Tumor Growth Rate Approximation-Assisted Estimation

Abstract

From tumor to tumor, there is a great variation in the proportion of cancer cells growing and making daughter cells that ultimately metastasize. The differential growth within a single tumor, however, has not been studied extensively and this may be helpful in predicting the aggressiveness of a particular cancer type. The estimation problem of tumor growth rates from several populations is studied. The baseline growth rate estimator is based on a family of interacting particle system models which generalize the linear birth process as models of tumor growth. These interacting models incorporate the spatial structure of the tumor in such a way that growth slows down in a crowded system. Approximation-assisted estimation strategy is proposed when initial values of rates are known from the previous study. Some alternative estimators are suggested and the relative dominance picture of the proposed estimator to the benchmark estimator is investigated. An over-riding theme of this article is that the suggested estimation method extends its traditional counterpart to non-normal populations and to more realistic cases.

Keywords

• growth rate
• interacting particle system
• tumor growth
• approximation-assisted estimation
• linear and non-linear shrinkage estimators
• large-sample bias and risk