Seamless phase II/III designs

In recent years, there has been a drive to save development costs and shorten time-to-market of new therapies. Research into novel trial designs to facilitate this goal has led to, amongst other approaches, the development of methodology for seamless phase II/III designs. Such designs allow treatment or dose selection at an interim analysis and comparative evaluation of efficacy with control, in the same study. Methods have gained much attention because of their potential advantages compared to conventional drug development programmes with separate trials for individual phases. In this article, we review the various approaches to seamless phase II/III designs based upon the group-sequential approach, the combination test approach and the adaptive Dunnett method. The objective of this article is to describe the approaches in a unified framework and highlight their similarities and differences to allow choice of an appropriate methodology by a trialist considering conducting such a trial.

Correction of atmospheric delay effects in radar interferometry using a nested mesoscale atmospheric model

The temporal variability of the atmosphere through which radio waves pass in the technique of differential radar interferometry can seriously limit the accuracy with which the method can measure surface motion. A forward, nested mesoscale model of the atmosphere can be used to simulate the variable water content along the radar path and the resultant phase delays. Using this approach we demonstrate how to correct an interferogram of Mount Etna in Sicily associated with an eruption in 2004-5. The regional mesoscale model (Unified Model) used to simulate the atmosphere at higher resolutions consists of four nested domains increasing in resolution (12, 4, 1, 0.3 km), sitting within the analysis version of a global numerical model that is used to initiate the simulation. Using the high resolution 3D model output we compute the surface pressure, temperature and the water vapour, liquid and solid water contents, enabling the dominant hydrostatic and wet delays to be calculated at specific times corresponding to the acquisition of the radar data. We can also simulate the second-order delay effects due to liquid water and ice.

Four-dimensional data assimilation and balanced dynamics

The problem of spurious excitation of gravity waves in the context of four-dimensional data assimilation is investigated using a simple model of balanced dynamics. The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode, and can be initialized such that the model evolves on a so-called slow manifold, where the fast motion is suppressed. Identical twin assimilation experiments are performed, comparing the extended and ensemble Kalman filters (EKF and EnKF, respectively). The EKF uses a tangent linear model (TLM) to estimate the evolution of forecast error statistics in time, whereas the EnKF uses the statistics of an ensemble of nonlinear model integrations. Specifically, the case is examined where the true state is balanced, but observation errors project onto all degrees of freedom, including the fast modes. It is shown that the EKF and EnKF will assimilate observations in a balanced way only if certain assumptions hold, and that, outside of ideal cases (i.e., with very frequent observations), dynamical balance can easily be lost in the assimilation. For the EKF, the repeated adjustment of the covariances by the assimilation of observations can easily unbalance the TLM, and destroy the assumptions on which balanced assimilation rests. It is shown that an important factor is the choice of initial forecast error covariance matrix. A balance-constrained EKF is described and compared to the standard EKF, and shown to offer significant improvement for observation frequencies where balance in the standard EKF is lost. The EnKF is advantageous in that balance in the error covariances relies only on a balanced forecast ensemble, and that the analysis step is an ensemble-mean operation. Numerical experiments show that the EnKF may be preferable to the EKF in terms of balance, though its validity is limited by ensemble size. It is also found that overobserving can lead to a more unbalanced forecast ensemble and thus to an unbalanced analysis.

Free gravity waves and balanced dynamics

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol’skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

Fine-grained multi-phase array designs

Hybrid multiprocessor architectures which combine re-configurable computing and multiprocessors on a chip are being proposed to transcend the performance of standard multi-core parallel systems. Both fine-grained and coarse-grained parallel algorithm implementations are feasible in such hybrid frameworks. A compositional strategy for designing fine-grained multi-phase regular processor arrays to target hybrid architectures is presented in this paper. The method is based on deriving component designs using classical regular array techniques and composing the components into a unified global design. Effective designs with phase-changes and data routing at run-time are characteristics of these designs. In order to describe the data transfer between phases, the concept of communication domain is introduced so that the producer–consumer relationship arising from multi-phase computation can be treated in a unified way as a data routing phase. This technique is applied to derive new designs of multi-phase regular arrays with different dataflow between phases of computation.

Balanced excitation and inhibition: Model based analysis of local field potentials

We have developed a model of the local field potential (LFP) based on the conservation of charge, the independence principle of ionic flows and the classical Hodgkin–Huxley (HH) type intracellular model of synaptic activity. Insights were gained through the simulation of the HH intracellular model on the nonlinear relationship between the balance of synaptic conductances and that of post-synaptic currents. The latter is dependent not only on the former, but also on the temporal lag between the excitatory and inhibitory conductances, as well as the strength of the afferent signal. The proposed LFP model provides a method for decomposing the LFP recordings near the soma of layer IV pyramidal neurons in the barrel cortex of anaesthetised rats into two highly correlated components with opposite polarity. The temporal dynamics and the proportional balance of the two components are comparable to the excitatory and inhibitory post-synaptic currents computed from the HH model. This suggests that the two components of the LFP reflect the underlying excitatory and inhibitory post-synaptic currents of the local neural population. We further used the model to decompose a sequence of evoked LFP responses under repetitive electrical stimulation (5 Hz) of the whisker pad. We found that as neural responses adapted, the excitatory and inhibitory components also adapted proportionately, while the temporal lag between the onsets of the two components increased during frequency adaptation. Our results demonstrated that the balance between neural excitation and inhibition can be investigated using extracellular recordings. Extension of the model to incorporate multiple compartments should allow more quantitative interpretations of surface Electroencephalography (EEG) recordings into components reflecting the excitatory, inhibitory and passive ionic current flows generated by local neural populations.

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.

Missing steps in a staircase: a qualitative study of the perspectives of key stakeholders on the use of adaptive designs in confirmatory trials

Background Despite the promising benefits of adaptive designs (ADs), their routine use, especially in confirmatory trials, is lagging behind the prominence given to them in the statistical literature. Much of the previous research to understand barriers and potential facilitators to the use of ADs has been driven from a pharmaceutical drug development perspective, with little focus on trials in the public sector. In this paper, we explore key stakeholders’ experiences, perceptions and views on barriers and facilitators to the use of ADs in publicly funded confirmatory trials. Methods Semi-structured, in-depth interviews of key stakeholders in clinical trials research (CTU directors, funding board and panel members, statisticians, regulators, chief investigators, data monitoring committee members and health economists) were conducted through telephone or face-to-face sessions, predominantly in the UK. We purposively selected participants sequentially to optimise maximum variation in views and experiences. We employed the framework approach to analyse the qualitative data. Results We interviewed 27 participants. We found some of the perceived barriers to be: lack of knowledge and experience coupled with paucity of case studies, lack of applied training, degree of reluctance to use ADs, lack of bridge funding and time to support design work, lack of statistical expertise, some anxiety about the impact of early trial stopping on researchers’ employment contracts, lack of understanding of acceptable scope of ADs and when ADs are appropriate, and statistical and practical complexities. Reluctance to use ADs seemed to be influenced by: therapeutic area, unfamiliarity, concerns about their robustness in decision-making and acceptability of findings to change practice, perceived complexities and proposed type of AD, among others. Conclusions There are still considerable multifaceted, individual and organisational obstacles to be addressed to improve uptake, and successful implementation of ADs when appropriate. Nevertheless, inferred positive change in attitudes and receptiveness towards the appropriate use of ADs by public funders are supportive and are a stepping stone for the future utilisation of ADs by researchers.

Generic construction of monitors for floating point unit designs

This paper proposes a set of well defined steps to design functional verification monitors intended to verify Floating Point Units (FPU) described in HDL. The first step consists on defining the input and output domain coverage. Next, the corner cases are defined. Finally, an already verified reference model is used in order to test the correctness of the Device Under Verification (DUV). As a case study a monitor for an IEEE754-2008 compliant design is implemented. This monitor is built to be easily instantiated into verification frameworks such as OVM. Two different designs were verified reaching complete input coverage and successful compliant results.