Segmented regression with errors in predictors: Semi-parametric and parametric methods
Segmented regression with errors in predictors: Semi-parametric and parametric methods
复制标题
DOI：
10.1002/(sici)1097-0258(19970130)16:2
复制
发表时间：
1997-01-15
影响因子：
2
通讯作者：
Carroll, RJ
中科院分区：
文献类型：
--
作者：
Kuchenhoff, H;Carroll, RJ
我们考虑了一个特殊的分段广义线性模型的参数估计，预测的附加测量误差，重点是线性和逻辑回归。在流行病学研究中，分段回归模型通常作为阈值模型出现，其中假设暴露对响应没有影响，直到可能未知的阈值。此外，在职业和环境研究中，通常无法准确测量接触量。忽略此测量误差会导致阈值的渐近有偏估计。结果表明，这种渐近偏差是不同的，从观察到的测量误差的存在下，估计标准的广义线性模型参数，是在不同的方向比预期的更大。在大多数情况下，认为阈值是渐近低估，两个标准的一般方法来纠正这种偏见被认为是回归校准和模拟外推（simex）。在普通的逻辑回归和线性回归中，这些过程的行为相似，但在阈值分段回归模型中，它们的操作却完全不同。回归校准估计量通常比simex估计量具有更大的偏差，但方差更小。回归校准和simex通常被认为是函数方法，也被称为半参数方法，因为它们没有对不可观测协变量X的分布做出假设。对比结构，参数最大似然估计假设X的参数分布形式。在普通的线性回归中，结构方法和功能方法之间通常没有什么区别，我们研究的一个主要的，令人惊讶的发现是，在阈值回归中，功能方法和结构方法在性能上有很大的不同。在我们的一个模拟中，近似一致的函数估计可以比适当指定的参数模型的最大似然估计多25倍。结构（参数）建模不应该是一个被忽视的工具，在测量误差模型。在慕尼黑的机械工程厂粉尘浓度和支气管炎的例子是用来说明的结果。
We consider the estimation of parameters in a particular segmented generalized linear model with additive measurement error in predictors, with a focus on linear and logistic regression. In epidemiologic studies segmented regression models often occur as threshold models, where it is assumed that the exposure has no influence on the response up to a possibly unknown threshold. Furthermore, in occupational and environmental studies the exposure typically cannot be measured exactly. Ignoring this measurement error leads to asymptotically biased estimators of the threshold. It is shown that this asymptotic bias is different from that observed for estimating standard generalized linear model parameters in the presence of measurement error, being both larger and in different directions than expected. In most cases considered the threshold is asymptotically underestimated, Two standard general methods for correcting for this bias are considered; regression calibration and simulation extrapolation (simex). In ordinary logistic and linear regression these procedures behave similarly, but in the threshold segmented regression model they operate quite differently, The regression calibration estimator usually has more bias but less variance than the simex estimator. Regression calibration and simex are typically thought of as functional methods, also known as semiparametric methods, because they make no assumptions about the distribution of the unobservable covariate X. The contrasting structural, parametric maximum likelihood estimate assumes a parametric distributional form for X. In ordinary linear regression there is typically little difference between structural and functional methods, One of the major, surprising findings of our study is that in threshold regression, the functional and structural methods differ substantially in their performance. In one of our simulations, approximately consistent functional estimates can be as much as 25 times more variable than the maximum likelihood estimate for a properly specified parametric model. Structural (parametric) modelling ought not be a neglected tool in measurement error models. An example involving dust concentration and bronchitis in a mechanical engineering plant in Munich is used to illustrate the results.