AN IMPROVED APPROXIMATION TO THE EXACT SOLUTION OF THE 2-STAGE CLONALGROWTH-MODEL OF CANCER

Multistage clonal growth models are of interest for cancer risk assess ment because they can explicitly incorporate data on cell replication. Both approximate and exact formulations of the two stage growth model have been described. The exact solution considers the conditional pro bability of tumors arising in previously tumor-free animals; the appro ximate solution estimates total probability of tumor formation. The ex act solution is much more computationally intensive when time-dependen t cell growth parameters are included. The approximate solution deviat es from the exact solution at high incidences and probabilities of tum or. This report describes a computationally tractable, 'improved appro ximation' to the exact solution. Our improved approximation includes a correction term to adjust the unconditional expectation of intermedia te cells based on the time history of formation of intermediate cells by mutation of normal cells (recruitment) or by cell division in the i ntermediate cell population (expansion). The improved approximation pr ovided a much better match to the exact solution than the approximate solution for a wide range of parameter values. The correction term als o appears to provide insight into the biological factors that contribu te to the variance of the expectation for the number of intermediate c ells over time.