Left Censored Missingness Simulation

left-censored-missingness-simulation

Summary

Simulate missing-not-at-random (MNAR) left-censored data in metabolomics matrices by applying detection limits and feature-dependent missing mechanisms, enabling benchmarking of imputation methods against realistic instrument censoring patterns.

When to use

When you have a complete metabolomics abundance table (e.g., targeted LC/MS or untargeted GC/MS counts) and need to generate synthetic left-censored missingness for evaluating imputation algorithm performance. This is appropriate when your goal is to benchmark multiple imputation methods (GSimp, QRILC, kNN-TN, HM) against known ground truth, or when real datasets have insufficient or unevenly distributed missing values for robust method comparison.

When NOT to use

• Input data already contains real missing values — mask and document those separately first to avoid confounding synthetic and real missingness.
• Missingness is right-censored (e.g., values above an upper saturation limit) — use hi=quantile() upper bounds instead of lo=-Inf, hi='min'.
• Analysis goal is exploratory or descriptive (not method comparison) — the synthetic ground truth may not reflect actual data patterns in your study.

Inputs

• Complete metabolomics data matrix (numeric data frame, no pre-existing NAs)
• Detection limit threshold (percentile quantile, absolute value, or per-variable vector)
• Missing-data mechanism specification (uniform MCAR, feature-dependent, or sample-dependent rates)
• Feature/sample indices for selective missingness (optional)

Outputs

• Left-censored data matrix (same dimensions, with NAs below threshold)
• NA position matrix (row/column indices of introduced missingness)
• Missingness metadata (threshold used, mechanism applied, count of missing elements, features/samples affected)

How to apply

Load a complete metabolomics data matrix into R and define a left-censoring threshold as either a percentile quantile of each variable's non-missing distribution or an absolute detection limit value. Randomly select features and samples according to a specified missing-data mechanism (e.g., uniformly random selection, or feature-dependent rates that increase for lower-abundance metabolites). Replace all values below the threshold with NA to simulate left-censored observations below the limit of quantification (LOQ). The workflow typically follows: (1) log-transformation for normality, (2) threshold application and NA masking, (3) optional initial imputation with QRILC, (4) centralization/scaling, (5) downstream imputation method application. Record the original positions of masked values (NA_pos) to enable later evaluation by comparing imputed values against ground truth.

Related tools

• GSimp_evaluation.R (Contains MNAR generation and evaluation functions that execute left-censoring threshold application and missing-data mechanism assignment) — https://github.com/WandeRum/GSimp
• impute.QRILC (Quantile Regression Imputation of Left-Censored data; used for initial imputation before Gibbs sampling in the pre_processing_GS_wrapper pipeline) — https://cran.r-project.org/package=imputeLCMD
• R base and tidyverse (magrittr, dplyr) (Data manipulation, matrix operations, and NA masking during threshold application)

Examples

source('GSimp_evaluation.R'); NA_pos <- which(is.na(untargeted_data), arr.ind=T); data_censored <- untargeted_data; data_censored[NA_pos] <- NA

Evaluation signals

• Count of NA elements introduced matches expected number given threshold and mechanism (e.g., if threshold=10th percentile, ~10% of values should be NA).
• NA positions correctly fall below the applied threshold: all original values at NA_pos should be ≤ threshold value for that variable.
• Remaining non-missing values are unchanged (bit-for-bit identical) compared to input matrix.
• Missingness map (visualized with missmap()) shows expected pattern: uniform random for MCAR, clustered by feature for feature-dependent mechanism.
• Ground-truth matrix (original values before censoring) is retained separately to enable imputation accuracy metrics (RMSE, MAE) during evaluation.

Limitations

• Simulated MNAR mechanism may not capture real-world instrument behavior (e.g., ion suppression, chromatographic interference); this is acknowledged as a simplification for controlled benchmarking.
• If threshold is too aggressive (e.g., 50th percentile), missingness becomes MCAR-like rather than left-censored; threshold choice should reflect actual LOQ/LOD in your instrument.
• log-transformation is required before threshold application to avoid distortion of the censoring boundary; exponential recovery must be applied after imputation to restore original scale.
• The simulated MNAR data assume conditional independence given the observed values; real metabolomics data may exhibit more complex missing-data dependencies (e.g., covariate-dependent censoring).

Evidence

• [readme] GSimp_evaluation.R contains MNAR generation and evaluation functions which are part of our missing value imputation evaluation pipeline.: "GSimp_evaluation.R contains MNAR generation and evaluation functions which are part of our missing value imputation evaluation pipeline."
• [other] Define left-censoring threshold parameters (detection limit as a percentile or absolute value). Randomly select features and samples according to a specified missing-data mechanism.: "Define left-censoring threshold parameters (detection limit as a percentile or absolute value). Randomly select features and samples according to a specified missing-data mechanism (e.g.,"
• [other] Replace values below the detection threshold with NA to simulate left-censored observations.: "Replace values below the detection threshold with NA to simulate left-censored observations."
• [readme] log-transformation is needed for non-normal data; initialization with QRILC; centralization and scaling for elastic-net prediction; imputation using GSimp; scaling recovery; exponential recovery.: "Log-transformation (for non-normal data), Initialization for missing values (e.g., QRILC), Centralization and scaling (for elastic-net prediction), Imputation using GSimp, Scaling recovery,"
• [readme] lo=-Inf, hi='min' are default setting for left-censored missing values where the upper bound is set to the minimum value of non-missing part: "Here, lo=-Inf, hi='min' are default setting for left-censored missing values where the upper bound is set to the minimum value of non-missing part"