A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data
A Comparison of the β-Substitution Method and a Bayesian Method for Analyzing Left-Censored Data
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DOI：
10.1093/annhyg/mev049
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发表时间：
2016-01-01
影响因子：
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通讯作者：
Stewart, Patricia A.
中科院分区：
文献类型：
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作者：
Tran Huynh;Quick, Harrison;Stewart, Patricia A.
职业卫生文献中详细描述了用于分析低于检测限值的暴露数据的经典统计方法，但目前缺乏对处理此类数据的贝叶斯方法的评价。在这里，我们首先描述了一个贝叶斯框架分析删失数据。然后，我们提出了一个模拟研究的结果进行比较的β-替代方法与贝叶斯方法的暴露数据集从对数正态分布和混合对数正态分布与不同的样本量，几何标准差（GSD），和审查的单一和多个检测限。对于每组因素，获得暴露分布的算术平均值（AM）、几何平均值、GSD和第95百分位数（X-0.95）的估计值。我们使用相对偏差、均方根误差（rMSE）和覆盖率（计算的95%不确定性区间中包含真实值的比例）评估了每种方法的性能。当估计AM和GM时，使用无信息先验的贝叶斯方法和β-替代方法在偏倚和rMSE方面通常相当。对于GSD和第95百分位数，无信息先验的贝叶斯方法比β-替代方法更有偏差，并且具有更高的rMSE，但使用更多信息先验通常会提高贝叶斯方法的性能，使偏差和rMSE与β-替代方法更具可比性。贝叶斯方法的一个优点是，它提供了这些感兴趣的参数的不确定性估计值和良好的覆盖范围，而β-替代方法只提供了AM的不确定性估计值，覆盖范围不一致。一种或另一种方法的选择取决于从业者的需求、先验信息的可用性以及测量数据的分布特征。如果从业者有计算资源和先验信息，我们建议使用贝叶斯方法，因为该方法通常会提供准确的估计，并提供所有参数的分布，这可能有助于在某些应用中做出决策。
Classical statistical methods for analyzing exposure data with values below the detection limits are well described in the occupational hygiene literature, but an evaluation of a Bayesian approach for handling such data is currently lacking. Here, we first describe a Bayesian framework for analyzing censored data. We then present the results of a simulation study conducted to compare the beta-substitution method with a Bayesian method for exposure datasets drawn from lognormal distributions and mixed lognormal distributions with varying sample sizes, geometric standard deviations (GSDs), and censoring for single and multiple limits of detection. For each set of factors, estimates for the arithmetic mean (AM), geometric mean, GSD, and the 95th percentile (X-0.95) of the exposure distribution were obtained. We evaluated the performance of each method using relative bias, the root mean squared error (rMSE), and coverage (the proportion of the computed 95% uncertainty intervals containing the true value). The Bayesian method using non-informative priors and the beta-substitution method were generally comparable in bias and rMSE when estimating the AM and GM. For the GSD and the 95th percentile, the Bayesian method with non-informative priors was more biased and had a higher rMSE than the beta-substitution method, but use of more informative priors generally improved the Bayesian method's performance, making both the bias and the rMSE more comparable to the beta-substitution method. An advantage of the Bayesian method is that it provided estimates of uncertainty for these parameters of interest and good coverage, whereas the beta-substitution method only provided estimates of uncertainty for the AM, and coverage was not as consistent. Selection of one or the other method depends on the needs of the practitioner, the availability of prior information, and the distribution characteristics of the measurement data. We suggest the use of Bayesian methods if the practitioner has the computational resources and prior information, as the method would generally provide accurate estimates and also provides the distributions of all of the parameters, which could be useful for making decisions in some applications.