Imputing defensible values for left-censored 'below level of quantitation' (LoQ) biomarker measurements

Biomarker datasets often include entries 'below the level of quantitation' (LoQ) wherein the instrumentation is no longer able to provide values that meet required analytical quality standards, a phenomenon referred to as 'left-censored' data. Generally, some form of imputation for missing values is required to allow calculating distributions and summary statistics for comparing datasets to each other. This article discusses the available options for imputing (modeling) left-censored data, presents the methods for implementing different procedures, and provides examples and guidelines using realistic data to assess relative performance. Ultimately, multiple ordered value imputation is identified as the best method; therein, the overall distribution of actual measures is used in conjunction with an estimate of relative order of the missing values to provide the most likely estimates below the LoQ.