Improvement of Parameter Estimations in Tumor Growth Inhibition Models on Xenografted Animals: a Novel Method to Handle the Interval Censoring Caused by Measurement of Smaller Tumors

Abstract

The purpose of this study was to explore the interval censoring induced by caliper measurements on smaller tumors during tumor growth experiments in preclinical studies and to show its impact on parameter estimations. A new approach, the so-called interval-M3 method, is proposed to specifically handle this type of data. Thereby, the interval-M3 method was challenged with different methods (including classical methods for handling below quantification limit values) using Stochastic Simulation and Estimation process to take into account the censoring. In this way, 1000 datasets were simulated under the design of a typical of tumor growth study in xenografted mice, and then, each method was used for parameter estimation on the simulated datasets. Relative bias and relative root mean square error (relative RMSE) were consequently computed for comparison purpose. By not considering the censoring, parameter estimations appeared to be biased and particularly the cytotoxic effect parameter, k 2 , which is the parameter of interest to characterize the efficacy of a compound in oncology. The best performance was noted with the interval-M3 method which properly takes into account the interval censoring induced by caliper measurement, giving overall unbiased estimations for all parameters and especially for the antitumor effect parameter (relative bias = 0.49%, and relative RMSE = 4.06%).

Keywords: below quantification limit; interval censoring; interval-M3 method; simultaneous modeling continuous and categorical data; xenograft model.

Fig. 1

Typical profiles for each dose group (control group in black, 10 μg/kg in red, 45 μg/kg in green, and 100 μg/kg in blue) of the tumor growth model

Fig. 2

Observed versus reported tumor growth volumes: visualization of the interval censoring

Fig. 3

Box plots of ratio of parameter estimates divided by the true parameter for each tested method. λ is the exponential growth parameter, TG₀ is the initial tumor size, k₂ is the cytotoxic effect parameter, and ω_λ ² and ω_k2 ² the corresponding inter individual variance parameters; σ_Prop is the magnitude of the proportional component of the residual error model

Fig. 4

Categorical Visual Predictive Check for method (a) and method (l) for a given dataset. The panels show simulation based 95% confidence intervals (area) around the observations (solid line) for the fraction of censored observations