Comparing the effects of continuous and discrete covariate mismeasurement, with emphasis on the dichotomization of mismeasured predictors
Comparing the effects of continuous and discrete covariate mismeasurement, with emphasis on the dichotomization of mismeasured predictors
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DOI：
10.1111/j.0006-341x.2002.00878.x
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发表时间：
2002-12-01
期刊：
影响因子：
1.9
通讯作者：
Le, ND
中科院分区：
文献类型：
--
作者：
Gustafson, P;Le, ND
众所周知，预测变量测量的不精确通常会导致估计回归系数的偏差。我们比较了在线性和逻辑回归的背景下，由连续预测的测量误差引起的偏差与由二进制预测的错误分类引起的偏差。为了使比较公平，我们考虑对应于二分法的所有不精确的连续预测代替其精确的对应物的二进制预测的误分类概率。在此基础上，非微分二进制误分类被认为比非微分连续测量误差产生更多的偏差。然而，它是已知的差分误分类结果，如果一个二进制预测实际上是由二分的连续预测受到非差分测量误差形成。当连接响应和精确连续预测的假设模型正确时，发现这种差分误分类产生的偏差比连续测量误差小，与非差分误分类相反，即，二分减少了由于误测量而引起的偏差。然而，这一发现对响应和连续预测之间的潜在关系的形式是敏感的。特别是，我们给出了一个场景，其中二分法涉及模型拟合和误分类偏差之间的权衡。我们还研究了在二分过程中的阈值的选择和不精确的预测和第二个精确的预测之间的相关性的偏差。
It is well known that imprecision in the measurement of predictor variables typically leads to bias in estimated regression coefficients. We compare the bias induced by measurement error in a continuous predictor with that induced by misclassification of a binary predictor in the contexts of linear and logistic regression. To make the comparison fair, we consider misclassification probabilities for a binary predictor that correspond to dichotomizing ail imprecise continuous predictor in lieu of its precise counterpart. On this basis, nondifferential binary misclassification is seen to yield more bias than nondifferential continuous measurement error. However, it is known that differential misclassification results if a binary predictor is actually formed by dichotomizing a continuous predictor subject to nondifferential measurement error. When the postulated model linking the response and precise continuous predictor is correct, this differential misclassification is found to yield less bias than continuous measurement error, in contrast with nondifferential misclassification, i.e., dichotomization reduces the bias due to mismeasurement. This finding, however, is sensitive to the form of the underlying relationship between the response and the continuous predictor. In particular, we give a scenario where dichotomization involves a trade-off between model fit and misclassification bias. We also examine bow the bias depends on the choice of threshold in the dichotomization process and on the correlation between the imprecise predictor and a second precise predictor.