Multiple imputation for left-censored biomarker data based on Gibbs sampling method

Biomarkers, increasingly used in biomedical studies for the diagnosis and prognosis of acute and chronic diseases, provide insight into the effectiveness of treatments and potential pathways that can be used to guide future treatment targets. The measurement of these markers is often limited by the sensitivity of the given assay, resulting in data that are censored either at the lower or at the upper limit of detection. For the Genetic and Inflammatory Markers of Sepsis (GenIMS) study, many different biomarkers were measured to examine the effect of different pathways on the development of sepsis. In this study, the left-censoring of several important inflammatory markers has led to the need for statistical methods that can incorporate this censoring into any analysis of the biomarker data. This paper focuses on the development of multiple imputation methods for the inclusion of multiple left-censored biomarkers in a logistic regression analysis. We assume a multivariate normal distribution to account for the correlations between biomarkers and use the Gibbs sampler for the estimation of the distributional parameters and the imputation of the censored markers. We evaluate and compare the proposed methods with some simple imputation methods through simulation. We use a data set of inflammatory and coagulation markers from the GenIMS study for illustration.