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Estimating Correlation with Multiply Censored Data Arising from the Adjustment of Singly Censored Data

机译：从单删截数据的调整估计与删截数相关的相关性

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摘要

Environmental data frequently are left censored due to detection limits of laboratory assay procedures. Left censored means that some of the observations are known only to fall below a censoring point (detection limit). This presents difficulties in statistical analysis of the data. In this paper, we examine methods for estimating the correlation between variables each of which is censored at multiple points. Multiple censoring frequently arises due to adjustment of singly censored laboratory results for physical sample size. We discuss maximum likelihood (ML) estimation of the correlation and introduce a new method (cp.mle2) that, instead of using the multiply censored data directly, relies on ML estimates of the covariance of the singly censored laboratory data. We compare the ML methods with Kendall's tau-b (ck.taub) which is a modification Kendall's tau adjusted for ties, and several commonly used simple substitution methods: correlations estimated with nondetects set to the detection limit divided by 2 and correlations based on detects only (cs.det) with nondetects setto missing. The methods are compared based on simulations and real data. In the simulations, censoring levels are varied from 0 to 90%, ρ from -0.8 to 0.8, and v (variance of physical sample size) is set to 0 and 0.5, for a total of 550 parameter combinations with 1000 replications at each combination. We find that with increasing levels of censoring most of the correlation methods are highly biased. The simple substitution methods in general tend toward zero if singly censored and one if multiply censored, ck.taub tends toward zero. Least biased is cp.mle2, however, it has higher variance than some of the other estimators. Overall, cs.det performs the worst and cp.mle2 the best.
机译：由于实验室分析程序的检测限制，经常会检查环境数据。左删失意味着某些观察结果仅落在删减点（检测极限）以下。这给数据的统计分析带来了困难。在本文中，我们研究了估计变量之间相关性的方法，每个变量都在多个点被检查。由于针对物理样本大小对单个检查的实验室结果进行了调整，因此经常会进行多次检查。我们讨论了相关性的最大似然（ML）估计，并介绍了一种新方法（cp.mle2），而不是直接使用乘法检查的数据，而是依赖于单个检查的实验室数据的协方差的ML估计。我们将ML方法与Kendall's tau-b（ck.taub）进行了比较，Kendall's tau-b是针对Kendall's tau进行调整的，对平局进行了调整，并比较了几种常用的简单替代方法：将未检测到的相关性设置为检测极限除以2，并基于检测到的相关性进行估计。仅（cs.det）且未检测到设置为丢失。根据模拟和实际数据对方法进行比较。在模拟中，检查级别从0到90％不等，ρ从-0.8到0.8不等，并且v（物理样本大小的方差）设置为0和0.5，总共550个参数组合，每个组合重复1000次。我们发现，随着审查水平的提高，大多数相关方法存在很大的偏见。如果单独检查，则简单替换方法通常趋向于零，如果被多重检查，则简单替代方法趋于于零，ck.taub趋向于零。偏差最小的是cp.mle2，但是，与其他一些估计量相比，它具有更高的方差。总体而言，cs.det的性能最差，而cp.mle2的性能最好。

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  • 来源
    《Environmental Science & Technology》 |2007年第1期|p.221-228|共8页
  • 作者

    ELIZABETH NEWTON; RUTHANN RUDEL;

  • 作者单位

    Silent Spring Institute, 29 Crafts Street, Newton, Massachusetts 02458;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 环境化学;
  • 关键词

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