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 vast majority of strategies aimed at controlling contagion processes on networks considers the connectivity pattern of the system as either quenched or annealed. However, in the real world many networks are highly dynamical and evolve in time con
currently to the contagion process. Here, we derive an analytical framework for the study of control strategies specifically devised for time-varying networks. We consider the removal/immunization of individual nodes according the their activity in the network and develop a block variable mean-field approach that allows the derivation of the equations describing the evolution of the contagion process concurrently to the network dynamic. We derive the critical immunization threshold and assess the effectiveness of the control strategies. Finally, we validate the theoretical picture by simulating numerically the information spreading process and control strategies in both synthetic networks and a large-scale, real-world mobile telephone call dataset
Interval designs are a class of phase I trial designs for which the decision of dose assignment is determined by comparing the observed toxicity rate at the current dose with a prespecified (toxicity tolerance) interval. If the observed toxicity rate
is located within the interval, we retain the current dose; if the observed toxicity rate is greater than the upper boundary of the interval, we deescalate the dose; and if the observed toxicity rate is smaller than the lower boundary of the interval, we escalate the dose. The most critical issue for the interval design is choosing an appropriate interval so that the design has good operating characteristics. By casting dose finding as a Bayesian decision-making problem, we propose new flexible methods to select the interval boundaries so as to minimize the probability of inappropriate dose assignment for patients. We show, both theoretically and numerically, that the resulting optimal interval designs not only have desirable finite- and large-sample properties, but also are particularly easy to implement in practice. Compared to existing designs, the proposed (local) optimal design has comparable average performance, but a lower risk of yielding a poorly performing clinical trial.
We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the
exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.
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.
We propose a generalized framework for the study of voter models in complex networks at the the heterogeneous mean-field (HMF) level that (i) yields a unified picture for existing copy/invasion processes and (ii) allows for the introduction of furthe
r heterogeneity through degree-selectivity rules. In the context of the HMF approximation, our model is capable of providing straightforward estimates for central quantities such as the exit probability and the consensus/fixation time, based on the statistical properties of the complex network alone. The HMF approach has the advantage of being readily applicable also in those cases in which exact solutions are difficult to work out. Finally, the unified formalism allows one to understand previously proposed voter-like processes as simple limits of the generalized model.
