A major practical impediment when implementing adaptive dose-finding designs is that the toxicity outcome used by the decision rules may not be observed shortly after the initiation of the treatment. To address this issue, we propose the data augment
ation continual reassessment method (DA-CRM) for dose finding. By naturally treating the unobserved toxicities as missing data, we show that such missing data are nonignorable in the sense that the missingness depends on the unobserved outcomes. The Bayesian data augmentation approach is used to sample both the missing data and model parameters from their posterior full conditional distributions. We evaluate the performance of the DA-CRM through extensive simulation studies and also compare it with other existing methods. The results show that the proposed design satisfactorily resolves the issues related to late-onset toxicities and possesses desirable operating characteristics: treating patients more safely and also selecting the maximum tolerated dose with a higher probability. The new DA-CRM is illustrated with two phase I cancer clinical trials.
The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the migration routes
among them. The connections have been so far mostly considered as static, but in general evolve in time. Here we address this case by investigating simple contagion processes on time-varying metapopulation networks. We focus on the SIR process and determine analytically the mobility threshold for the onset of an epidemic spreading in the framework of activity-driven network models. We find profound differences from the case of static networks. The threshold is entirely described by the dynamical parameters defining the average number of instantaneously migrating individuals and does not depend on the properties of the static network representation. Remarkably, the diffusion and contagion processes are slower in time-varying graphs than in their aggregated static counterparts, the mobility threshold being even two orders of magnitude larger in the first case. The presented results confirm the importance of considering the time-varying nature of complex networks.
