A comparison of a mixture likelihood method and the EM algorithm for an estimation problem in animal carcinogenicity studies

Both a mixture likelihood method and the EM algorithm are implemented to estimate the time-to-onset-of and the time-to-death-from the tumor of interest in animal carcinogenicity studies. Both methods are implemented using Box's Complex Method for finding the maximum likelihood estimates of parameters for a nonlinear log-likelihood function subject to nonlinear inequality constraints. A comparison of the mixture likelihood method with the EM algorithm suggests that the mixture method may be more efficient for the problem of constrained nonparametric maximum likelihood estimation in carcinogenicity studies. The advantages of using the mixture likelihood method are illustrated with data from benzidine dihydrochloride and caloric restriction studies.