Estimating multiple tumor transition rates based on data from survival-sacrifice experiments

The development of two types of tumors in an animal survival-sacrifice experiment can be described by a Markov illness-and-death process with four unknown tumor transition rates and four unknown death rates. Due to the occult nature of tumors, these transition rates cannot be identified through the use of a completely nonparametric model. We propose a semiparametric model that assumes that the four tumor transition rates are proportional to each other and can be described by a known parametric function. We show that these tumor transition rates can be estimated using an ECM algorithm and that inferences about these parameters can be drawn using the likelihood ratio test. We illustrate this model and the algorithm with data from the ED01 study.