Computer simulation of clonal growth cancer models. I. Parameter estimation using an iterative absolute bisection...

Quantitative models of the relationship between exposure to chemical carcinogens and carcinogenic response are useful for hypothesis evaluation and risk assessment. The degree to which such models accurately depict the underlying biology is often a function of the need for mathematical tractability. When closed-form expressions are used, the need for tractability may significantly limit their complexity. This problem can be minimized by using numerical computer simulation methods to solve the model, thereby allowing more complex and realistic descriptions of the biology to be used. Unfortunately, formal methods of parameter estimation for numerical models are not as well developed as they are for analytical models. In this report, we develop a formal parameter estimation routine and apply it to a numerical clonal growth simulation (CGS) model of the growth of preneoplastic lesions consisting of initiated cells. An iterative bisection algorithm was used to estimate parameters from time-course data on the number of initiated cells and the number of clones of these cells. The algorithm successfully estimated parameter values to give a best fit to the observed dataset and was robust vis-à-vis starting values of the parameters. Furthermore, the number of data points to which the model was fit, the number of stochastic repetitions and other variables were examined with respect to their effects on the parameter estimates. This algorithm facilitates the application of CGS models for hypothesis evaluation and risk assessment by ensuring uniformity and reproducibility of parameter estimates.