A Newton-based approach for attributing tumor lethality in animal carcinogenicity studies

A new Newton-based approach is proposed for finding the global maximum of a nonlinear function subject to various inequality constraints. This method can be applied to nonparametric maximum likelihood estimation problems to attribute tumor lethality in long-term carcinogenicity studies. This method is substantially faster and easier to implement than the Complex Method used in Ahn et al. (2000). This approach is very useful especially when there exist a large number of parameters of interest to be estimated and many nonlinear inequality constraints. A Monte Carlo simulation study is conducted to evaluate the computational efficiency and accuracy of the estimates obtained from the new approach. The advantages of using the Newton-based approach are illustrated with a real data set.