Gart J J, Tarone R E
Biometrics. 1987 Mar;43(1):235-44.
Based on asymptotic relative efficiency calculations, Ryan (1985, Biometrics 41, 525-531) concludes that, in the analysis of animal carcinogenicity experiments, age-adjusted tests of tumor rates should be routinely preferred to simple proportions tests for both lethal and nonlethal tumors. We recalculate the asymptotic efficiencies of the simple proportions test relative to the log-rank test for the lethal tumor case. For a simplified model it is shown that the relative efficiency may be easily computed as a function of the crude tumor rate and the survival rate at the time of terminal sacrifice. More generally, we calculate by numerical quadrature the asymptotic relative efficiency for all models considered by Ryan and, using simulations, examine the relevance of asymptotic efficiencies to typical sample sizes. Contrary to the numerical results of Ryan, we find, for experiments with good survival and typical tumor rates, that the relative efficiencies are greater than 95%, usually about 99%. In the nonlethal tumor case, similar results follow from Ryan for tumor rates and survival rates typically encountered in practice. As it is often difficult to determine whether or not a tumor is lethal, we conclude for equal interim mortality rates, that the simple proportions test is usually adequate in evaluating animal carcinogenicity experiments.
基于渐近相对效率计算，瑞安（1985年，《生物统计学》41卷，525 - 531页）得出结论，在动物致癌性实验分析中，对于致死性和非致死性肿瘤，在肿瘤发生率的分析中，年龄调整后的检验通常应优先于简单比例检验。我们重新计算了在致死性肿瘤情况下简单比例检验相对于对数秩检验的渐近效率。对于一个简化模型，结果表明相对效率可以很容易地作为粗肿瘤发生率和终末处死时生存率的函数来计算。更一般地，我们通过数值积分计算了瑞安所考虑的所有模型的渐近相对效率，并通过模拟检验了渐近效率与典型样本量的相关性。与瑞安的数值结果相反，我们发现，对于具有良好生存率和典型肿瘤发生率的实验，相对效率大于95%，通常约为99%。在非致死性肿瘤情况下，对于实际中通常遇到的肿瘤发生率和生存率，瑞安也得出了类似的结果。由于通常很难确定肿瘤是否为致死性，我们得出结论，对于相等的中期死亡率，简单比例检验在评估动物致癌性实验中通常是足够的。
