A data-driven single substitution to overcome bias from conventional single substitution for LOD missingness in covariates in least squares regression

Abstract

The Limit of Detection (LOD) is the threshold below which a measurement is considered too low to be reliably quantified. Even though advanced statistical methods exist for dealing with the values below the LOD, simple approaches are still frequently used in real-world settings. Common methods include complete-case analysis, which must use a reduced sample size, and single substitution using fixed constants (e.g. LOD/√2) or other alternatives, which can introduce bias. We propose a data-driven single substitution method for addressing LOD-related missingness in covariates in least squares regression analyses. Instead of relying on constants determined by LODs, our approach computes substitution values based on both unbiased estimates of outcome values associated with the LOD-missing covariates and the linear relationship assumed in the least squares framework. To facilitate hypothesis testing of association effects, we incorporate a bootstrap-based variance estimation procedure. Our simulation studies demonstrate that the proposed method yields unbiased estimates compared to conventional single substitution, achieves lower mean squared errors than the complete-case approach, and provides greater statistical power to detect associations.