Efficient designs for three-sequence stepped wedge trials with continuous recruitment

BACKGROUND/AIMS

The standard approach to designing stepped wedge trials that recruit participants in a continuous stream is to divide time into periods of equal length. But the choice of design in such cases is infinitely more flexible: each cluster could cross from the control to the intervention at any point on the continuous time-scale. We consider the case of a stepped wedge design with clusters randomised to just three sequences (designs with small numbers of sequences may be preferred for their simplicity and practicality) and investigate the choice of design that minimises the variance of the treatment effect estimator under different assumptions about the intra-cluster correlation.

METHODS

We make some simplifying assumptions in order to calculate the variance: in particular that we recruit the same number of participants, m , from each cluster over the course of the trial, and that participants present at regularly spaced intervals. We consider an intra-cluster correlation that decays exponentially with separation in time between the presentation of two individuals from the same cluster, from a value of ρ for two individuals who present at the same time, to a value of ρ τ for individuals presenting at the start and end of the trial recruitment interval. We restrict attention to three-sequence designs with centrosymmetry - the property that if we reverse time and swap the intervention and control conditions then the design looks the same. We obtain an expression for the variance of the treatment effect estimator adjusted for effects of time, using methods for generalised least squares estimation, and we evaluate this expression numerically for different designs, and for different parameter values.

RESULTS

There is a two-dimensional space of possible three-sequence, centrosymmetric stepped wedge designs with continuous recruitment. The variance of the treatment effect estimator for given ρ and τ can be plotted as a contour map over this space. The shape of this variance surface depends on τ and on the parameter m ρ / ( 1 - ρ ) , but typically indicates a broad, flat region of close-to-optimal designs. The 'standard' design with equally spaced periods and 1:1:1 allocation rarely performs well, however.

CONCLUSIONS

In many different settings, a relatively simple design can be found (e.g. one based on simple fractions) that offers close-to-optimal efficiency in that setting. There may also be designs that are robustly efficient over a wide range of settings. Contour maps of the kind we illustrate can help guide this choice. If efficiency is offered as one of the justifications for using a stepped wedge design, then it is worth designing with optimal efficiency in mind.

Enhanced second harmonic generation from a quasi-periodic silver dendritic metasurface

The preparation of the vast majority of nonlinear optical metal metasurfaces currently relies on complex top-down methods such as electron beam or ion beam etching, which are expensive and difficult to meet the requirement of large area preparation. In this paper, an easily prepared quasi-periodic silver dendritic metasurface model with highQfactor is established in the near-infrared band based on a simple and easy-to-operate electrochemical deposition method. The simulations prove that the silver dendritic metasurface has a highQfactor (exceeds 104) because of its strong electric field localization ability, which is analogous to the superposition of multiple split-ring resonators. It is demonstrated that the second harmonic generation (SHG) intensity of the dendritic metasurface at a large incident angle (such as 85°) is about 30 times that of the metasurface at a small incident angle when thex-polarized pump light is incident obliquely to break the centrosymmetry of the metasurface. The influences of the incident angle or dendritic structure's dimensions on theQfactor and SHG efficiency have also been researched through a lot of simulation. This easily prepared quasi-periodic silver dendritic metasurface SHG device may provide a new avenue for the development and application of miniature, integratable nonlinear optical devices.

Generalizing the information content for stepped wedge designs: A marginal modeling approach

Stepped wedge trials are increasingly adopted because practical constraints necessitate staggered roll-out. While a complete design requires clusters to collect data in all periods, resource and patient-centered considerations may call for an incomplete stepped wedge design to minimize data collection burden. To study incomplete designs, we expand the metric of information content to discrete outcomes. We operate under a marginal model with general link and variance functions, and derive information content expressions when data elements (cells, sequences, periods) are omitted. We show that the centrosymmetric patterns of information content can hold for discrete outcomes with the variance-stabilizing link function. We perform numerical studies under the canonical link function, and find that while the patterns of information content for cells are approximately centrosymmetric for all examined underlying secular trends, the patterns of information content for sequences or periods are more sensitive to the secular trend, and may be far from centrosymmetric.

The first non-helical Aib-containing hexapeptide: The crystal structure of Z-Gly-Aib-Gly-Aib-Gly-Aib-OtBu

The synthetic peptide Z-Gly-Aib-Gly-Aib-Gly-Aib-OtBu was crystallized from a mixture of ethyl acetate and n-hexane. The crystals belong to the centrosymmetric space group Pbca. There are three molecules in the asymmetric unit. The three molecules differ mainly in the Z-group conformation. The first Gly residue adopts a fully extended conformation, residues 2 and 3 lie in the left-handed helical region, residues 4 and 5 in the right-handed helical region, and residue 6 again in the left-handed helical region of the Ramachandran plot. There are only two of four possible intramolecular hydrogen bonds formed, namely, between Aib4 and Gly1 forming a β-turn of type III' and between Aib6 and Gly3 forming a β-turn of type I. The inverted molecules (by space group symmetry) lie in the regions with opposite handedness and form β-turns of type III and I'. In contrast to all known long synthetic and naturally occurring Aib-containing peptides that fold as 3₁₀ - or α-helix, Z-(Gly-Aib)₃ -OtBu folds in a quite flat structure from which only the protecting groups bulge out.