A comparison of least squares and conditional maximum likelihood estimators under volume endpoint censoring in tumor growth experiments

Abstract

Measurements in tumor growth experiments are stopped once the tumor volume exceeds a preset threshold: a mechanism we term volume endpoint censoring. We argue that this type of censoring is informative. Further, least squares (LS) parameter estimates are shown to suffer a bias in a general parametric model for tumor growth with an independent and identically distributed measurement error, both theoretically and in simulation experiments. In a linear growth model, the magnitude of bias in the LS growth rate estimate increases with the growth rate and the standard deviation of measurement error. We propose a conditional maximum likelihood estimation procedure, which is shown both theoretically and in simulation experiments to yield approximately unbiased parameter estimates in linear and quadratic growth models. Both LS and maximum likelihood estimators have similar variance characteristics. In simulation studies, these properties appear to extend to the case of moderately dependent measurement error. The methodology is illustrated by application to a tumor growth study for an ovarian cancer cell line.