The Use of Historical Control Information in Testing for a Trend in Proportions
The Use of Historical Control Information in Testing for a Trend in Proportions
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使用历史控制信息检验比例趋势
DOI：
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发表时间：
1982
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通讯作者：
R. Tarone
中科院分区：
文献类型：
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作者：
R. Tarone
在生物识别应用中通常面临的问题是测试2 x k列联表中比例的趋势，其中k列具有自然排序。例如，测试化合物可以以增加的剂量水平给予测试动物组，以确定发展肿瘤的动物的比例是否随着剂量水平的增加而增加。Cochran（1954）和Armitage（1955）提出了一种卡方统计量来检验比例趋势。对于具有大量历史数据的问题，结合历史数据的趋势测试将很有用。本文开发了这样一个测试，统计的基础上，这是密切相关的科克伦和阿米蒂奇。二项比例的这种方法类似于Pocock（1976）对正态分布数据导出的方法。这个问题将在动物致癌实验的背景下发展。考虑一个涉及r+1组测试动物的实验。一组作为对照组，其余r组以增加的剂量水平给予试验化合物，dld2<dr。对动物进行固定时间的跟踪，并记录每组在特定器官发生肿瘤的动物数量。设ni表示第i组中动物的数量，并将在实验过程中发生肿瘤的这些动物的数量表示为xi，i 0，1，. . ., R.该实验的结果可以总结在2x（r + 1）表中，例如表1。为了检验比例Pi = xJni随剂量水平增加而增加的ap，Cochran和Armitage建议检验统计量
A problem commonly faced in biometric applications is to test for a trend in proportions in a 2 x k contingency table in which the k columns have a natural ordering. For example, a test compound may be administered at increasing dose levels to groups of test animals to determine if the proportion of animals developing a tumor increases with increasing dose level. Cochran (1954) and Armitage (1955) proposed a chi square statistic for testing for a trend in proportions. For problems with a large amount of historical data, a test for trend incorporating the historical data would be useful. This paper develops such a test, based on a statistic which is closely related to that of Cochran and Armitage. This method for binomial proportions is analogous to the method derived by Pocock (1976) for normallydistributed data. The problem will be developed in the context of an animal carcinogenesis experiment. Consider an experiment involving r+1 groups of test animals. One group serves as a control group, and the remaining r groups are given a test compound at increasing dose levels, dld2<<<<<dr The animals are followed for a fixed period of time, and the number of animals which develop a tumor at a particular organ is recorded for each group. Let ni denote the number of animals in the ith group, and let the number of these animals which develop a tumor during the course of the experiment be denoted by xi, i 0, 1, . . ., r. The results of this experiment can be summarized in a 2 x (r + 1) table such as Table 1. To test for ap increase in the proportions Pi = xJni with increasing dose level, Cochran and Armitage suggested the test statistic