Chenlin Cheng - Randomized Gompertzian Growth Models for Solid Rat Tumors

Abstract

This project is concerned with parameter estimation for growth curves in implanted tumors in rats. The Gompertz curve, an asymmetric sigmoid, and its corresponding first order nonlinear differential equation was used as the model. The model has 3 parameters: r -- a growth rate, K -- the saturation value, the variance parameter in the noise term. The data consisted of measurements every 7 days up to day 77 on two groups of rats, one with initial size 63 mg, and the other 108 mg. This is a subset of the data used in Simpson-Herren and Lloyd, Cancer Chemotherapy Reports 54:143-174 (1970). Conditional on knowing the value of K, a double log transformation reduces the problem to a linear regression model. The value of K was determined by optimizing the coefficient of determination, R^2, of the linear regression model over different values of K. The estimated parameters for one group of rats were used to fit the other group with only the initial condition changed.