A dose-response test via closed-form solutions for constrained MLEs in survival/sacrifice experiments

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.