A comparison of methods for constructing confidence intervals after phase II/III clinical trials

Recently, in order to accelerate drug development, trials that use adaptive seamless designs such as phase II/III clinical trials have been proposed. Phase II/III clinical trials combine traditional phases II and III into a single trial that is conducted in two stages. Using stage 1 data, an interim analysis is performed to answer phase II objectives and after collection of stage 2 data, a final confirmatory analysis is performed to answer phase III objectives. In this paper we consider phase II/III clinical trials in which, at stage 1, several experimental treatments are compared to a control and the apparently most effective experimental treatment is selected to continue to stage 2. Although these trials are attractive because the confirmatory analysis includes phase II data from stage 1, the inference methods used for trials that compare a single experimental treatment to a control and do not have an interim analysis are no longer appropriate. Several methods for analysing phase II/III clinical trials have been developed. These methods are recent and so there is little literature on extensive comparisons of their characteristics. In this paper we review and compare the various methods available for constructing confidence intervals after phase II/III clinical trials.

Data-driven treatment selection for seamless phase II/III trials incorporating early-outcome data

Seamless phase II/III clinical trials are conducted in two stages with treatment selection at the first stage. In the first stage, patients are randomized to a control or one of k > 1 experimental treatments. At the end of this stage, interim data are analysed, and a decision is made concerning which experimental treatment should continue to the second stage. If the primary endpoint is observable only after some period of follow-up, at the interim analysis data may be available on some early outcome on a larger number of patients than those for whom the primary endpoint is available. These early endpoint data can thus be used for treatment selection. For two previously proposed approaches, the power has been shown to be greater for one or other method depending on the true treatment effects and correlations. We propose a new approach that builds on the previously proposed approaches and uses data available at the interim analysis to estimate these parameters and then, on the basis of these estimates, chooses the treatment selection method with the highest probability of correctly selecting the most effective treatment. This method is shown to perform well compared with the two previously described methods for a wide range of true parameter values. In most cases, the performance of the new method is either similar to or, in some cases, better than either of the two previously proposed methods.

Sea surface temperature datasets for climate applications from Phase 1 of the European Space Agency Climate Change Initiative (SST CCI)

Sea surface temperature (SST) datasets have been generated from satellite observations for the period 1991–2010, intended for use in climate science applications. Attributes of the datasets specifically relevant to climate applications are: first, independence from in situ observations; second, effort to ensure homogeneity and stability through the time-series; third, context-specific uncertainty estimates attached to each SST value; and, fourth, provision of estimates of both skin SST (the fundamental measure- ment, relevant to air-sea fluxes) and SST at standard depth and local time (partly model mediated, enabling comparison with his- torical in situ datasets). These attributes in part reflect requirements solicited from climate data users prior to and during the project. Datasets consisting of SSTs on satellite swaths are derived from the Along-Track Scanning Radiometers (ATSRs) and Advanced Very High Resolution Radiometers (AVHRRs). These are then used as sole SST inputs to a daily, spatially complete, analysis SST product, with a latitude-longitude resolution of 0.05°C and good discrimination of ocean surface thermal features. A product user guide is available, linking to reports describing the datasets’ algorithmic basis, validation results, format, uncer- tainty information and experimental use in trial climate applications. Future versions of the datasets will span at least 1982–2015, better addressing the need in many climate applications for stable records of global SST that are at least 30 years in length.

Sources, sinks, and transatlantic transport of North African dust aerosol: a multimodel analysis and comparison with remote sensing data

This study evaluates model-simulated dust aerosols over North Africa and the North Atlantic from five global models that participated in the Aerosol Comparison between Observations and Models phase II model experiments. The model results are compared with satellite aerosol optical depth (AOD) data from Moderate Resolution Imaging Spectroradiometer (MODIS), Multiangle Imaging Spectroradiometer (MISR), and Sea-viewing Wide Field-of-view Sensor, dust optical depth (DOD) derived from MODIS and MISR, AOD and coarse-mode AOD (as a proxy of DOD) from ground-based Aerosol Robotic Network Sun photometer measurements, and dust vertical distributions/centroid height from Cloud Aerosol Lidar with Orthogonal Polarization and Atmospheric Infrared Sounder satellite AOD retrievals. We examine the following quantities of AOD and DOD: (1) the magnitudes over land and over ocean in our study domain, (2) the longitudinal gradient from the dust source region over North Africa to the western North Atlantic, (3) seasonal variations at different locations, and (4) the dust vertical profile shape and the AOD centroid height (altitude above or below which half of the AOD is located). The different satellite data show consistent features in most of these aspects; however, the models display large diversity in all of them, with significant differences among the models and between models and observations. By examining dust emission, removal, and mass extinction efficiency in the five models, we also find remarkable differences among the models that all contribute to the discrepancies of model-simulated dust amount and distribution. This study highlights the challenges in simulating the dust physical and optical processes, even in the best known dust environment, and stresses the need for observable quantities to constrain the model processes.

Predicting the orientation of lipid cubic phase films

Lipid cubic phase films are of increasingly widespread importance, both in the analysis of the cubic phases themselves by techniques including microscopy and X-ray scattering, and in their applications, especially as electrode coatings for electrochemical sensors and for templates for the electrodeposition of nanostructured metal. In this work we demonstrate that the crystallographic orientation adopted by these films is governed by minimization of interfacial energy. This is shown by the agreement between experimental data obtained using grazing-incidence small-angle X-ray scattering (GI-SAXS), and the predicted lowest energy orientation determined using a theoretical approach we have recently developed. GI-SAXS data show a high degree of orientation for films of both the double diamond phase and the gyroid phase, with the [111] and [110] directions respectively perpendicular to the planar substrate. In each case, this matches the lowest energy facet calculated for that particular phase.

A comparison of methods for treatment selection in seamless phase II/III clinical trials incorporating information on short-term endpoints

In an adaptive seamless phase II/III clinical trial interim analysis, data are used for treatment selection, enabling resources to be focused on comparison of more effective treatment(s) with a control. In this paper, we compare two methods recently proposed to enable use of short-term endpoint data for decision-making at the interim analysis. The comparison focuses on the power and the probability of correctly identifying the most promising treatment. We show that the choice of method depends on how well short-term data predict the best treatment, which may be measured by the correlation between treatment effects on short- and long-term endpoints.

Season of birth and sheep husbandry in late Roman and Medieval coastal Flanders: a pilot study using tooth enamel d18O analysis

From the early Roman period, there is archaeological evidence for the exploitation of the Flemish coastal plain (Belgium) for a range of activities, such as sheep herding on the then developing salt-marshes and salt-meadows for the production of wool. During the early Middle Ages, this culminated in the establishment of dedicated ‘sheep estates’. This phase of exploitation was followed by extensive drainage and land reclamation measures in the high Medieval period, transforming areas into grassland, suited for cattle breeding. As part of a larger project investigating the onset, intensification and final decline of sheep management in coastal Flanders in the historical period, this pilot study presents the results of sequential sampling and oxygen isotope analysis of a number of sheep teeth (M2, n = 8) from four late Roman and Medieval sites (dating from 4th to 15th century AD), in order to assess potential variations in season of birth between the different sites and through time. In comparison with published data from herds of known birth season, incremental enamel data from the Flemish sites are consistent with late winter/spring births, with the possibility of some instances of slightly earlier parturition. These findings suggest that manipulation of season of birth was not a feature of the sheep husbandry-based economies of early historic Flanders, further evidencing that wool production was the main purpose of contemporary sheep rearing in the region. Manipulation of season of birth is not likely to have afforded economic advantage in wool-centred economies, unlike in some milk- or meat-based regimes.

The ecological impact of conquest and colonization on a medieval frontier landscape: combined palynological and geochemical analysis of lake sediments from Radzyń Chełminski, northern Poland

Slavic and German colonization of the southern Baltic between the 8th and 15th centuries A.D. is well-documented archaeologically and historically. Despite the large number of pollen profiles from Poland, few palaeoecological studies have examined the ecological impact of a process that was central to the expansion of European, Christian, societies. This study aims to redress this balance through multiproxy analysis of lake sediments from Radzyń Chełminski, Northern Poland, using pollen, element geochemistry (Inductively Coupled-Optical Emission Spectroscopy [ICP-OES]), organic content, and magnetic susceptibility. The close association between lake and medieval settlements presents the ideal opportunity to reconstruct past vegetation and land-use dynamics within a well-documented archaeological, historical, and cultural context. Three broad phases of increasing landscape impact are visible in the pollen and geochemical data dating from the 8th/9th, 10th/11th, and 13th centuries, reflecting successive phases of Slavic and German colonization. This involved the progressive clearance of oak-hornbeam dominated woodland and the development of an increasingly open agricultural landscape. Although the castles and towns of the Teutonic Order remain the most visible signs of medieval colonization, the palynological and geochemical data demonstrate that the major phase of woodland impact occurred during the preceding phase of Slavic expansion; Germans colonists were entering a landscape already significantly altered.

Climate versus carbon dioxide controls on biomass burning: a model analysis of the glacial–interglacial contrast

Climate controls fire regimes through its influence on the amount and types of fuel present and their dryness. CO2 concentration constrains primary production by limiting photosynthetic activity in plants. However, although fuel accumulation depends on biomass production, and hence on CO2 concentration, the quantitative relationship between atmospheric CO2 concentration and biomass burning is not well understood. Here a fire-enabled dynamic global vegetation model (the Land surface Processes and eXchanges model, LPX) is used to attribute glacial–interglacial changes in biomass burning to an increase in CO2, which would be expected to increase primary production and therefore fuel loads even in the absence of climate change, vs. climate change effects. Four general circulation models provided last glacial maximum (LGM) climate anomalies – that is, differences from the pre-industrial (PI) control climate – from the Palaeoclimate Modelling Intercomparison Project Phase~2, allowing the construction of four scenarios for LGM climate. Modelled carbon fluxes from biomass burning were corrected for the model's observed prediction biases in contemporary regional average values for biomes. With LGM climate and low CO2 (185 ppm) effects included, the modelled global flux at the LGM was in the range of 1.0–1.4 Pg C year-1, about a third less than that modelled for PI time. LGM climate with pre-industrial CO2 (280 ppm) yielded unrealistic results, with global biomass burning fluxes similar to or even greater than in the pre-industrial climate. It is inferred that a substantial part of the increase in biomass burning after the LGM must be attributed to the effect of increasing CO2 concentration on primary production and fuel load. Today, by analogy, both rising CO2 and global warming must be considered as risk factors for increasing biomass burning. Both effects need to be included in models to project future fire risks.

Flexible selection of a single treatment incorporating short-term endpoint information in a phase II/III clinical trial

Seamless phase II/III clinical trials in which an experimental treatment is selected at an interim analysis have been the focus of much recent research interest. Many of the methods proposed are based on the group sequential approach. This paper considers designs of this type in which the treatment selection can be based on short-term endpoint information for more patients than have primary endpoint data available. We show that in such a case, the familywise type I error rate may be inflated if previously proposed group sequential methods are used and the treatment selection rule is not specified in advance. A method is proposed to avoid this inflation by considering the treatment selection that maximises the conditional error given the data available at the interim analysis. A simulation study is reported that illustrates the type I error rate inflation and compares the power of the new approach with two other methods: a combination testing approach and a group sequential method that does not use the short-term endpoint data, both of which also strongly control the type I error rate. The new method is also illustrated through application to a study in Alzheimer's disease. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen–Cahn/Cahn–Hilliard/Navier–Stokes–Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.

Process analysis of trauma-focused cognitive behavioural therapy for individuals with schizophrenia

Objective. Therapeutic alliance, modality, and ability to engage with the process of therapy have been the main focus of research into what makes psychotherapy successful. Individuals with complex trauma histories or schizophrenia are suggested to be more difficult to engage and may be less likely to benefit from therapy. This study aimed to track the in-session ‘process’ of working alliance and emotional processing of trauma memories for individuals with schizophrenia. Design. The study utilized session recordings from the treatment arm of an open randomized clinical trial investigating trauma-focused cognitive behavioural therapy (TF-CBT) for individuals with schizophrenia (N = 26). Method. Observer measures of working alliance, emotional processing, and affect arousal were rated at early and late phases of therapy. Correlation analysis was undertaken for process measures. Temporal analysis of expressed emotions was also reported. Results. Working alliance was established and maintained throughout the therapy; however, agreement on goals reduced at the late phase. The participants appeared to be able to engage in emotional processing, but not to the required level for successful cognitive restructuring. Conclusion. This study undertook novel exploration of process variables not usually explored in CBT. It is also the first study of process for TF-CBT with individuals with schizophrenia. This complex clinical sample showed no difficulty in engagement; however, they may not be able to fully undertake the cognitive–emotional demands of this type of therapy. Clinical and research implications and potential limitations of these methods are considered.

Interim analyses and sequential designs in phase III studies

Recruitment of patients to a clinical trial usually occurs over a period of time, resulting in the steady accumulation of data throughout the trial's duration. Yet, according to traditional statistical methods, the sample size of the trial should be determined in advance, and data collected on all subjects before analysis proceeds. For ethical and economic reasons, the technique of sequential testing has been developed to enable the examination of data at a series of interim analyses. The aim is to stop recruitment to the study as soon as there is sufficient evidence to reach a firm conclusion. In this paper we present the advantages and disadvantages of conducting interim analyses in phase III clinical trials, together with the key steps to enable the successful implementation of sequential methods in this setting. Examples are given of completed trials, which have been carried out sequentially, and references to relevant literature and software are provided.

Stopping rules for phase II studies

This paper, the second in a series of three papers concerned with the statistical aspects of interim analyses in clinical trials, is concerned with stopping rules in phase II clinical trials. Phase II trials are generally small-scale studies, and may include one or more experimental treatments with or without a control. A common feature is that the results primarily determine the course of further clinical evaluation of a treatment rather than providing definitive evidence of treatment efficacy. This means that there is more flexibility available in the design and analysis of such studies than in phase III trials. This has led to a range of different approaches being taken to the statistical design of stopping rules for such trials. This paper briefly describes and compares the different approaches. In most cases the stopping rules can be described and implemented easily without knowledge of the detailed statistical and computational methods used to obtain the rules.

The combined influences of westerly phase of the quasi biennial oscillation and 11-year solar maximum conditions on the Northern Hemisphere extratropical winter circulation

The combined influences of the westerly phase of the quasi-biennial oscillation (QBO-W) and solar maximum (Smax) conditions on the Northern Hemisphere extratropical winter circulation are investigated using reanalysis data and Center for Climate System Research/National Institute for Environmental Studies chemistry climate model (CCM) simulations. The composite analysis for the reanalysis data indicates strengthened polar vortex in December followed by weakened polar vortex in February–March for QBO-W during Smax (QBO-W/Smax) conditions. This relationship need not be specific to QBO-W/Smax conditions but may just require strengthened vortex in December, which is more likely under QBO-W/Smax. Both the reanalysis data and CCM simulations suggest that dynamical processes of planetary wave propagation and meridional circulation related to QBO-W around polar vortex in December are similar in character to those related to Smax; furthermore, both processes may work in concert to maintain stronger vortex during QBO-W/Smax. In the reanalysis data, the strengthened polar vortex in December is associated with the development of north–south dipole tropospheric anomaly in the Atlantic sector similar to the North Atlantic oscillation (NAO) during December–January. The structure of the north–south dipole anomaly has zonal wavenumber 1 (WN1) component, where the longitude of anomalous ridge overlaps with that of climatological ridge in the North Atlantic in January. This implies amplification of the WN1 wave and results in the enhancement of the upward WN1 propagation from troposphere into stratosphere in January, leading to the weakened polar vortex in February–March. Although WN2 waves do not play a direct role in forcing the stratospheric vortex evolution, their tropospheric response to QBO-W/Smax conditions appears to be related to the maintenance of the NAO-like anomaly in the high-latitude troposphere in January. These results may provide a possible explanation for the mechanisms underlying the seasonal evolution of wintertime polar vortex anomalies during QBO-W/Smax conditions and the role of troposphere in this evolution.