Abstract
In many biological studies, biomarkers are measured with errors. In addition, study samples are often divided and measured in separate batches, and data collected from different experiments are used in a single analysis. Generally speaking, the structure of the measurement error is unknown and is not easy to ascertain. While the conditions under which the measurements are taken vary from one batch/experiment to another, they are often held steady within each batch/experiment. Thus, the measurement error can be considered batch/experiment specific, that is, fixed within each batch/experiment, which results into a rank-preserving property within each batch/experiment. Under this condition, we study robust statistical methods for analyzing the association between an outcome variable and predictors measured with error, and evaluating the diagnostic or predictive accuracy of these biomarkers. Our methods require no assumptions on the structure and distribution of the measurement error, which are often unrealistic. Compared with existing methods that are predicated on normality and additive structure of measurement errors, our methods still yield valid inferences under departure from these assumptions. The proposed methods are easy to implement using off-shelf software. Simulation studies show that under various measurement error structures, the performance of the proposed methods is satisfactory even for a fairly small sample size, whereas existing methods under misspecified structures and a naive approach exhibited substantial bias. Our methods are illustrated using a biomarker validation case-control study for colorectal neoplasms.