Xenograft model is a common in vivo model in cancer research, where human cancer (e.g., sliced tumor tissue blocks, or tumor cells) are grafted and grown in severe combined immunodeficient (scid) nude mice. In cancer drug development, demonstrated anti-tumor activity in this model is an important step to bring a promising experimental treatment to human. These experiments provide important data on the mechanism of action of the drug and for the design of future clinical trials. For therapy with single agent, the experimental design and sample size formulae are quite well established. However, cancer therapy typically involves combination of multiple agents. Such studies should be optimally designed, so that with moderate sample size, the joint action of two drugs can be estimated and the best combinations identified. A typical outcome variable in these experiments is tumor volume measured over a period of time. The resulting data have several unique features. Since a mouse may die during the experiment or may be sacrificed when its tumor volume quadruples, then incomplete repeated measurements arise. The incompleteness or missingness is also caused by drastic tumor shrinkage (<0.01 cm3) or random truncation. In addition, if no treatment were given to the tumor-bearing mice, the tumors would keep growing until the mice die or are sacrificed. This intrinsic growth of tumor in the absence of treatment constrains the parameters in the regression and causes further difficulties in statistical analysis. This chapter reviews the current methods of experimental design and data analysis for xenograft experiments. We describe the optimal experimental design for combination studies in xenograft models and likelihood-based methods for estimating the dose-response relationship while accounting for the special features of data such as informative censoring and model parameter constraints.
