Repeated-measures models with constrained parameters for incomplete data in tumour xenograft experiments

Abstract

In cancer drug development, xenograft experiments (models) where mice are grafted with human cancer cells are used to elucidate the mechanism of action and/or to assess efficacy of a promising compound. Demonstrated activity in this model is an important step to bring a promising compound to humans. A key outcome variable in these experiments is tumour volumes measured over a period of time, while mice are treated with an anticancer agent following certain schedules. However, a mouse may die during the experiment or may be sacrificed when its tumour volume quadruples and then incomplete repeated measurements arise. The incompleteness or missingness is also caused by drastic tumour shrinkage (<0.01 cm3) or random truncation. In addition, if no treatment were given to the tumour-bearing mice, the tumours would keep growing until the mice die or are sacrificed. This intrinsic growth of tumour in the absence of treatment constrains the parameters in the regression and causes further difficulties in statistical analysis. We develop a maximum likelihood method based on the expectation/conditional maximization (ECM) algorithm to estimate the dose-response relationship while accounting for the informative censoring and the constraints of model parameters. A real xenograft study on a new anti-tumour agent temozolomide combined with irinotecan is analysed using the proposed method.

Tumor models for efficacy determination

“…The results showed that irinotecan was highly active whereas temozolomide had little activity in the Rh18 xenograft. The data analysis showed some evidence for synergism but it fell short of statistical significance (39).…”

“…Response surface modeling provides an effective statistical approach to modeling complex patterns of synergy, additivity, and antagonism in the same data set (39,88). Tan et al (39) developed a class of repeated-measures models to analyze the dose-response relationship in xenograft experiments while accounting for incomplete (missing at random and informative censoring) and variable constraints.…”

“…Tan et al (39) developed a class of repeated-measures models to analyze the dose-response relationship in xenograft experiments while accounting for incomplete (missing at random and informative censoring) and variable constraints. The method is based on the expectation/conditional maximization algorithm to estimate the dose-response relationship.…”

Contributions of Human Tumor Xenografts to Anticancer Drug Development

“…Not all tumor systems are useful for study, with for example, the occurrence of ''no takes, '' rendering the statistical definition of activity problematic (6). Guidance and advice from a biostatistical consultant is key and plays to the value of mouse xenografts in contrast to transgenic systems in that appropriately staged tumors can be reliably and economically generated to allow evaluation of a series of compounds (19). Second, as we evolve toward the more routine evaluation of targeted therapeutics, for a new molecular entity whose target is defined, understanding the in vitro area under the pharmacologic plasma concentration-time curve producing the desired target effect is an essential piece of information that is not as frequently addressed as it should.…”

Improved Statistical Modeling of Tumor Growth and Treatment Effect in Preclinical Animal Studies with Highly Heterogeneous Responses In Vivo

“…In particular, mixed-effects models have become a convenient approach to model various experimental factors, such as treatment effects or base levels (fixed effects) while accounting for variation expressed by individual animals or tumors (random effects). This model family has successfully been used to analyze specific types of xenograft experiments or study questions (12)(13)(14)(15)(16)(17). However, further challenges remain.…”