Ogden R Todd
Department of Biostatistics, Columbia University, New York, USA.
Stat Med. 2003 Nov 30;22(22):3557-68. doi: 10.1002/sim.1562.
Positron emission tomography (PET) imaging is a useful tool for quantifying various aspects of the distribution of neuroreceptors throughout the human brain in vivo. A typical analysis consists of applying a pharmacokinetic model to the data, estimating the parameters of the model using non-linear least squares methods, then taking the appropriate function of estimated model parameters as a final estimate of the parameter(s) of interest. As an alternative for fitting these models, it has been shown previously that taking a particular transformation of the data results in two variables that have a linear relationship, and that the slope of this linear relationship is the parameter of primary interest. However, estimating the slope using ordinary least squares (OLS) regression results in a large negative bias. By rearranging the terms in the relationship, the problem may be reformed to allow direct application of standard estimation principles. Estimators resulting from this approach are shown via simulation to have better estimation properties as compared to the OLS estimators.
正电子发射断层扫描（PET）成像是一种在体内定量分析神经受体在全脑分布各方面情况的有用工具。典型的分析包括将药代动力学模型应用于数据，使用非线性最小二乘法估计模型参数，然后将估计的模型参数的适当函数作为感兴趣参数的最终估计值。作为拟合这些模型的一种替代方法，先前已经表明对数据进行特定变换会产生两个具有线性关系的变量，并且这种线性关系的斜率就是主要感兴趣的参数。然而，使用普通最小二乘法（OLS）回归估计斜率会导致较大的负偏差。通过重新排列关系中的项，可以对问题进行重新构建，以便直接应用标准估计原理。通过模拟表明，与OLS估计器相比，这种方法得到的估计器具有更好的估计特性。
