Kim Wonkuk, Ahn Hongshik, Moon Hojin
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA.
Stat Med. 2007 Feb 10;26(3):694-708. doi: 10.1002/sim.2549.
In most survival-sacrifice experiments in animal carcinogenicity studies, the onset of the tumour of interest is not clinically observable. Due to the complexity of constraints for a biological justification, recently developed methods for estimating the tumour onset function and tumour-specific survival function employ computer-intensive numerical solutions. In this paper, closed-form solutions for nonparametric maximum likelihood estimators are derived under explicit and implicit inequality constraints obtained from the monotonicity of the survival functions. Our methods do not require cause-of-death information. The proposed methods can be used to estimate the tumour onset function and the survival function of the tumour of interest. We use the proposed estimators for the development of our new dose-response trend test. A modification of the Poly-k test is made by replacing the time-at-risk weight to a function of the tumour onset survival function. The weighted least square regression method is applied to the estimated survival functions in order to construct a dose-response trend test. A simulation study is conducted to evaluate the performance of the proposed test and compare it with existing trend tests. A real example is used to illustrate the methods.
在大多数动物致癌性研究的生存-牺牲实验中，目标肿瘤的发病在临床上是无法观察到的。由于生物学合理性约束的复杂性，最近开发的用于估计肿瘤发病函数和肿瘤特异性生存函数的方法采用了计算机密集型数值解。在本文中，非参数最大似然估计量的闭式解是在从生存函数的单调性获得的显式和隐式不等式约束下推导出来的。我们的方法不需要死因信息。所提出的方法可用于估计目标肿瘤的发病函数和生存函数。我们使用所提出的估计量来开发新的剂量反应趋势检验。通过将风险时间权重替换为肿瘤发病生存函数的函数，对Poly-k检验进行了修改。将加权最小二乘回归方法应用于估计的生存函数，以构建剂量反应趋势检验。进行了一项模拟研究，以评估所提出检验的性能，并将其与现有趋势检验进行比较。使用一个实际例子来说明这些方法。
