Zheng Junyu, Frey H Christopher
Department of Civil, Construction, and Environmental Engineering, North Carolina State University, Raleigh, NC 27695, USA.
Risk Anal. 2005 Jun;25(3):663-75. doi: 10.1111/j.1539-6924.2005.00620.x.
The appearance of measurement error in exposure and risk factor data potentially affects any inferences regarding variability and uncertainty because the distribution representing the observed data set deviates from the distribution that represents an error-free data set. A methodology for improving the characterization of variability and uncertainty with known measurement errors in data is demonstrated in this article based on an observed data set, known measurement error, and a measurement-error model. A practical method for constructing an error-free data set is presented and a numerical method based upon bootstrap pairs, incorporating two-dimensional Monte Carlo simulation, is introduced to address uncertainty arising from measurement error in selected statistics. When measurement error is a large source of uncertainty, substantial differences between the distribution representing variability of the observed data set and the distribution representing variability of the error-free data set will occur. Furthermore, the shape and range of the probability bands for uncertainty differ between the observed and error-free data set. Failure to separately characterize contributions from random sampling error and measurement error will lead to bias in the variability and uncertainty estimates. However, a key finding is that total uncertainty in mean can be properly quantified even if measurement and random sampling errors cannot be separated. An empirical case study is used to illustrate the application of the methodology.
暴露和风险因素数据中测量误差的出现可能会影响任何有关变异性和不确定性的推断，因为代表观测数据集的分布偏离了代表无误差数据集的分布。本文基于一个观测数据集、已知测量误差和一个测量误差模型，展示了一种用于改进对数据中已知测量误差情况下变异性和不确定性特征描述的方法。提出了一种构建无误差数据集的实用方法，并引入了一种基于自展对的数值方法，结合二维蒙特卡罗模拟，以解决所选统计量中测量误差引起的不确定性。当测量误差是不确定性的一个重要来源时，代表观测数据集变异性的分布与代表无误差数据集变异性的分布之间会出现显著差异。此外，观测数据集和无误差数据集的不确定性概率带的形状和范围也不同。未能分别表征随机抽样误差和测量误差的贡献将导致变异性和不确定性估计出现偏差。然而，一个关键发现是，即使测量误差和随机抽样误差无法分离，均值的总不确定性也可以得到恰当量化。一个实证案例研究用于说明该方法的应用。
