Stochastic Analysis of Multistate Systems

Abstract

The treatment necessary to remove all cells for a periodic cell cycle specific regimen is analyzed using stochastic equations of a multistate model with state transition governed by residence time distributions. While the objective is to remove all cells, exactly when this occurs is uncertain due to the random timing of state transitions. Previous work has shown that removal of all cells requires great certainty that the number of cells is small; an expected population that is six standard deviations less than one cell is an indicator when cure is nearly likely. In developing the necessary stochastic framework, the expression for the standard deviation for multistate processes is derived and a simple two-state example is presented that illustrates the potential coupling between subpopulations. Finally, the methodology is applied to cell cycle specific chemotherapy and the number of cycles required to nearly be assured that zero cells remain is calculated. This method has computational advantages over Monte Carlo simulations when the initial number of cells is not small and only the variation in the total number of cells is of interest.