversarial) win on large complex cohorts but are more prone to learning-and-removing biology that tracks order/batch. Always confirm QC RSD dropped AND biological-sample RSD did not rise.

Filter Features by QC Quality (RSD and D-ratio)

Goal: Keep only reproducible features whose technical variance is small relative to biological variance.

Approach: Compute per-feature QC RSD and the robust D-ratio (technical SD / biological SD), then apply a boolean mask. Lead with D-ratio: CV alone is matrix-blind, scoring a precisely-measured-but-flat feature as good and a noisy-but-biologically-huge feature as bad.

library(matrixStats)

robust_dratio_filter <- function(data, is_qc, dratio_max = 0.5, rsd_max = 0.3) {
    qc <- as.matrix(data[is_qc, ])
    bio <- as.matrix(data[!is_qc, ])
    # MAD-based (robust) form, because MS intensities are right-skewed
    sd_qc <- colMads(qc, na.rm = TRUE)
    sd_bio <- colMads(bio, na.rm = TRUE)
    dratio <- sd_qc / sd_bio
    rsd <- colSds(qc, na.rm = TRUE) / colMeans(qc, na.rm = TRUE)
    keep <- dratio <= dratio_max & rsd <= rsd_max
    keep[is.na(keep)] <- FALSE
    message(sprintf('D-ratio<=%.2f & RSD<=%.0f%%: kept %d / %d features',
                    dratio_max, rsd_max * 100, sum(keep), ncol(data)))
    data[, keep]
}

Correct Within-Batch Drift (QC-RSC)

Goal: Flatten per-feature, injection-order-dependent signal drift using the QC trajectory.

Approach: Fit a QC-robust smoothing spline of intensity vs injection order per feature, interpolate at every sample position, and divide. pmp's QCRSC selects the spline smoothing by leave-one-out CV when spar=0, requires minQC QCs per batch, and excludes features too weak in QC automatically.

library(pmp)

# df: features in ROWS, samples in COLUMNS (pmp convention)
corrected <- QCRSC(df = feature_matrix, order = injection_order, batch = batch_id,
                   classes = sample_class, spar = 0, log = TRUE,
                   minQC = 5, qc_label = 'QC')
# Verify correction worked on HELD-OUT QCs / dilution linearity, not on QC clustering.

statTarget alternative (MLmethod='QCRFSC' for RF, 'QCRLSC' for LOESS; QCspan=0 auto-GCV span applies to QCRLSC; inputs are two order-aligned CSVs):

library(statTarget)
shiftCor(samPeno = 'meta.csv', samFile = 'peaks.csv', Frule = 0.8,
         MLmethod = 'QCRFSC', ntree = 500, QCspan = 0, degree = 2,
         imputeM = 'KNN', coCV = 30, plot = FALSE)

Normalize Per-Sample Dilution (PQN)

Goal: Remove per-sample global intensity differences (dilution, extraction efficiency) without subtracting genuine fold changes.

Approach: Build a reference spectrum (median of QCs), compute per-feature sample/reference quotients, take the median quotient as the dilution factor, and divide. The median is robust because it ignores the minority of genuinely-changed features.

library(pmp)
# df: features in ROWS, samples in COLUMNS; reference built from QC samples
normalized <- pqn_normalisation(df = feature_matrix, classes = sample_class,
                                qc_label = 'QC')

Impute by Missingness Mechanism

Goal: Fill residual sparse holes with the method matched to why the value is missing.

Approach: Diagnose the mechanism per feature -- missingness correlated with low abundance is MNAR (left-censored) and needs QRILC/GSimp; sporadic missingness across the abundance range is MAR and needs RF/kNN. Using a MAR method on MNAR zeros pulls the censored group's mean up and erases the on/off signal.

library(imputeLCMD)
library(missForest)

# MNAR / left-censored: random draws from a fitted truncated-normal (features in ROWS)
qrilc_imputed <- impute.QRILC(feature_matrix_features_in_rows, tune.sigma = 1)[[1]]

# MAR / sporadic: iterative random-forest prediction (samples in ROWS, features in COLS)
rf_imputed <- missForest(sample_by_feature_matrix, maxiter = 10, ntree = 100)$ximp

Half-min imputation collapses the imputed subset's variance to zero, understating SE and inflating false significance -- prefer QRILC/GSimp, which draw a distribution of plausible low values. Re-run key results under >=2 imputation methods; if headline metabolites flip, the finding lives in the imputation.

Per-Method Failure Modes

QC-spline / LOESS over-correction

• Trigger: Span too small, too few QCs, or a cubic spline using each QC as a lock-point.
• Mechanism: The fit threads the QCs perfectly, modeling inter-QC noise as drift and injecting it into samples.
• Symptom: QC RSD drops toward 0% while biological-sample RSD rises and the number of significant features explodes.
• Fix: CV-select the span, validate on held-out QCs and dilution-QC linearity, compare biological-sample RSD before/after, not just QC RSD.

Edge extrapolation

• Trigger: Samples injected before the first QC or after the last QC.
• Mechanism: LOESS/spline interpolate between QCs but extrapolate beyond them, producing unstable correction factors.
• Fix: Bracket samples with QCs at both ends; exclude conditioning injections.

TIC closure artifact

• Trigger: One dominant or up-regulated feature under TIC/sum normalization.
• Mechanism: The constant-sum constraint forces every other feature's normalized value down, manufacturing apparent coordinated down-regulation (Aitchison closure; spurious negative correlations).
• Fix: Use PQN/MSTUS or log-ratios; if "many features moved together," suspect closure from one big mover before believing coordination.

ComBat under imbalance

• Trigger: Biological groups unbalanced across batches.
• Mechanism: Empirical-Bayes shrinkage confounds class with batch; under imbalance it can fabricate thousands of false differences or, without the covariate, delete real ones (Nygaard 2016).
• Fix: Prefer QC-anchored between-batch alignment (the pool has no group, so it cannot confound). Reserve ComBat for balanced designs and always pass the biological covariate via mod=. Randomize so it is never needed.

Wrong imputation mechanism

• Trigger: kNN/RF applied to below-LOD (MNAR) values.
• Mechanism: MAR methods borrow abundance from detected samples, pulling the censored group's mean up and shrinking the very difference under test.
• Fix: Diagnose mechanism per feature; QRILC/GSimp for left-censored, RF/kNN only for sporadic MAR.

Quantitative Thresholds

Thresholds are conventions, not laws: choose them a priori, report each one, and report how many features each filter removed (mQACC reporting standard).

Common Errors

References

• Dunn WB, Broadhurst D, Begley P, et al. 2011. Procedures for large-scale metabolic profiling of serum and plasma using gas chromatography and liquid chromatography coupled to mass spectrometry. Nature Protocols 6:1060-1083.
• Broadhurst D, Goodacre R, Reinke SN, et al. 2018. Guidelines and considerations for the use of system suitability and quality control samples in mass spectrometry assays applied in untargeted clinical metabolomic studies. Metabolomics 14:72.
• Dieterle F, Ross A, Schlotterbeck G, Senn H. 2006. Probabilistic Quotient Normalization as Robust Method to Account for Dilution of Complex Biological Mixtures. Application in 1H NMR Metabonomics. Analytical Chemistry 78:4281-4290.
• Fan S, Kind T, Cajka T, et al. 2019. Systematic Error Removal Using Random Forest for Normalizing Large-Scale Untargeted Lipidomics Data. Analytical Chemistry 91:3590-3596.
• Brunius C, Shi L, Landberg R. 2016. Large-scale untargeted LC-MS metabolomics data correction using between-batch feature alignment and cluster-based within-batch signal intensity drift correction. Metabolomics 12:173.
• Luan H, Ji F, Chen Y, Cai Z. 2018. statTarget: A streamlined tool for signal drift correction and interpretations of quantitative mass spectrometry-based omics data. Analytica Chimica Acta 1036:66-72.
• Wei R, Wang J, Su M, et al. 2018. Missing Value Imputation Approach for Mass Spectrometry-based Metabolomics Data. Scientific Reports 8:663.
• Wei R, Wang J, Jia E, et al. 2018. GSimp: A Gibbs sampler based left-censored missing value imputation approach for metabolomics studies. PLoS Computational Biology 14:e1005973.
• Stekhoven DJ, Buhlmann P. 2012. MissForest -- non-parametric missing value imputation for mixed-type data. Bioinformatics 28:112-118.
• Nygaard V, Rodland EA, Hovig E. 2016. Methods that remove batch effects while retaining group differences may lead to exaggerated confidence in downstream analyses. Biostatistics 17:29-39.
• van den Berg RA, Hoefsloot HCJ, Westerhuis JA, et al. 2006. Centering, scaling, and transformations: improving the biological information content of metabolomics data. BMC Genomics 7:142.
• Warrack BM, Hnatyshyn S, Ott KH, et al. 2009. Normalization strategies for metabonomic analysis of urine samples. Journal of Chromatography B 877:547-552.
• Thonusin C, IglayReger HB, Soni T, et al. 2017. Evaluation of intensity drift correction strategies using MetaboDrift, a normalization tool for multi-batch metabolomics data. Journal of Chromatography A 1523:265-274.
• Chamberlain CA, Rubio VY, Garrett TJ. 2019. Impact of matrix effects and ionization efficiency in non-quantitative untargeted metabolomics. Metabolomics 15:135.
• Wehrens R, Hageman JA, van Eeuwijk F, et al. 2016. Improved batch correction in untargeted MS-based metabolomics. Metabolomics 12:88.

Related Skills

• metabolomics/xcms-preprocessing - Generates the feature table this skill consumes
• metabolomics/msdial-preprocessing - Alternative feature-table source
• metabolomics/statistical-analysis - Transformation/scaling and downstream multivariate stats
• experimental-design/batch-design - Randomization and design that make correction valid
• differential-expression/batch-correction - ComBat/SVA mechanics shared with transcriptomics