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The STEP 1 randomized trial evaluated the effect of taking semaglutide vs placebo on body weight over a 68 week duration. As with any study evaluating an intervention delivered over a sustained period, non-adherence was observed. This was addressed in the original trial analysis within the Estimand Framework by viewing non-adherence as an intercurrent event. The primary analysis applied a treatment policy strategy which viewed it as an aspect of the treatment regimen, and thus made no adjustment for its presence. A supplementary analysis used a hypothetical strategy, targeting an estimand that would have been realised had all participants adhered, under the assumption that no post-baseline variables confounded adherence and change in body weight. In this paper we propose an alternative Instrumental Variable method to adjust for non-adherence which does not rely on the same `unconfoundedness' assumption and is less vulnerable to positivity violations (e.g., it can give valid results even under conditions where non-adherence is guaranteed). Unlike many previous Instrumental Variable approaches, it makes full use of the repeatedly measured outcome data, and allows for a time-varying effect of treatment adherence on a participant's weight. We show that it provides a natural vehicle for defining two distinct hypothetical estimands: the treatment effect if all participants would have adhered to semaglutide, and the treatment effect if all participants would have adhered to both semaglutide and placebo. When applied to the STEP 1 study, they both suggest a sustained, slowly decaying weight loss effect of semaglutide treatment.

Quantitative decision-making (QDM) principles address the issues related to the mapping of results to decisions, the synthesis of information and the quantification of uncertainty. Since the clinical drug development involves a succession of decisions to be made, QDM methods can be applied at various levels. At the study level, it can be used to properly design a study, and improve the decisions that are made either during the trial or at its end. Establishing decision criteria ahead of the study is essential here to address the need for speedy decisions, potentially in real time. At the project level, QDM can be used to inform decisions to continue, adapt or stop a drug development programme based on results from previous studies. At the portfolio level, QDM can be used to choose, prioritise and optimise the development portfolio, e.g. using the probability to reach market access or target sales within a predefined timeline. The increasing interest in QDM and its statistical nature led in 2017 to the development a cross-industry and academia Special Interest Group on QDM within the Society and the European Federation of Statisticians in the Pharmaceutical Industry (PSI and EFSPI). The activities of the group included discussing QDM examples, some published in the literature and some real anonymised ones covering several settings. While the methodologies, and to some extent the terminology, employed also varied depending on the context, discussions within the group distilled common principles to be considered when implementing QDM, particularly around the construction of QDM frameworks, assessment of operating characteristics and communication with the clinical team. The present manuscript presents those points to consider, hoping they can be helpful to statisticians interested in implementing QDM., Comment: 14 pages, 1 table, 3 figures

We present a minimal model for simulating dynamics of assorted lipid assemblies in a computationally efficient manner. Our model is particle-based and consists of coarse-grained beads put together on a modular platform to give generic molecular lipids with tunable properties. The interaction between coarse-grained beads is governed by soft, short-ranged potentials that account for the renormalized hydrophobic effect in implicit solvent. The model faithfully forms micelles, tubular micelles, or bilayers (periodically infinite, bicelles, or vesicles) depending on the packing ratio of the lipid molecules. Importantly, for the self-assembled bilayer membranes it is straightforward to realize gel and fluid phases, the latter of which is most often of primary interest. We show that the emerging physics over a wide range of scales and resolutions is (with some restrictions) universal. The model, when compared to other popular lipid models, demonstrates improvements in the form of increased numerical stability and boosted dynamics. Possible strategies for customizing the models (e.g., adding chemical specificity) are briefly discussed. An implementation is available for the LAMMPS molecular dynamics simulator [Plimpton. J. Comp. Phys. 117, 1-19. (1995)] including illustrative input examples from the simulations we present., Comment: 9 pages, 11 figures, supplemental material online at https://doi.org/10.5281/zenodo.3479543

We generalize the notion of planar bicycle tracks -- a.k.a. one-trailer systems -- to so-called tractor/tractrix systems in general Riemannian manifolds and prove explicit expressions for the length of the ensuing tractrices and for the area of the domains that are swept out by any given tractor/tractrix system. These expressions are sensitive to the curvatures of the ambient Riemannian manifold, and we prove explicit estimates for them based on Rauch's and Toponogov's comparison theorems. Moreover, the general length shortening property of tractor/tractrix systems is used to generate geodesics in homotopy classes of curves in the ambient manifold., Comment: 29 pages, 15 figures