Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA.
Epidemiology. 2010 Jul;21 Suppl 4:S10-6. doi: 10.1097/EDE.0b013e3181d60e56.
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.
收集并分析已知和测量分析物值之间关系的原始数据，以确定分析物的定量限 (LOQ)。在大多数 LOQ 问题中，如果感兴趣的标志物的值大于 LOQ，则会给研究人员一个观察值，否则为缺失值（<LOQ）。从统计学的角度来看，隐含的假设是大于 LOQ 的值没有测量误差，而小于 LOQ 的值则存在不可接受的测量误差。更合理的假设是整个测量范围内都存在测量误差。
我们描述了一种贝叶斯测量误差模型，该模型可在分析物值的整个范围内为真实分析值生成预测区间，并允许测量误差存在异方差性。
我们在脂溶性维生素的校准数据上说明了我们的模型，特别关注β-隐黄质。LOQ 以上值的预测区间很宽，且随着测量值的增加而增加。LOQ 以下值的预测区间比值小于 LOQ 的声明提供了更多信息。
目前从校准分析中传输数据的方法存在缺陷，因为它歪曲了实际测量误差的情况。讨论了对后续分析的影响。
