The Ci3+3 Design for Dual-Agent Combination Dose-Finding Clinical Trials

We propose a rule-based statistical design for combination dose-finding trials with two agents. The Ci3+3 design is an extension of the i3+3 design with simple decision rules comparing the observed toxicity rates and equivalence intervals that define the maximum tolerated dose combination. Ci3+3 consists of two stages to allow fast and efficient exploration of the dose-combination space. Statistical inference is restricted to a beta-binomial model for dose evaluation, and the entire design is built upon a set of fixed rules. We show via simulation studies that the Ci3+3 design exhibits similar and comparable operating characteristics to more complex designs utilizing model-based inferences. We believe that the Ci3+3 design may provide an alternative choice to help simplify the design and conduct of combination dose-finding trials in practice

Concavity property of minimal L2L^{2} integrals with Lebesgue measurable gain VIII -- partial linearity and log-concavity

In this article, we give some necessary conditions for the concavity property of minimal $L^2$ integrals degenerating to partial linearity, a charaterization for the concavity degenerating to partial linearity for open Riemann surfaces, and some relations between the concavity property for minimal $L^2$ integrals and the log-convexity for Bergman kernels.Comment: 37 pages, all comments are welcome! arXiv admin note: text overlap with arXiv:2211.00470, arXiv:2211.0525

Concavity property of minimal L2L^2 integrals with Lebesgue measurable gain V--fibrations over open Riemann surfaces

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of fibrations over open Riemann surfaces. As applications, we obtain characterizations of the holding of equality in optimal jets $L^2$ extension problem from fibers over analytic subsets to fibrations over open Riemann surfaces, which implies characterizations of the fibration versions of the equality parts of Suita conjecture and extended Suita conjecture.Comment: 60 pages. arXiv admin note: substantial text overlap with arXiv:2205.07512, arXiv:2204.0726

The log-plurisubharmonicity of fiberwise ξ−\xi-Bergman kernels for variant functional

In the present paper, we obtain the log-plurisubharmonicity of fiberwise $\xi-$Bergman kernels for variant functional.Comment: 9 pages. All comments are welcome

The Backfill i3+3 Design for Dose-Finding Trials in Oncology

We consider a formal statistical design that allows simultaneous enrollment of a main cohort and a backfill cohort of patients in a dose-finding trial. The goal is to accumulate more information at various doses to facilitate dose optimization. The proposed design, called Bi3+3, combines the simple dose-escalation algorithm in the i3+3 design and a model-based inference under the framework of probability of decisions (POD), both previously published. As a result, Bi3+3 provides a simple algorithm for backfilling patients to lower doses in a dose-finding trial once these doses exhibit safety profile in patients. The POD framework allows dosing decisions to be made when some backfill patients are still being followed with incomplete toxicity outcomes, thereby potentially expediting the clinical trial. At the end of the trial, Bi3+3 uses both toxicity and efficacy outcomes to estimate an optimal biological dose (OBD). The proposed inference is based on a dose-response model that takes into account either a monotone or plateau dose-efficacy relationship, which are frequently encountered in modern oncology drug development. Simulation studies show promising operating characteristics of the Bi3+3 design in comparison to existing designs

BaySize: Bayesian Sample Size Planning for Phase I Dose-Finding Trials

We propose BaySize, a sample size calculator for phase I clinical trials using Bayesian models. BaySize applies the concept of effect size in dose finding, assuming the MTD is defined based on an equivalence interval. Leveraging a decision framework that involves composite hypotheses, BaySize utilizes two prior distributions, the fitting prior (for model fitting) and sampling prior (for data generation), to conduct sample size calculation under desirable statistical power. Look-up tables are generated to facilitate practical applications. To our knowledge, BaySize is the first sample size tool that can be applied to a broad range of phase I trial designs

Tame maximal weights, relative types and valuations

In this article, we obtain a class of tame maximal weights (Zhou weights), whose relative types (Zhou numbers) satisfy the tropical multiplicativity and tropical additivity, and characterize the multiplier ideal sheaves of plurisubharmonic functions. Especially, the relative types to them are valuations (Zhou valuations) on the ring of germs of holomorphic functions, and characterize the division relations of the ring. We consider a global version of these weights on domains in $\mathbb{C}^n$, and obtain some properties of them, including the continuity and some approximation results.Comment: 51 pages, all comments are welcome

Prognostic Values of Filamin-A Status for Topoisomerase II Poison Chemotherapy

Filamin-A, also called Actin Binding Protein-280, is not only an essential component of the cytoskeleton networks, but also serves as the scaffold in various signaling networks. It has been shown that filamin-A facilitates DNA repair and filamin-A proficient cells are more resistant to ionizing radiation, bleomycin, and cisplatin. In this study, we assessed the role of filamin-A in modulating cancer cell sensitivity to Topo II poisons, including etoposide and doxorubicin. Intriguingly, we found that cells with filamin-A expression are more sensitive to Topo II poisons than those with defective filamin-A, and filamin-A proficient xenograft melanomas have better response to etoposide treatment than the filamin-A deficient tumors. This is associated with more potent induction of DNA double strand breaks (DSBs) by Topo II poisons in filamin-A proficient cells than the deficient cells. Although the expression of filamin-A enables cells a slightly stronger capability to repair DSB, the net outcome is that filamin-A proficient cells bear more DSBs due to the significantly enhanced DSB induction by Topo II poisons in these cells. We further found that filamin-A proficient cells have increased drug influx and decreased drug efflux, suggesting that filamin-A modulates the intra-cellular drug kinetics of Topo II poisons to facilitate the generation of DSB after Topo II poison exposure. These data suggest a novel function of filamin-A in regulating the pharmacokinetics of Topo II poisons, and that the status of filamin-A may be used as a prognostic marker for Topo II poisons based cancer treatments