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Treatment of cancer has rapidly evolved over time in quite dramatic ways, for example from chemotherapies, targeted therapies to immunotherapies and chimeric antigen receptor T-cells. Nonetheless, the basic design of early phase I trials in oncology still follows pre-dominantly a dose-escalation design. These trials monitor safety over the first treatment cycle in order to escalate the dose of the investigated drug. However, over time studying additional factors such as drug combinations and/or variation in the timing of dosing became important as well. Existing designs were continuously enhanced and expanded to account for increased trial complexity. With toxicities occurring at later stages beyond the first cycle and the need to treat patients over multiple cycles, the focus on the first treatment cycle only is becoming a limitation in nowadays multi-cycle treatment therapies. Here we introduce a multi-cycle time-to-event model (TITE-CLRM: Time-Interval-To-Event Complementary-Loglog Regression Model) allowing guidance of dose-escalation trials studying multi-cycle therapies. The challenge lies in balancing the need to monitor safety of longer treatment periods with the need to continuously enroll patients safely. The proposed multi-cycle time to event model is formulated as an extension to established concepts like the escalation with over dose control principle. The model is motivated from a current drug development project and evaluated in a simulation study., Comment: 18 pages, 8 figures, 1 table, 4 supplementary figures

Duration of response (DOR) and time to response (TTR) are typically evaluated as secondary endpoints in early-stage clinical studies in oncology when efficacy is assessed by the best overall response (BOR) and presented as the overall response rate (ORR). Despite common use of DOR and TTR in particular in single-arm studies, the definition of these endpoints and the questions they are intended to answer remain unclear. Motivated by the estimand framework, we present relevant scientific questions of interest for DOR and TTR and propose corresponding estimand definitions. We elaborate on how to deal with relevant intercurrent events which should follow the same considerations as implemented for the primary response estimand. A case study in mantle cell lymphoma illustrates the implementation of relevant estimands of DOR and TTR. We close the paper with practical recommendations to implement DOR and TTR in clinical study protocols.

A net $(x_\gamma)_{\gamma\in\Gamma}$ in a locally solid Riesz space $(X,\tau)$ is said to be unbounded $\tau$-convergent to $x$ if $|x_\gamma-x|\wedge u\mathop{\overset{\tau}{\longrightarrow}} 0$ for all $u\in X_+$. We recall that there is a locally solid linear topology $\mathfrak{u}\tau$ on $X$ such that unbounded $\tau$-convergence coincides with $\mathfrak{u}\tau$-convergence, and moreover, $\mathfrak{u}\tau$ is characterised as the weakest locally solid linear topology which coincides with $\tau$ on all order bounded subsets. It is with this motivation that we introduce, for a uniform lattice $(L,u)$, the weakest lattice uniformity $u^\ast$ on $L$ that coincides with $u$ on all the order bounded subsets of $L$. It is shown that if $u$ is the uniformity induced by the topology of a locally solid Riesz space $(X,\tau)$, then the $u^*$-topology coincides with $\mathfrak{u}\tau$. This allows comparing the results of this paper with earlier results on unbounded $\tau$-convergence. It will be seen that despite the fact that in the setup of uniform lattices most of the machinery used in the techniques of [M. A. Taylor 2019: Unbounded topologies and uo-convergence in locally solid vector spaces, J. Math. Anal. Appl. \bf{472} no.1, 981--1000] is lacking, the concept of `unbounded convergence' well fittingly generalizes to uniform lattices. We shall also answer Questions 2.13, 3.3, 5.10 of [M. A. Taylor 2019: Unbounded topologies and uo-convergence in locally solid vector spaces, J. Math. Anal. Appl. \bf{472} no.1, 981--1000] and Question 18.51 of [M. A. Taylor 2018: Unbounded convergence in vector lattices, Thesis University of Alberta]., Comment: 19 pages

For the analysis of a time-to-event endpoint in a single-arm or randomized clinical trial it is generally perceived that interpretation of a given estimate of the survival function, or the comparison between two groups, hinges on some quantification of the amount of follow-up. Typically, a median of some loosely defined quantity is reported. However, whatever median is reported, is typically not answering the question(s) trialists actually have in terms of follow-up quantification. In this paper, inspired by the estimand framework, we formulate a comprehensive list of relevant scientific questions that trialists have when reporting time-to-event data. We illustrate how these questions should be answered, and that reference to an unclearly defined follow-up quantity is not needed at all. In drug development, key decisions are made based on randomized controlled trials, and we therefore also discuss relevant scientific questions not only when looking at a time-to-event endpoint in one group, but also for comparisons. We find that different thinking about some of the relevant scientific questions around follow-up is required depending on whether a proportional hazards assumption can be made or other patterns of survival functions are anticipated, e.g. delayed separation, crossing survival functions, or the potential for cure. We conclude the paper with practical recommendations., Comment: 31 pages

The ICH E9 (R1) Estimands Guidance1 terminology does not completely address the conceptual needs of time-to-event estimands in the complex oncology context. We previously described how censoring and censoring mechanisms for time-to-event endpoints can be embedded into the ICH E9 (R1) Estimands Guidance terminology. This second paper by the Pharmaceutical Industry Working Group on Estimands in Oncology Censoring Mechanisms Subteam discusses special issues in the oncology clinical context that may require different approaches than some other therapeutic areas as well as an extensions of the ICH E9 (R1) guidance. The concept of censoring is discussed in the broader context of occluding events, with occlusion representing any loss to further follow-up and/or removal of further collected data from analysis. Occlusion constitutes a broader concept than the estimand guidance's intercurrent event and terminal event terminology and is appropriate to describe and handle situations like withdrawal from assessments or situations where the requirements of different estimands conflict. We characterize, provide additional details, practical implications, and examples on the application of each estimands strategy for handling occluding events.

Time-to-event estimands are central to many oncology clinical trials. The estimand framework (addendum to the ICH E9 guideline) calls for precisely defining the treatment effect of interest to align with the clinical question of interest and requires predefining the handling of intercurrent events that occur after treatment initiation and either preclude the observation of an event of interest or impact the interpretation of the treatment effect. We discuss a practical problem in clinical trial design and execution, i.e. in some clinical contexts it is not feasible to systematically follow patients to an event of interest. Loss to follow-up in the presence of intercurrent events can affect the meaning and interpretation of the study results. We provide recommendations for trial design, stressing the need for close alignment of the clinical question of interest and study design, impact on data collection and other practical implications. When patients cannot be systematically followed, compromise may be necessary to select the best available estimand that can be feasibly estimated under the circumstances. We discuss the use of sensitivity and supplementary analyses to examine assumptions of interest.

Different notions for order convergence have been considered by various authors. Associated to every notion of order convergence corresponds a topology, defined by taking as the closed sets those subsets of the poset satisfying that no net in them order converges to a point that is outside of the set. We shall give a thorough overview of these different notions and provide a systematic comparison of the associated topologies. Then, in the last section we shall give an application of this study by giving a result on von Neumann algebras complementing the study started in \cite{ChHaWe}. We show that for every atomic von Neumann algebra (not necessarily $\sigma$-finite) the restriction of the order topology to bounded parts of $M$ coincides with the restriction of the $\sigma$-strong topology $s(M,M_\ast)$. We recall that the methods of \cite{ChHaWe} rest heavily on the assumption of $\sigma$-finiteness. Further to this, for a semi-finite measure space, we shall give a complete picture of the relations between the topologies on $L^\infty$ associated with the duality $\langle L^1, L^\infty\rangle$ and its order topology.

The estimand framework included in the addendum to the ICH E9 guideline facilitates discussions to ensure alignment between the key question of interest, the analysis, and interpretation. Therapeutic knowledge and drug mechanism play a crucial role in determining the strategy and defining the estimand for clinical trial designs. Clinical trials in patients with hematological malignancies often present unique challenges for trial design due to complexity of treatment options and existence of potential curative but highly risky procedures, e.g. stem cell transplant or treatment sequence across different phases (induction, consolidation, maintenance). Here, we illustrate how to apply the estimand framework in hematological clinical trials and how the estimand framework can address potential difficulties in trial result interpretation. This paper is a result of a cross-industry collaboration to connect the International Conference on Harmonisation (ICH) E9 addendum concepts to applications. Three randomized phase 3 trials will be used to consider common challenges including intercurrent events in hematologic oncology trials to illustrate different scientific questions and the consequences of the estimand choice for trial design, data collection, analysis, and interpretation. Template language for describing estimand in both study protocols and statistical analysis plans is suggested for statisticians' reference., Comment: 5 tables, 1 figure

Motivated by the Hilbert-space model for quantum mechanics, we define a pre-Hilbert space logic to be a pair $(S,\el)$, where $S$ is a pre-Hilbert space and $\el$ is an orthocomplemented poset of orthogonally closed linear subspaces of $S$, closed w.r.t. finite dimensional perturbations, (i.e. if $M\in\el$ and $F$ is a finite dimensional linear subspace of $S$, then $M+F\in \el$). We study the order topology $\tau_o(\el)$ on $\el$ and show that completeness of $S$ can by characterized by the separation properties of the topological space $(\el,\tau_o(\el))$. It will be seen that the remarkable lack of a proper probability-theory on pre-Hilbert space logics -- for an incomplete $S$ -- comes out elementarily from this topological characterization., Comment: 13 pages

Globulettes are small (radii $< 10$ kAU) dark dust clouds, seen against the background of bright nebulae. A majority of the objects have planetary mass. These objects may be a source of brown dwarfs and free floating planetary mass objects in the galaxy. In this paper we investigate how many globulettes could have formed in the Milky Way and how they could contribute to the total population of free floating planets. In order to do that we examine H-alpha images of 27 H~II regions. In these images, we find 778 globulettes. We find that a conservative value of the number of globulettes formed is $5.7\times 10^{10}$. If 10 \% of the globulettes form free floating planets then they have contributed with $5.7\times 10^{9}$ free floating planets in the Milky Way. A less conservative number of globulettes would mean that the globulettes could contribute $2.0\times 10^{10}$ free floating planets. Thus the globulettes could represent a non-negligible source of free floating planets in the Milky Way., Comment: 11 pages, 3 figures, submitted to Astrophysics and Space Science

The order topology $\tau_o(P)$ (resp. the sequential order topology $\tau_{os}(P)$) on a poset $P$ is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra $M$ we consider the following three posets: the self-adjoint part $M_{sa}$, the self-adjoint part of the unit ball $M_{sa}^1$, and the projection lattice $P(M)$. We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology to the other standard locally convex topologies on $M$, and relate the properties of the order topology to the underlying operator-algebraic structure of $M$.

Specific heat measurements show that the introduction of amorphous columnar defects considerably affects the transition from the normal to the superconducting state in zero magnetic field. Experimental results are compared to numerical simulations of the 3D XY model for both the pure system and the system containing random columnar disorder. The numerics reproduce the salient features of experiment, showing in particular that the specific heat peak changes from cusp-like to smoothly rounded when columnar defects are added. By considering the specific heat critical exponent alpha, we argue that such behavior is consistent with recent numerical work [Vestergren et al., PRB 70, 054508 (2004)] showing that the introduction of columnar defects changes the universality class of the transition., Comment: 4 pages, 2 figures

We study the superfluid transition of $^4$He in aerogel by Monte Carlo simulations and finite size scaling analysis. Aerogel is a highly porous silica glass, which we model by a diffusion limited cluster aggregation model. The superfluid is modeled by a three dimensional XY model, with excluded bonds to sites on the aerogel cluster. We obtain the correlation length exponent $\nu=0.73 \pm 0.02$, in reasonable agreement with experiments and with previous simulations. For the heat capacity exponent $\alpha$, both experiments and previous simulations suggest deviations from the Josephson hyperscaling relation $\alpha=2-d\nu$. In contrast, our Monte Carlo results support hyperscaling with $\alpha= -0.2\pm 0.05$. We suggest a reinterpretation of previous experiments, which avoids scaling violations and is consistent with our simulation results., Comment: 4 pages, 3 figures