Exploring Parameter Relations for Multi-Stage Models in Stage-Wise Constant and Time Dependent Hazard Rates

Abstract

Summary Single cohort stage-frequency data are considered when assessing the stage reached by individuals through destructive sampling. For this type of data, when all hazard rates are assumed constant and equal, Laplace transform methods have been applied in the past to estimate the parameters in each stage-duration distribution and the overall hazard rates. If hazard rates are not all equal, estimating stage-duration parameters using Laplace transform methods becomes complex. In this paper, two new models are proposed to estimate stage-dependent maturation parameters using Laplace transform methods where non-trivial hazard rates apply. The first model encompasses hazard rates that are constant within each stage but vary between stages. The second model encompasses time-dependent hazard rates within stages. Moreover, this paper introduces a method for estimating the hazard rate in each stage for the stage-wise constant hazard rates model. This work presents methods that could be used in specific types of laboratory studies, but the main motivation is to explore the relationships between stage maturation parameters that, in future work, could be exploited in applying Bayesian approaches. The application of the methodology in each model is evaluated using simulated data in order to illustrate the structure of these models.