Bayesian hierarchical model for dose-finding trial incorporating historical data.

The Multiple Comparison Procedure and Modelling (MCPMod) approach has been shown to be a powerful statistical technique that can significantly improve the design and analysis of dose-finding studies under model uncertainty. Due to its frequentist nature, however, it is difficult to incorporate information into MCPMod from historical trials on the same drug. BMCPMod, a recently introduced Bayesian version of MCPMod, is designed to take into account historical information on the placebo dose group. We introduce a Bayesian hierarchical framework capable of incorporating historical information on an arbitrary number of dose groups, including both placebo and active ones, taking into account the relationship between responses of these dose groups. Our approach can also model both prognostic and predictive between-trial heterogeneity and is particularly useful in situations where the effect sizes of two trials are different. Our goal is to reduce the necessary sample size in the dose-finding trial while maintaining its target power.

Bayesian MCPMod.

Multiple comparison procedures and modeling (MCPMod) has established itself as a method for dose-finding under model uncertainty. A downside of MCPMod is that due to its frequentist nature in particular with respect to the multiple comparison part it is tough to incorporate historical information in a systematic fashion. A typical situation where such historical information is available is existing data for the placebo group from previous trials. There are multiple Bayesian concepts for integrating historical data in a systematic and even dynamic fashion like the meta-analytic prior approach. In this article, we define Bayesian MCPMod (BMCPMod) that is build upon these two aspects. BMCPMod is able to mimic the results of the classical MCPMod for non-informative priors. At the same time, it allows for the inclusion of historical data in a systematic fashion. After the definition of BMCPMod related characteristics for a Bayesian approach similar to the MCP-testing part are derived. The BMCPMod is compared to classical MCPMod/non-informative priors via simulations. Aspects of mixture priors, optimal contrast vectors, and impact of allocation ratios are discussed and an example for designing a BMPCMod trial is given.

Bayesian Phase II optimization for time-to-event data based on historical information.

After exploratory drug development, companies face the decision whether to initiate confirmatory trials based on limited efficacy information. This proof-of-concept decision is typically performed after a Phase II trial studying a novel treatment versus either placebo or an active comparator. The article aims to optimize the design of such a proof-of-concept trial with respect to decision making. We incorporate historical information and develop pre-specified decision criteria accounting for the uncertainty of the observed treatment effect. We optimize these criteria based on sensitivity and specificity, given the historical information. Specifically, time-to-event data are considered in a randomized 2-arm trial with additional prior information on the control treatment. The proof-of-concept criterion uses treatment effect size, rather than significance. Criteria are defined on the posterior distribution of the hazard ratio given the Phase II data and the historical control information. Event times are exponentially modeled within groups, allowing for group-specific conjugate prior-to-posterior calculation. While a non-informative prior is placed on the investigational treatment, the control prior is constructed via the meta-analytic-predictive approach. The design parameters including sample size and allocation ratio are then optimized, maximizing the probability of taking the right decision. The approach is illustrated with an example in lung cancer.

A comparison of group sequential and fixed sample size designs for bioequivalence trials with highly variable drugs.

PURPOSE: A drug is defined as highly variable if its intra-individual coefficient of variation (CV) is greater than or equal to 30%. In such a case, bioequivalence may be assessed by means of methods that take the (high) variability into account. The Scaled Average Bioequivalence (SABE) approach is such a procedure and represents the recommendations of FDA. The aim of this investigation is to compare the performance characteristics of classical group sequential designs (GSD) and fixed design settings for three-period crossover bioequivalence studies with highly variable drugs, where the SABE procedure is utilized. METHODS: Monte Carlo simulations were performed to assess type I error rate, power, and average sample size for GSDs with Pocock's and O'Brien-Fleming's stopping rules and various timings of the interim analysis and for fixed design settings. RESULTS: Based on our investigated scenarios, the GSDs show comparable properties with regard to power and type I error rate as compared to the corresponding fixed designs. However, due to an advantage in average sample size, the most appealing design is Pocock's approach with interim analysis after 50% information fraction. CONCLUSIONS: Due to their favorable performance characteristics, two-stage GSDs are an appealing alternative to fixed sample designs when assessing bioequivalence in highly variable drugs.

A randomized, open-label, phase I/II trial to investigate the maximum tolerated dose of the Polo-like kinase inhibitor BI 2536 in elderly patients with refractory/relapsed acute myeloid leukaemia.

Polo-like kinases (Plks) play an important role in cell cycle checkpoint controls and are over-expressed in acute myeloid leukaemia (AML). BI 2536, a novel Plk inhibitor, induces mitotic arrest and apoptosis. In this phase I/II trial of BI 2536 in 68 elderly patients with relapsed/refractory AML, three schedules were investigated (day 1, days 1-3, and days 1 + 8). Maximum tolerated dose was 350 and 200 mg in the day 1 and days 1 + 8 schedules, respectively. The day 1-3 schedule appeared equivalent to the day 1 schedule and was discontinued early. BI 2536 exhibited multi-compartmental pharmacokinetic behaviour. The majority of patients showed an increase of bone marrow cells in G2/M with a characteristic pattern of mitotic catastrophe. The overall response rate in the day 1 and day 1 + 8 schedules was 9% (5/54) with 2 complete and 3 partial responses. The majority of drug-related adverse events grade ≥3 were haematological. Taken together, Plk inhibition induced cell cycle arrest in AML blasts in vivo and BI 2536 monotherapy showed modest clinical activity in this poor prognosis patient group.

A phase II trial to assess efficacy and safety of afatinib in extensively pretreated patients with HER2-negative metastatic breast cancer.

Afatinib (BIBW 2992) is an ErbB-family blocker that irreversibly inhibits signaling from all relevant ErbB-family dimers. Afatinib has demonstrated preclinical activity in human epidermal growth factor receptor HER2 (ErbB2)-positive and triple-negative xenograft models of breast cancer, and clinical activity in phase I studies. This was a multicenter phase II study enrolling patients with HER2-negative metastatic breast cancer progressing following no more than three lines of chemotherapy. No prior epidermal growth factor receptor-targeted therapy was allowed. Patients received 50-mg afatinib once daily until disease progression. Tumor assessment was performed at every other 28-day treatment course. The primary endpoint was clinical benefit (CB) for ≥4 treatment courses in triple-negative (Cohort A) metastatic breast cancer (TNBC) and objective responses measured by Response Evaluation Criteria in Solid Tumors in patients with HER2-negative, estrogen receptor-positive, and/or progesterone receptor-positive breast cancer (Cohort B). Fifty patients received treatment, including 29 patients in Cohort A and 21 patients in Cohort B. No objective responses were observed in either cohort. Median progression-free survival was 7.4 and 7.7 weeks in Cohorts A and B, respectively. Three patients with TNBC had stable disease for ≥4 treatment courses, one of them for 12 courses (median 26.3 weeks; range 18.9-47.9 weeks). The most frequently observed afatinib-associated adverse events (AEs) were gastrointestinal and skin-related side effects, which were manageable by symptomatic treatment and dose reductions. Afatinib pharmacokinetics were comparable to those observed in previously reported phase I trials. In conclusion, afatinib had limited activity in HER2-negative breast cancer. AEs were generally manageable and mainly affected the skin and the gastrointestinal tract.

How is retrospective independent review influenced by investigator-introduced informative censoring: a quantitative approach.

A reliable determination of progression is of key importance in determining progression-free survival in oncology trials. An independent review of tumour assessments made by investigators is often implemented with the aim of reducing a possible bias. Often, the independent review is performed in a prespecified but retrospective fashion by reviewing a patient after all assessments have been performed. It has been discussed that this mechanism can lead to informative censoring with respect to independent review. This is caused by the fact that often no further assessments are available after the investigator has declared the patient to be progressive, possibly leading to a considerable amount of patients being judged progressive by the investigator and being censored by independent review. We introduce and investigate a model for the error in assessment with the aim of quantifying the bias in independent review. The model is based on single error probabilities at each assessment time-point that are independent from each other but dependent on the time to the true progression time-point. The bias introduced for the independent review is described and quantified. We show that the investigator assessments of progression can lead to less bias for progression-free survival than the results for independent review. Results show that a within-arm discordance rate is not necessarily correlated with the bias in independent review. Finally, we propose an approach for a sensitivity analysis that is a useful tool to sandwich the true underlying distribution by the results for independent review itself and the described sensitivity analysis.

Unifying cluster-based structure models of decagonal Al-Co-Ni, Al-Co-Cu and Al-Fe-Ni.

The geometrical building principles of Al-based decagonal quasicrystals and their approximants are discussed from a cluster-based approach. Our investigations cover 11 modifications with two- or four-layer periodicity in the systems Al-Co-Ni, Al-Co-Cu and Al-Fe-Ni. We identified a cluster that leads to a unifying view of all these phases. This unit cluster has ~20 Å diameter, four-layer periodicity along its tenfold axis and rod symmetry group p102m. The models obtained are in agreement with all the electron-density maps and electron-microscopy images available.

Ab initio reconstruction of difference densities by charge flipping.

The charge-flipping algorithm in its band-flipping variant is capable of ab initio reconstructions of scattering densities with positive and negative values. It is shown that the method can be applied to reconstructions of difference electron densities of superstructures, i.e. densities obtained as a difference between the true scattering density and the average density over two or more subcells of the true structure. The amplitudes of reflections lying on the reciprocal lattice of the subcell are not required for the procedure. A series of examples shows applications of the method to the solution of superstructures in periodic crystals or quasicrystals as well as the application to ab initio solution of modulation of an incommensurately modulated structure from satellite reflections only and solution of a structure from a crystal twinned by reticular pseudomerohedry. The method is especially suited for solving pseudosymmetry problems occurring frequently in superstructures.

Modelling tree roots in mixed forest stands by inhomogeneous marked Gibbs point processes.

The aim of the paper is to apply point processes to root data modelling. We propose a new approach to parametric inference when the data are inhomogeneous replicated marked point patterns. We generalize Geyer's saturation point process to a model, which combines inhomogeneity, marks and interaction between the marked points. Furthermore, the inhomogeneity influences the definition of the neighbourhood of points. Using the maximum pseudolikelihood method, this model is then fitted to root data from mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) to quantify the degree of root aggregation in such mixed stands. According to the analysis there is no evidence that the two root systems are not independent.

A statistical model for the dependence between progression-free survival and overall survival.

Among the surrogate endpoints for overall survival (OS) in oncology trials, progression-free survival (PFS) is more and more taking the leading role. Although there have been some empirical investigations on the dependence structure between OS and PFS (in particular between the median OS and the median PFS), statistical models are almost non-existing. This paper aims at filling this gap by introducing an easy-to-handle model based on exponential time-to-event distributions that describe the dependence structure between OS and PFS. Based on this model, explicit formulae for individual correlations are derived together with a lower bound for the correlation of OS and PFS, which is given by the fraction of the two medians for OS and PFS. Two methods on how to estimate the parameter of the model from real data are discussed. One method is based on a maximum-likelihood estimator whereas the other method uses a plug-in approach. Three examples from non-small cell lung cancer are considered. In the first example, the parameters of the model are determined and the estimated survival curce is compared with the observed one. The second example explains how to obtain sample size estimates for OS based on assumptions on median PFS and OS. Finally, the third example provides a way of modelling and quantifying confounding effects that might explain a levelling of differences in OS although a difference in PFS is observed.

Myc regulates embryonic vascular permeability and remodeling.

Previous work has shown that c-Myc is required for adequate vasculogenesis and angiogenesis. To further investigate the contribution of Myc to these processes, we conditionally expressed c-Myc in embryonic endothelial cells using a tetracycline-regulated system. Endothelial Myc overexpression resulted in severe defects in the embryonic vascular system. Myc-expressing embryos undergo widespread edema formation and multiple hemorrhagic lesions. They die between embryonic days 14.5 and 17.5. The changes in vascular permeability are not caused by deficiencies in vascular basement membrane composition or pericyte coverage. However, the overall turnover of endothelial cells is elevated as is revealed by increased levels of both proliferation and apoptosis. Whole-mount immunohistochemical analysis revealed alterations in the architecture of capillary networks. The dermal vasculature of Myc-expressing embryos is characterized by a reduction in vessel branching, which occurs despite upregulation of the proangiogenic factors vascular endothelial growth factor-A and angiopoietin-2. Thus, the net outcome of an excess of vascular endothelial growth factor-A and angiopoietin-2 in the face of an elevated cellular turnover appears to be a defect in vascular integrity.

Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process.

Keratin intermediate filament networks are part of the cytoskeleton in epithelial cells. They were found to regulate viscoelastic properties and motility of cancer cells. Due to unique biochemical properties of keratin polymers, the knowledge of the mechanisms controlling keratin network formation is incomplete. A combination of deterministic and stochastic modeling techniques can be a valuable source of information since they can describe known mechanisms of network evolution while reflecting the uncertainty with respect to a variety of molecular events. We applied the concept of piecewise-deterministic Markov processes to the modeling of keratin network formation with high spatiotemporal resolution. The deterministic component describes the diffusion-driven evolution of a pool of soluble keratin filament precursors fueling various network formation processes. Instants of network formation events are determined by a stochastic point process on the time axis. A probability distribution controlled by model parameters exercises control over the frequency of different mechanisms of network formation to be triggered. Locations of the network formation events are assigned dependent on the spatial distribution of the soluble pool of filament precursors. Based on this modeling approach, simulation studies revealed that the architecture of keratin networks mostly depends on the balance between filament elongation and branching processes. The spatial distribution of network mesh size, which strongly influences the mechanical characteristics of filament networks, is modulated by lateral annealing processes. This mechanism which is a specific feature of intermediate filament networks appears to be a major and fast regulator of cell mechanics.

Statistical modelling of the geometry of planar sections of prostatic capillaries on the basis of stationary Strauss hard-core processes.

In a recent study, the capillarization of normal prostatic tissue and prostatic carcinoma tissue was characterized by means of explorative methods of spatial statistics. In the present paper, an attempt was made to go beyond the explorative approach and to characterize the observed point patterns of the capillary profiles on sections by means of a parametric model. For this purpose, the flexible class of Gibbs processes was considered. Specifically, stationary Strauss hard-core processes were fitted to the observed point patterns. The goodness of fit achieved by the model was checked by simulations with the Markov chain Monte Carlo method using the Metropolis-Hastings algorithm. Model fitting and simulations were performed with the help of the spatstat package under R. The observed point patterns were in some cases compatible with realizations of stationary Strauss hard-core processes for all ranges of spatial interaction. However, deviations from the model were found for one or more domains of ranges in other cases. In the tumour tissue, a highly significant decrease of the interaction parameter of the Strauss hard-core process could be found as compared to the normal prostatic tissue. This finding is discussed in terms of a loss of the normal lobular architecture of the glands in the tumour tissue.

Quantitative investigation of murine cytomegalovirus nucleocapsid interaction.

In this study, we quantitatively investigate the role of the M97 protein for viral morphogenesis in murine cytomegalovirus (MCMV)-infected fibroblast cells. For this purpose, a statistical analysis is performed for the spatial distribution of nuclear B-capsids (devoid of DNA, containing the scaffold) and C-capsids (filled with DNA). Cell nuclei infected with either wild-type or an M97 deletion mutant were compared. Univariate and multivariate point process characteristics (like Ripley's K-function, the L-function and the nearest neighbour distance distribution function) are investigated in order to describe and quantify the effects that the deletion of M97 causes to the process of DNA packaging into nucleocapsids. The estimation of the function L(r) -r reveals that with respect to the wild type there is an increased frequency of point pairs at a very short distance (less than approximately 100 nm) for both the B-capsids as well as for the C-capsids. For the M97 deletion mutant type this is no longer true. Here only the C-capsids show such a clustering behaviour, whereas for B-capsids it is almost nonexistant. Estimations of functionals such as the nearest neighbour distance distribution function confirmed these results. Thereby, a quantification is provided for the effect that the deletion of M97 leads to a loss of typical nucleocapsid clustering in MCMV-infected nuclei.

Spatial arrangement of microglia in the mouse hippocampus: a stereological study in comparison with astrocytes.

Microglia are classically considered to be immune cells in the brain, but have now been proven to be involved in neuronal activity as well. Here we stereologically analyzed the spatial arrangement of microglia in the mouse hippocampus. First, we estimated the numerical densities (NDs) of microglia identified by ionized calcium-binding adaptor molecule 1 (Iba1). Despite that microglia appeared to be evenly distributed throughout the hippocampal area, the NDs demonstrated significant dorsoventral, interregional, and interlaminar differences. Briefly, the NDs in the ventral hippocampus were significantly lower in the CA3 region than in the CA1 region and dentate gyrus, although no interregional differences were detectable in the dorsal hippocampus. Both in the CA1 and CA3 regions, the NDs were significantly higher in the stratum lacunosum-moleculare than in the remaining layers. Next, we investigated the spatial patterns of distribution of Iba1-labeled microglia and S100beta-labeled astrocytes. So far as we examined, the somato-somatic contacts were not seen among microglia or among astrocytes, whereas the close apposition between microglia and astrocytes were occasionally detected. The 3D point process analysis showed that the spatial distribution of microglia was significantly repulsive. Because the statistical territory of single microglia was larger than that estimated from process tracing, they are not likely to touch each other with their processes. Astrocytes were distributed slightly repulsively with overlapping areas. The 3D point process analysis also revealed a significant spatial attraction between microglia and astrocytes. The present findings provide a novel anatomical basis for glial research.

Measurement of the decay rate of the negative ion of positronium (Ps-).

A new determination of the decay rate of the negative ion of positronium (Ps-), using a beam-foil method and a stripping-based detection technique, is reported. The measured result of gamma = 2.089(15) ns(-1) is a factor of 6 more precise than the previous experimental value of gamma = 2.09(9) ns(-1), and is in excellent agreement with the theoretical value of gamma = 2.086(6) ns(-1).

Fitting of random tessellation models to keratin filament networks.

The role of specific structural patterns in keratin filament networks for regulating biophysical properties of epithelial cells is poorly understood. This is at least partially due to a lack of methods for the analysis of filament network morphology. We have previously developed a statistical approach to the analysis of keratin filament networks imaged by scanning electron microscopy. The segmentation of images in this study resulted in graph structures, i.e. tessellations, whose structural characteristics are now further investigated by iteratively fitting geometrical statistical models. An optimal model as well as corresponding optimal parameters are detected from a given set of possible random tessellation models, i.e. Poisson-Line tessellations (PLT), Poisson-Voronoi tessellations (PVT) and Poisson-Delaunay tessellations (PDT). Using this method, we investigated the remodeling of keratin filament networks in pancreatic cancer cells in response to transforming growth factor alpha (TGFalpha), which is involved in pancreatic cancer progression. The results indicate that the fitting of random tessellation models represents a suitable method for the description of complex filament networks.

Preparation of 5-brominated and 5,5'-dibrominated 2,2'-bipyridines and 2,2'-bipyrimidines.

Efficient syntheses of 5-brominated and 5,5'-dibrominated 2,2'-bipyridines and 2,2'-bipyrimidines, useful for the preparation of metal-complexing molecular rods, have been developed. 5-Bromo-2,2'-bipyridine, 5-bromo-5'-n-butyl-2,2'-bipyridine, and 5-bromo-5'-n-hexyl-2,2'-bipyridine were obtained by Stille coupling of 2,5-dibromopyridine with 2-trimethylstannylpyridine or the requisite 5-alkyl-2-trimethylstannylpyridine, obtained via regioselective zincation of a 3-alkylpyridine.BF(3) complex in the less hindered of the two reactive positions with lithium di-tert-butyl-(2,2,6,6-tetramethylpiperidino)zincate. 5,5'-Dibromo-2,2'-bipyridine was obtained by the reductive symmetric coupling of 2,5-dibromopyridine with hexa-n-butyldistannane. The yields of these coupling reactions ranged from 70 to 90%. 5-Bromo- and 5,5'-dibromo-2,2'-bipyrimidines were obtained in yields of 30 and 15%, respectively, by bromination of 2,2'-bipyrimidine, prepared from 2-chloropyrimidine in 80% yield by an improved reductive symmetric coupling procedure.