Lim Changwon, Sen Pranab K, Peddada Shyamal D
Biostatistics Branch, NIEHS, NIH, 111 T. W. Alexander Dr, RTP, NC 27709.
J Stat Plan Inference. 2012 May 1;142(5):1047-1062. doi: 10.1016/j.jspi.2011.11.003.
Toxicologists and pharmacologists often describe toxicity of a chemical using parameters of a nonlinear regression model. Thus estimation of parameters of a nonlinear regression model is an important problem. The estimates of the parameters and their uncertainty estimates depend upon the underlying error variance structure in the model. Typically, a priori the researcher would know if the error variances are homoscedastic (i.e., constant across dose) or if they are heteroscedastic (i.e., the variance is a function of dose). Motivated by this concern, in this article we introduce an estimation procedure based on preliminary test which selects an appropriate estimation procedure accounting for the underlying error variance structure. Since outliers and influential observations are common in toxicological data, the proposed methodology uses M-estimators. The asymptotic properties of the preliminary test estimator are investigated; in particular its asymptotic covariance matrix is derived. The performance of the proposed estimator is compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using a data set obtained from the National Toxicology Program.
毒理学家和药理学家经常使用非线性回归模型的参数来描述化学物质的毒性。因此，非线性回归模型参数的估计是一个重要问题。参数估计及其不确定性估计取决于模型中潜在的误差方差结构。通常，研究者事先会知道误差方差是否为同方差（即，在不同剂量下恒定），或者它们是否为异方差（即，方差是剂量的函数）。出于这种考虑，在本文中，我们引入了一种基于初步检验的估计程序，该程序会根据潜在的误差方差结构选择合适的估计程序。由于异常值和有影响的观测值在毒理学数据中很常见，所提出的方法使用M估计量。研究了初步检验估计量的渐近性质；特别推导了其渐近协方差矩阵。通过模拟研究将所提出估计量的性能与几种标准估计量进行了比较。还使用从国家毒理学计划获得的数据集说明了所提出的方法。
