Improvement of parameter estimations in tumor growth inhibition models on xenografted animals: a novel method to handle the interval-censoring caused by experimental measurement on smaller tumor sizes
Pierrillas Philippe (1), Tod Michel (1), Bouzom François (2), Hénin Emilie (1)
(1) Université Claude Bernard, Lyon, France ; EMR 3738 Ciblage Thérapeutique en Oncologie (2) Technologie Servier, Orléans, France
Objectives: Censored data is a practical and overriding question when analysing data and handling it does not yield to a unique and simple answer. If not considered properly, censoring may cause bias and misspecification during data analysis [1,2]. The xenografted mice model is a widely used experimental model to evaluate anticancer effects of new compounds and possibly predict the efficacy in human thanks to translational approaches [3]. During tumor growth experiments on xenografted mice, the tumor size is measured by a technical operator using a caliper, and reported as the measures of 2 diameters, often converted into tumor volumes. For smaller tumor sizes, due to the imprecision induced by skin thickness and palpability of the tumor, when the length/width is less than 5 mm, reported tumor diameters are rounded to the nearest integer value, resulting in interval-censored tumor volumes. Hence we propose and evaluate a method to handle interval-censored data.
Methods: Different methods to handle this interval-censoring (including standard methods for handling below quantification limit values and our new method, the so-called interval-M3 method considering the likelihood of observations being in each interval) were compared using Stochastic Simulations and Estimations processes: 1000 datasets were simulated under a classical design of tumor growth experimental study in xenografted mice and then model parameters were estimated in each simulated datasets for each method. Simulation-based diagnostics, relative bias and relative root mean square error were consequently computed to compare each method.
Results: By not considering correctly the interval-censoring and by omitting or applying classical methods used for censored data, model parameter estimations appeared to be biased and especially the antitumor effect parameter, whose information lies mainly on smaller tumor volumes. Overall, the best performance was noted with the interval-M3 method giving less biased and more precise estimations for parameters (|bias|<0.55% and RMSE<12% for typical parameters) whereas for classical methods bias could reach up to 15%.
Conclusions: We showed that during xenograft mice experiments, parameters estimations with classical methods could be biased due to the limitation of caliper measurement. The new method proposed here, can thus be used to estimate parameters as precisely as possible and to optimally handle all the information provided by the available data in order to quantify the antitumor effect.
References:
[1] Beal SL (2001) Ways to fit a PK model with some data below the quantification limit. Journal of pharmacokinetics and pharmacodynamics 28 (5):481-504
[2] Bergstrand M, Karlsson MO (2009) Handling data below the limit of quantification in mixed effect models. The AAPS journal 11 (2):371-380. doi:10.1208/s12248-009-9112-5
[3] Rocchetti M, Simeoni M, Pesenti E, De Nicolao G, Poggesi I (2007) Predicting the active doses in humans from animal studies: a novel approach in oncology. Eur J Cancer 43 (12):1862-1868. doi:S0959-8049(07)00380-2 [pii] 10.1016/j.ejca.2007.05.011