LOW-DOSE-RATE EXTRAPOLATION OF DATA FROM ANIMAL CARCINOGENICITY EXPERIMENTS - ANALYSIS OF A NEW STATISTICAL TECHNIQUE
LOW-DOSE-RATE EXTRAPOLATION OF DATA FROM ANIMAL CARCINOGENICITY EXPERIMENTS - ANALYSIS OF A NEW STATISTICAL TECHNIQUE
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DOI：
10.1016/0025-5564(76)90051-1
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发表时间：
1976-01-01
影响因子：
4.3
通讯作者：
CRUMP, KS
中科院分区：
文献类型：
--
作者：
GUESS, HA;CRUMP, KS
使用动物实验的数据来估计由于长期暴露在环境中的低剂量化学物质而导致的人类癌症风险，造成了一些生物学和统计学问题。统计学问题之一是从高剂量范围推断动物剂量-反应关系，在高剂量范围内，测试数据可用于低剂量，而人类可能会遇到这种情况。发展了一种进行这种外推的新技术的数学性质。(严格地说，这是一种内插，因为一些动物总是在背景剂量作为对照进行测试。)这项技术是基于剂量-反应关系中参数的最大似然估计，其形式来自于一般的多阶段致癌模型。由于阶段的数量本身是未知的，所以要估计的参数的数量是无限的，尽管对于任何给定的数据集，只有有限多的参数是非零的。利用Karlin和Studden以及Krein和Rehtman在非负系数多项式插值理论中的结果证明了估计的存在唯一性。计算估计的算法是基于利用字典排序的性质将无限的Kuhn-Tucker条件集归结为等价的有限条件集。本文讨论了估计技术的数学性质。统计特性将在随后的论文中讨论。
Use of data from animal experiments to estimate the human cancer risk due to long-term exposure to low doses of chemicals in the environment poses a number of biological and statistical problems. One of the statistical problems is to extrapolate the animal dose-response relation from the high dose range where test data are available to low doses, which humans might encounter. The mathematical properties of a new technique for performing this extrapolation were developed. (Strictly speaking, it is an interpolation, since some animals are always tested at the background dose as a control.) The technique is based on maximum likelihood estimation of parameters in dose-response relations whose form is derived from a general multistage carcinogenesis model. Since the number of stages is itself an unknown, the number of parameters to be estimated is infinite, although only finitely many will be nonzero for any given set of data. Existence and uniqueness properties of the estimates are proved using results of Karlin and Studden and Krein and Rehtman from the theory of interpolation of polynomials with nonnegative coefficients. The algorithm for calculating the estimates is based on reducing an infinite set of Kuhn-Tucker conditions to an equivalent finite set of conditions, by exploiting properties of lexicographic ordering. This paper deals with the mathematical properties of the estimation technique. Statistical properties will be discussed in a subsequent paper.