Estimating Outcome-Exposure Associations when Exposure Biomarker Detection Limits vary Across Batches

Limit of detection (LOD) issues are ubiquitous in exposure assessment. Although there is an extensive literature on modeling exposure data under such imperfect measurement processes, including likelihood-based methods and multiple imputation, the standard practice continues to be naïve single imputation by a constant (e.g., (Equation is included in full-text article.)). In this article, we consider the situation where, due to the practical logistics of data accrual, sampling, and resource constraints, exposure data are analyzed in multiple batches where the LOD and the proportion of censored observations differ across batches. Compounding this problem is the potential for nonrandom assignment of samples to each batch, often driven by enrollment patterns and biosample storage. This issue is particularly important for binary outcome data where batches may have different levels of outcome enrichment. We first consider variants of existing methods to address varying LODs across multiple batches. We then propose a likelihood-based multiple imputation strategy to impute observations that are below the LOD while simultaneously accounting for differential batch assignment. Our simulation study shows that our proposed method has superior estimation properties (i.e., bias, coverage, statistical efficiency) compared to standard alternatives, provided that distributional assumptions are satisfied. Additionally, in most batch assignment configurations, complete-case analysis can be made unbiased by including batch indicator terms in the analysis model, although this strategy is less efficient relative to the proposed method. We illustrate our method by analyzing data from a cohort study in Puerto Rico that is investigating the relation between endocrine disruptor exposures and preterm birth.