Geometry-Aware Reproducibility of Imputation Protocol (GRIP): diagnosing two failure modes of single imputation for heavy-tailed, collinear variables in biomedical data
Park, C. S.-Y.
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Background: Imputation accuracy is typically summarized by a single figure computed from one set of random deletions. For the heavy-tailed, collinear variables common in biomedical data, this study asks whether that figure can be trusted, and introduces a diagnostic protocol that determines when it cannot. Methods: This paper introduces GRIP (Geometry-aware Reproducibility of Imputation Protocol), a three-step diagnostic that profiles each variable's geometry and collinearity, stress-tests reproducibility under MCAR, MAR, and MNAR missingness with fixed seeds, and classifies the failure mode. GRIP was demonstrated on 1,885 United States Centers for Medicare & Medicaid Services (CMS) home-health agencies (15 numeric variables), comparing missForest, votingForest, mean, and median imputation. A supplementary k-nearest-neighbour (k-NN) grid (20 bivariate lognormal parameter combinations; n = 500) verified the SILENT failure boundary across imputer types. The simulation component followed the ADEMP framework. Results: Geometry profiling prospectively flagged two variables combining extreme right-skew (skewness 38.6, 43.3) with near-collinearity (|r| = 0.96). Under MCAR and MAR, missForest normalized root mean squared error (NRMSE) ranged from below 1 to 152 across otherwise identical replications (SD 14-30); the difficulty ordering of the two variables reversed in 69% of replications. Under MNAR self-masking, instability vanished (SD = 0), yet only 14% of true extreme magnitudes were recovered. Both failure modes arise from one mechanism: instability requires an extreme value to be absent while its collinear partner remains observed. A k-NN proxy grid confirmed SILENT failure in 11 of 15 high-skew parameter combinations under MNAR, regardless of correlation level. Conclusions: For heavy-tailed, collinear variables, one imputation-accuracy number can mislead in two opposite ways. GRIP detects both before an imputer is committed and is provided as reusable, open-source R code.
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