Design and analysis of three-arm trials with negative binomially distributed endpoints.

A three-arm clinical trial design with an experimental treatment, an active control, and a placebo control, commonly referred to as the gold standard design, enables testing of non-inferiority or superiority of the experimental treatment compared with the active control. In this paper, we propose methods for designing and analyzing three-arm trials with negative binomially distributed endpoints. In particular, we develop a Wald-type test with a restricted maximum-likelihood variance estimator for testing non-inferiority or superiority. For this test, sample size and power formulas as well as optimal sample size allocations will be derived. The performance of the proposed test will be assessed in an extensive simulation study with regard to type I error rate, power, sample size, and sample size allocation. For the purpose of comparison, Wald-type statistics with a sample variance estimator and an unrestricted maximum-likelihood estimator are included in the simulation study. We found that the proposed Wald-type test with a restricted variance estimator performed well across the considered scenarios and is therefore recommended for application in clinical trials. The methods proposed are motivated and illustrated by a recent clinical trial in multiple sclerosis. The R package Three Armed Trials, which implements the methods discussed in this paper, is available on CRAN

On 1-factorizations of Bipartite Kneser Graphs

It is a challenging open problem to construct an explicit 1-factorization of the bipartite Kneser graph $H(v,t)$, which contains as vertices all $t$-element and $(v-t)$-element subsets of $[v]:=\{1,\ldots,v\}$ and an edge between any two vertices when one is a subset of the other. In this paper, we propose a new framework for designing such 1-factorizations, by which we solve a nontrivial case where $t=2$ and $v$ is an odd prime power. We also revisit two classic constructions for the case $v=2t+1$ --- the \emph{lexical factorization} and \emph{modular factorization}. We provide their simplified definitions and study their inner structures. As a result, an optimal algorithm is designed for computing the lexical factorizations. (An analogous algorithm for the modular factorization is trivial.)Comment: We design the first explicit 1-factorization of H(2,q), where q is a odd prime powe

Comminution Characteristics of Lithium Bearing Mica Ores From Different Devices

This paper highlights on the comminution and to the lesser extent liberation properties of two greisen-type lithium bearing-mica ores (L1, L2) subjected to different breakage devices; cone crusher (CC), roller crusher (RC), rotor beater mill (RBM) and a screen mill (SM). The particle size distributions (PSD) of the products from each device were evaluated to search for an appropriate PSD model using Gates-Gaudin-Schuhmann (GGS) and Rosin-Rammler (RR) functions. To determine an appropriate function, coefficients of determination (R2 ) were used as a criterion. Due to budget constraint, only products from rotor beater mill (RBM) were examined for mineral liberation by an automated scanning electron microscope (SEM) technique. It was found that RBM, RC and SM products were better described by the RR model than the GGS model with higher R2 values of 0.97 to 1.0. However, cone crusher products for L1 were better described by GSS model, while that for L2 were better described by RR model. In terms of the spread of size distribution as indicated by RR model parameters, RC products were more uniformly distributed compared to those from other devices, for both ores. Also the RBM products were more scattered than those from other devices. The results indicate that the composition of individual ores affected the comminution products PSDs as different PSD model parameters were obtained for samples comminuted by same devices. The modal mineralogy indicated that both ores are rich in quartz, topaz, zinnwaldite and muscovite. Furthermore, the result indicates that, for both ores, the zinnwaldite phase is more enriched in the fraction < 250 µm. Moreover, better liberation of zinnwaldite is observed for L1 compared to L2. This could be explained by differences of the two ores in three aspects; the nature of mineral association, reduction ratio of the fractions analysed and the spread of the size distribution

Sparse Kneser graphs are Hamiltonian

For integers k≥1 and n≥2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1,…,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k≥3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k≥3 and a≥0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k−6 distinct Hamilton cycles for k≥6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words

Tissue Clearing and Deep Imaging of the Kidney Using Confocal and Two-Photon Microscopy

Microscopic and macroscopic evaluation of biological tissues in three dimensions is becoming increasingly popular. This trend is coincident with the emergence of numerous tissue clearing strategies, and advancements in confocal and two-photon microscopy, enabling the study of intact organs and systems down to cellular and sub-cellular resolution. In this chapter, we describe a wholemount immunofluorescence technique for labeling structures in renal tissue. This technique combined with solvent-based tissue clearing and confocal imaging, with or without two-photon excitation, provides greater structural information than traditional sectioning and staining alone. Given the addition of paraffin embedding to our method, this hybrid protocol offers a powerful approach to combine confocal or two-photon findings with histological and further immunofluorescent analysis within the same tissue

Photoactivatable drugs for nicotinic optopharmacology

Photoactivatable pharmacological agents have revolutionized neuroscience, but the palette of available compounds is limited. We describe a general method for caging tertiary amines by using a stable quaternary ammonium linkage that elicits a red shift in the activation wavelength. We prepared a photoactivatable nicotine (PA-Nic), uncageable via one- or two-photon excitation, that is useful to study nicotinic acetylcholine receptors (nAChRs) in different experimental preparations and spatiotemporal scales

Bayesian Model Selection Applied to the Analysis of Fluorescence Correlation Spectroscopy Data of Fluorescent Proteins in Vitro and in Vivo

Fluorescence correlation spectroscopy (FCS) is a powerful technique to investigate molecular dynamics with single molecule sensitivity. In particular, in the life sciences it has found widespread application using fluorescent proteins as molecularly specific labels. However, FCS data analysis and interpretation using fluorescent proteins remains challenging due to typically low signal-to-noise ratio of FCS data and correlated noise in autocorrelated data sets. As a result, naive fitting procedures that ignore these important issues typically provide similarly good fits for multiple competing models without clear distinction of which model is preferred given the signal-to-noise ratio present in the data. Recently, we introduced a Bayesian model selection procedure to overcome this issue with FCS data analysis. The method accounts for the highly correlated noise that is present in FCS data sets and additionally penalizes model complexity to prevent over interpretation of FCS data. Here, we apply this procedure to evaluate FCS data from fluorescent proteins assayed in vitro and in vivo. Consistent with previous work, we demonstrate that model selection is strongly dependent on the signal-to-noise ratio of the measurement, namely, excitation intensity and measurement time, and is sensitive to saturation artifacts. Under fixed, low intensity excitation conditions, physical transport models can unambiguously be identified. However, at excitation intensities that are considered moderate in many studies, unwanted artifacts are introduced that result in nonphysical models to be preferred. We also determined the appropriate fitting models of a GFP tagged secreted signaling protein, Wnt3, in live zebrafish embryos, which is necessary for the investigation of Wnt3 expression and secretion in development. Bayes model selection therefore provides a robust procedure to determine appropriate transport and photophysical models for fluorescent proteins when appropriate models are provided, to help detect and eliminate experimental artifacts in solution, cells, and in living organisms.National Science Foundation (U.S.). Physics of Living Systems ProgramNational Institute of Mental Health (U.S.) (Award U01MH106011

Cognitive decline in Huntington's disease expansion gene carriers

BACKGROUND: In Huntington's Disease (HD) cognitive decline can occur before unequivocal motor signs become apparent. As cognitive decline often starts early in the course of the disease and has a progressive nature over time, cognition can be regarded as a key target for symptomatic treatment. The specific progressive profile of cognitive decline over time is unknown. OBJECTIVE: The aim of this study is to quantify the progression of cognitive decline across all HD stages, from pre-motormanifest to advanced HD, and to investigate if CAG length mediates cognitive decline. METHODS: In the European REGISTRY study 2669 HD expansion gene carriers underwent annual cognitive assessment. General linear mixed models were used to model the cognitive decline for each cognitive task across all disease stages. Additionally, a model was developed to evaluate the cognitive decline based on CAG length and age rather than disease stage. RESULTS: There was significant cognitive decline on all administered tasks throughout pre-motormanifest (close to estimated disease onset) participants and the subsequent motormanifest participants from stage 1 to stage 4. Performance on the Stroop Word and Stroop Color tests additionally declined significantly across the two pre-motormanifest groups: far and close to estimated disease onset. The evaluation of cognition performance in relation to CAG length and age revealed a more rapid cognitive decline in participants with longer CAG length than participants with shorter CAG length over time. CONCLUSION: Cognitive performance already shows decline in pre-motormanifest HD gene expansion carriers and gradually worsens to late stage HD. HD gene expansion carriers with certain CAG length have their own cognitive profile, i.e., longer CAG length is associated with more rapid decline

Long-term effects of medical management on growth and weight in individuals with urea cycle disorders

Low protein diet and sodium or glycerol phenylbutyrate, two pillars of recommended long-term therapy of individuals with urea cycle disorders (UCDs), involve the risk of iatrogenic growth failure. Limited evidence-based studies hamper our knowledge on the long-term effects of the proposed medical management in individuals with UCDs. We studied the impact of medical management on growth and weight development in 307 individuals longitudinally followed by the Urea Cycle Disorders Consortium (UCDC) and the European registry and network for Intoxication type Metabolic Diseases (E-IMD). Intrauterine growth of all investigated UCDs and postnatal linear growth of asymptomatic individuals remained unaffected. Symptomatic individuals were at risk of progressive growth retardation independent from the underlying disease and the degree of natural protein restriction. Growth impairment was determined by disease severity and associated with reduced or borderline plasma branched-chain amino acid (BCAA) concentrations. Liver transplantation appeared to have a beneficial effect on growth. Weight development remained unaffected both in asymptomatic and symptomatic individuals. Progressive growth impairment depends on disease severity and plasma BCAA concentrations, but cannot be predicted by the amount of natural protein intake alone. Future clinical trials are necessary to evaluate whether supplementation with BCAAs might improve growth in UCDs