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Generalized Norton‐Simon models of tumour growth
Author(s) -
Heitjan Daniel F.
Publication year - 1991
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780100708
Subject(s) - growth curve (statistics) , autocorrelation , logistic function , generalization , parametric model , growth model , mathematics , function (biology) , monte carlo method , parametric statistics , statistics , logistic regression , biology , mathematical analysis , mathematical economics , evolutionary biology
This paper considers the analysis of serial data on the growth of tumours in laboratory rodents. I propose a model ‐ a generalization of the tumour growth model of Norton and Simon ‐ that leads to a rich family of growth and decay curves. The model assumes that unperturbed growth follows the generalized logistic form; it accommodates time‐varying treatment effects through an effective dose function. I fit two such models to data on a human prostate tumour growing in nude mice and compare the fitted curves and dose functions with a non‐parametric curve and dose function estimated from a cubic spline model. All three models account for both random animal effects and autocorrelation. Monte Carlo results suggest that (a) maximum likelihood estimates of growth parameters are biased, although not severely, and (b) standard errors are conservative in small samples but become increasingly accurate in larger samples.