Kokoska S M, Hardin J M, Grubbs C J, Hsu C
Department of Mathematics and Computer Science, Bloomsburg University, PA 17815.
Anticancer Res. 1993 Sep-Oct;13(5A):1357-63.
The purpose of this paper is to address the very important problem of accurate statistical analysis of certain types of cancer inhibition/promotion (IP) experiments. These experiments are routinely used by the National Cancer Institute to test the effects of potential chemopreventative agents. The statistical analysis is difficult since there is Type I censoring. In the IP experiments under investigation, laboratory animals (rats) are injected with a single dose of either a direct or indirect acting carcinogen. In the mammary tumor system, animals in the control group generally develop 5-7 tumors and typical experiments are usually terminated after 4-6 months. Animals are sacrificed at the end of the experiment and all observed tumors are confirmed. The two most common response variables are the number of observed tumors per animal and the rate of tumor development. The difficulty in analyzing these experiments occurs because experiments are terminated before all induced tumors have been observed. Fewer observed tumors in one group compared to another could be the result of a decreased number of induced tumors, a decrease in growth rate, or a combination of both. It is essential for the experimenter to distinguish between these two different biological actions. Present statistical techniques do not account for this confounding and since they rely primarily on nonparametric procedures, do not present an accurate description of potential IP agents. In this paper we introduce a parametric procedure that explicitly acknowledges the confounding present in experiments of this nature. The analysis is based on the comparison of the mean number of tumors per group (lambda) and the mean time to tumor appearance (mu). A longer mean time to development is believed to indicate a slower tumor growth rate. Hypothesis tests are developed to determine if there is an overall experiment effect, to isolate which groups are contributing to an observed experiment effect, and to isolate factors (tumor number and/or growth rate) contributing to an observed group difference. Confidence regions for (lambda, mu) are also generated. This analysis leads to a better understanding of how potential IP agents function.
本文的目的是解决某些类型的癌症抑制/促进（IP）实验的准确统计分析这一非常重要的问题。美国国立癌症研究所经常使用这些实验来测试潜在化学预防剂的效果。由于存在I型删失，统计分析很困难。在所研究的IP实验中，给实验动物（大鼠）注射单剂量的直接或间接致癌剂。在乳腺肿瘤系统中，对照组的动物通常会长出5 - 7个肿瘤，典型的实验通常在4 - 6个月后终止。实验结束时处死动物，并确认所有观察到的肿瘤。两个最常见的反应变量是每只动物观察到的肿瘤数量和肿瘤发生速率。分析这些实验的困难在于实验在所有诱发肿瘤都被观察到之前就终止了。与另一组相比，一组中观察到的肿瘤较少可能是诱发肿瘤数量减少、生长速率降低或两者兼而有之的结果。实验者区分这两种不同的生物学作用至关重要。现有的统计技术没有考虑到这种混杂因素，并且由于它们主要依赖非参数程序，所以不能准确描述潜在的IP剂。在本文中，我们引入了一种参数程序，该程序明确承认了这类实验中存在的混杂因素。分析基于每组肿瘤平均数（λ）和肿瘤出现的平均时间（μ）的比较。较长的平均发生时间被认为表明肿瘤生长速率较慢。开发了假设检验来确定是否存在总体实验效应，确定哪些组对观察到的实验效应有贡献，以及确定导致观察到的组间差异的因素（肿瘤数量和/或生长速率）。还生成了（λ，μ）的置信区域。这种分析有助于更好地理解潜在的IP剂是如何起作用的。
