Abstract: In cancer drug development, demonstrated efficacy in tumor xenograft models is an important step to bring a promising compound to human. A key outcome variable is tumor volume measured over a period of time, while mice are treated with certain treatment regimens. The statistical challenges include that sample sizes in xenograft experiments are usually limited because these experiments are costly, tumors in mice without treatment would keep growing until the tumor-bearing mice die or are sacrificed, and missing data are unavoidable because a mouse may die of toxicity or may be sacrificed when its tumor volume reaches certain threshold (i.e. quadruples) or the tumor volume is too small and becomes unmeasurable. Furthermore, since the drug concentration in the blood of a mouse or its tissues may be stabilized at a certain level and maintained during a period of time, the treatment effect due to sustained drug release in tumor xenograft models should be taken into account. In this talk I will focus on this issue. We propose a novel comprehensive statistical model that accounts for the sustained release effects in tumor xenograft experiments and parameter constraints with incomplete longitudinal data. The ECM algorithm and Gibbs sampling for incomplete data are applied to estimating the dose-response relationship in the proposed model. The model selection based on likelihood functions is given and a simulation study is conducted to investigate the performance of the proposed estimator. A real xenograft study on the antitumor agent temozolomide combined with irinotecan against the rhabdomyosarcoma is analyzed using the proposed methods.

Abstract: We show that any k-uniform hypergraph with n edges contains two edge disjoint subgraphs of size Ω̃(n^2/(k+1)) for k=4, 5, and 6. This is best possible up to a logarithmic factor due to a upper bound construction of Erdős, Pach, and Pyber who show there exist k-uniform hypergraphs with n edges and with no two edge disjoint isomorphic subgraphs with size larger than $Õ(n^2/(k+1))$. Furthermore, our result extends results of Erdős, Pach and Pyber who also established the lower bound for k=2 (i.e. for graphs), and of Gould and Rödl who established the result for k=3. In this talk, we'll discuss some of the main ideas of the proof, which is probabilistic, and the obstructions which prevent us from establishing the result for higher values of k.