Quantifying the position and steepness of radiation dose-response curves
Quantifying the position and steepness of radiation dose-response curves
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DOI：
10.1080/095530097143860
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发表时间：
1997-05-01
影响因子：
2.6
通讯作者：
Tucker, SL
中科院分区：
文献类型：
--
作者：
Bentzen, SM;Tucker, SL
辐射剂量-反应曲线在实际的放射治疗中具有根本的重要性，并且作为更多的理论考虑的基础，这些理论考虑涉及从修改的剂量分割时间表或剂量测定和生物可变性的影响中获得的潜在益处。剂量反应曲线的陡度是一个关键参数，强烈需要从临床数据中获得陡度的定量测量。不幸的是，有许多模糊性与量化的辐射剂量响应曲线的陡度，这些被确定和讨论在本文中。现对以下问题进行评述。(1)在文献中，各种描述'陡度'的报道。我们专注于归一化的剂量-反应梯度，伽玛，和剂量-反应斜率，θ。讨论了它们的数学性质及其相互关系。(2)陡度估计值取决于用于描述剂量-反应关系的数学模型。三个标准的配方被认为是：泊松，逻辑和概率单位剂量反应模型。模型依赖性的大小受可用的经验剂量-反应数据范围的影响，并且对于集中在非常低或非常高的反应水平周围的数据最为明显。(3)给出了标准模型在位置和陡度方面的重新参数化，并指出以前发表的一些公式只是近似的。(4)分析方法会影响陡度估计。对特定数据集的分析表明，使用最小二乘法而不是首选的最大似然法可能会影响陡度估计值及其置信区间。(5)使用固定数量的部分而不是每个部分的固定剂量生成的剂量-反应数据将产生更陡峭的剂量-反应曲线。在描述这样一组剂量-反应数据的位置和一个单一的陡度参数的近似进行了讨论。(6)强调了陡度估计的统计不确定性的重要性。所有这些问题都说明了一个实际的例子，其中剂量-反应数据从文献中重新分析。
Radiation dose-response curves are of fundamental importance both in practical radiotherapy and as the basis of more theoretical considerations concerning the potential benefit to be gained from modified dose-fractionation schedules or of the effects of dosimetric and biological variability. The steepness of the dose-response curve is a key parameter and quantitative measures of steepness derived from clinical data are strongly needed. Unfortunately, there are many ambiguities associated with quantifying the steepness of radiation dose-response curves and these are identified and discussed in the present paper. The following problems are reviewed. (1) In the literature, various descriptors of 'steepness' are reported. We focus on the normalized dose-response gradient, gamma, and the dose-response slope, theta. The mathematical properties and the relationship between these are discussed. (2) Steepness estimates depend on the mathematical model used to describe the dose-response relationship. Three standard formulations are considered: the Poisson, the logistic and the probit dose-response model. The magnitude of the model dependence is influenced by the range of the empirical dose-response data available, and is most pronounced for data concentrated around very low or very high response levels. (3) Reparametrizations of the standard models in terms of position and steepness are given, and it is pointed out that some previously published formulas are only approximations. (4) The method of analysis can influence the steepness estimate. An analysis of a specific data set shows that the use of the least-squares method rather than the preferred maximum likelihood method may influence both the steepness estimate and its confidence interval. (5) Dose-response data generated with a fixed number of fractions rather than a fixed dose per fraction will produce steeper dose-response curves. The approximation involved in describing such a set of dose-response data by a position and a single steepness parameter is discussed. (6) The importance of specifying the statistical uncertainty of the steepness estimate is stressed. All of these problems are illustrated by a practical example, in which dose-response data from the literature are re-analysed.