A Bayesian approach estimating treatment effects on biomarkers containing zeros with detection limits

Often in randomized clinical trials and observational studies in occupational and environmental health, a non-negative continuously distributed response variable denoting some metabolites of environmental toxicants is measured in treatment and control groups. When observations occur in both unexposed and exposed subjects, the biomarker measurement can be bimodally distributed with an extra spike at zero reflecting those unexposed. In the presence of left censoring due to values falling below biomarker assay detection limits, those unexposed with true zeros are indistinguishable from those exposed with left-censored values. Since interventions usually do not enhance or eliminate exposure, they do not have any impact on those unexposed. Thus, only the subset of individuals who are exposed should be used to make comparisons to estimate the effect of interventions. In this article, we present Bayesian approaches using non-standard mixture distributions to account for true zeros. The performance of the proposed Bayesian methods is compared with the maximum likelihood methods presented in Chu et al. (Stat. Med. 2005; 24:2053-2067) through simulation studies and a randomized chemoprevention trial conducted in Qidong, People's Republic of China.