Raw data on the relationship between known and measured values of an analyte are collected and analyzed to determine the limit of quantification (LOQ) of an assay. In most LOQ problems, the researcher is given an observed value for the marker of interest if this value is greater than the LOQ, and a missing value (<LOQ) otherwise. From a statistical perspective, the implicit assumption is that there is no measurement error for values greater than the LOQ, and unacceptable measurement error for values less than the LOQ. A more plausible assumption is that there is measurement error throughout the measure's support.
We describe a Bayesian measurement error model that yields prediction intervals for the true assay value throughout the range of analyte values, and allows for heteroscedasticity of the measurement errors.
We illustrate our model on calibration data for fat-soluble vitamins, focusing particularly on beta-cryptoxanthin. Prediction intervals for values above the LOQ are wide, and the width increases with the measured value. Prediction intervals below the LOQ provide more information than the statement that the value is less than the LOQ.
The current approach to transmitting data from calibration assays is flawed, since it provides a distorted picture of the actual measurement error. Implications for subsequent analyses of assay measurements are discussed.
From the aDepartment of Biostatistics, University of Michigan, Ann Arbor, MI; and bDepartment of Statistics, University of Connecticut, Storrs, CT.
Submitted 27 July 2008; accepted 25 November 2009.
Supported by the American Chemistry Council and the Eunice Kennedy Shriver National Institute for Child and Human Development, National Institutes of Health.
Correspondence: Roderick J. Little, Department of Biostatistics, University of Michigan, 1420 Washington Heights, Ann Arbor, MI 48109. E-mail: firstname.lastname@example.org.