Parameter estimation of Gompertz model for tumorgrowth: which likelihood to choose?

Abstract The Gompertz model, a mainstay in tumor growth kinetics analysis, requires an accurate likelihood function for its parameterestimation, applicable in both classical and Bayesian methodologies. This study compares five distinct error models, eachrepresenting a different likelihood function. Our comparative analysis employs the Bayesian Information Criterion (BIC), theDeviance Information Criterion (DIC), the Bayes Factor (BF), and hypothesis tests on residuals. Applying these criteria to fitthe Gompertz model to Ehrlich and fibrosarcoma Sa-37 tumor data, we find that error models with tumor volume-dependentdispersion consistently outperform others in quantitative evaluations. However, the conventional Normal error model withconstant variance remains a vital tool, offering significant clinical insights. This study underscores the complexity of likelihoodmodel selection in tumor growth kinetics and highlights the need for a multifaceted approach in such analysis.