Randomization-based nonparametric methods for the analysis of multicentre trials

Multicentre trials offer several advantages over single centre trials in clinical research, including the ability to recruit patients at a faster rate over the course of the study, increased generalizability through the use of a broader patient population, and the ability to shed light on the replication of findings at multiple centres in a single study. A nonparametric approach to the analysis of multicentre trial data provides a convenient way for addressing the role of centres as well as baseline covariables during data analysis. With the use of randomization-based nonparametric methods, the strategy for evaluating the null hypothesis of no treatment effect can be prespecified during study planning without requiring a specific structure for the relationship of response criteria (or endpoints) to centres, covariables, or potential interaction terms. Further, the basis of inference for the application of these methods is the randomization mechanism, and the population to which inference can be directly made is the study population itself. No assumptions about underlying distributions, data structures, likelihood functions, or samples from super populations of inference are required. A three-step approach is proposed for handling centres via randomization-based nonparametric methods. In Step 1, a test of overall treatment effect is carried out using data from all centres simultaneously, without any assumption about treatment by centre interaction. In Step 2, the question of treatment by centre interaction is addressed, usually through the use of parametric multiple regression methods. In cases with suggestion of such interaction, Step 3 is conducted to evaluate different weighting schemes in forming pairwise treatment comparisons averaged across centres to assess the robustness of treatment effects observed in Step 1. An attractive inferential feature of this three-step approach is that the Type I error for the test of treatment effect is controlled by requiring statistical significance at each step to proceed to the next step. Extended Mantel-Haenszel methods with stratification adjustment for centre can be used to provide a nonparametric assessment of treatment effect. When adjustment for other covariates, such as baseline values, is desired, the more recent nonparametric analysis of covariance methods are available. Both methods are easy to use, require no assumptions beyond that of a valid randomization mechanism, and can be applied in a similar manner to dichotomous, ordinal, failure time, or continuous response criteria (endpoints). The methods are illustrated using data from a confirmatory clinical trial of a therapeutic agent for the treatment of dry eye disease.     

The design of multicentre trials

The analysis of data collected in multicentre trials offers challenges because the data from the individual centres must be combined in some way to give an overall evaluation of the differences between the treatments in the trial. We propose that the combined response to treatment (CRT) be used as this overall measure. The definition and estimation of the CRT can be derived from either a fixed-effects or a random-effects model. For the latter we introduce the ECRT--the expected combined response to treatment. We describe and compare both types of model and express our preference for the random-effects model. We stress that the number of patients enrolled at a centre is a random variable and show that this source of randomness inflates the variance of the estimated ECRT. Variability in enrolment rates over the centres further inflates this variance. A simple conclusion from our results is that if variability in the treatment and centre effects, in the enrolment time, in the number of patients enrolled at a centre and in the enrolment rates is not properly accounted for, then an underpowered trial may result. Using properties of estimators generated by the random-effects model we propose methods for determining the optimal number of centres and total number of patients to enrol in a trial to minimize a loss function that accounts for centre and patient costs and loss of revenue. We discuss variants of the loss function and corresponding optimization problems for different types of enrolment. We end the paper with brief generalizations of the developed techniques to the case where the response is binary.     

Bayesian analysis of multicentre trial outcomes

Bayesian methods provide flexibility in the analysis of data from multicentre trials that would be difficult to achieve by other means. This paper illustrates some useful applications of Bayesian methods to the analysis of multicentre trials, with emphasis on insights that would be difficult to obtain using conventional frequentist methods. Two trials provide data for illustration: a large multicentre trial comparing two doses of a drug with placebo with respect to an essentially continuous measurement for which the original analysis revealed a significant treatment by centre effect, and a large multicentre trial with intraclass correlation induced by a categorical outcome of up to four episodes of heartburn reported by individual patients. The data from both trials had been analysed previously using conventional frequentist methods. Both sets of data were reanalysed using Bayesian and empirical Bayesian methods; all of the analyses provided the same conclusions for the key questions regarding treatment differences. The Bayesian methods provided some insights useful for model checking and also provided a way to explore some important quantitative aspects about the magnitude of treatment effects.     

Relative efficiency of unequal cluster sizes for variance component estimation in cluster randomized and multicentre trials

Cluster randomized and multicentre trials evaluate the effect of a treatment on persons nested within clusters, for instance patients within clinics or pupils within schools. Although equal sample sizes per cluster are generally optimal for parameter estimation, they are rarely feasible. This paper addresses the relative efficiency (RE) of unequal versus equal cluster sizes for estimating variance components in cluster randomized trials and in multicentre trials with person randomization within centres, assuming a quantitative outcome. Starting from maximum likelihood estimation, the RE is investigated numerically for a range of cluster size distributions. An approximate formula is presented for computing the RE as a function of the mean and variance of cluster sizes and the intraclass correlation. The accuracy of this approximation is checked and found to be good. It is concluded that the loss of efficiency for variance component estimation due to variation of cluster sizes rarely exceeds 20% and can be compensated by sampling 25% more clusters.     

Deviations from the population-averaged versus cluster-specific relationship for clustered binary data

There has been much debate about the relative merits of mixed effects and population-averaged logistic models. We present a different perspective on this issue by noting that the investigation of the relationship between these models for a given dataset offers a type of sensitivity analysis that may reveal problems with assumptions of the mixed effects and/or population-averaged models for clustered binary response data in general and longitudinal binary outcomes in particular. We present several datasets in which the following violations of assumptions are associated with departures from the expected theoretical relationship between these two models: 1) negative intra-cluster correlations; 2) confounding of the response-covariate relationship by cluster effects; and 3) confounding of autoregressive relationships by the link between baseline outcomes and subject effects. Under each of these conditions, the expected theoretical attenuation of the population-averaged odds ratio relative to the cluster-specific odds ratio does not necessarily occur. In all cases, the naive fitting of a random intercept logistic model appears to lead to bias. In response, the random intercept model is modified to accommodate negative intra-cluster correlations, confounding due to clusters, or baseline correlations with random effects. Comparisons are made with GEE estimation of population-averaged models and conditional likelihood estimation of cluster-specific models. Several examples, including a cross-over trial, a multicentre nonrandomized treatment study, and a longitudinal observational study are used to illustrate these modifications.     

Eosinophilic gastroenteritis with refractory ulcer disease and gastrointestinal bleeding as a rare manifestation of seronegative gastrointestinal food allergy

Diabetes mellitus is a major cause of morbidity and mortality worldwide, with a prevalence of 347 million in 2013. Complementary and Alternative Medicines (CAM) are a group of remedies that is fast gaining acceptance among individuals. Cinnamon, Bitter gourd (Momordica charantia) and Fenugreek (Trigonella foenum-graecum) are 3 widely used CAMs used worldwide for the treatment of diabetes. Data on safety and efficacy is limited, but the consumption is wide. Crepe ginger (Costus speciosus) and Ivy gourd (Coccinia grandis) are 2 plants used widely in the Asian region for their presumed hypoglycaemic properties. In this review, we analyzed the available evidence for the 5 CAMs mentioned above in terms of in-vitro studies, animal studies sand clinical trials. We also describe the mechanisms of hypoglycaemia and safety concerns where there is available evidence. Clinical trials that studied the hypoglycaemic effects of Cinnamon, bitter gourd, fenugreek and ivy gourd showed conflicting results. Direct comparison between studies remains a challenge in view of the baseline heterogeneity of subjects, differences in substrate preparation, variable end points and poor trial design. Short durations of study and small number of subjects studied is universal. Crepe ginger has not been studied adequately in humans to draw conclusions. In view of the high prevalence of use and safety and efficacy issues, there is an urgent need to study their hypoglycaemic and adverse effects in well-designed long-term clinical trials.     

Multicentre trials: a US regulatory perspective

Multicentre trials are very common in the field of drug development. In recent years, multicentre trials have taken on a multinational and multiregional aspect. We provide a conceptual framework for the use of multicentre trials in the context of drug development, from the perspective of drug regulation in the United States. In this paper, we review some regulatory history, milestones and standards as they relate to multicentre trials. Special attention is given to the similarities and differences in the approaches to multicentre trials in the following documents; Guideline for the Format and Content of the Clinical and Statistical Sections of New Drug Applications, International Conference on Harmonization, Draft Guideline on Statistical Principles for clinical trials and the Guidance for Industry Providing Clinical Evidence of Effectiveness for Human Drug and Biologic Products. The paper includes a consideration of some of the issues in the analysis of data from multicentre trials.     

Effects of adhesion on mixing homogeneity part I: ordered adhesion—random adhesion

According to Hersey, adhesion of a finely powdered, monosized ingredient to a course, monosized diluent may yield ordered powder mixtures of a higher degree of homogeneity than conforming to random mixtures.However, this concept implies the adherence of an identical (or almost identical) number of the fine particles to each of the carriers (‘ordered adhesion’). If, on the contrary, a random variation of the number of adhering fines per diluent particle is assumed (‘random adhesion’), pseudorandom mixtures can be formed at best. This type of mixture shows the degree of homogeneity as well as the statistical properties of fully randomized systems.To produce ordered powder mixtures, it is thus the basic requirement that ordered but not random adhesion must be achieved during mixing. So far, no mechanism has been established that may yield ordered adhesion.     

Thermodynamic control of electron transfer rates in multicentre redox proteins

In the analysis of kinetic data from multicentre redox proteins, it is essential to distinguish between the observable macroscopic rate constants and the structurally relevant microscopic properties. This distinction is complicated by the existence of interactions between centres. The problem is illustrated by the case of two interacting redox centres and generalised for the analysis of stopped-flow kinetic data for the reduction of cytochrome c(3), in which four redox centres and at least one proteolytic centre are mutually interacting. It is shown that fast intramolecular electron transfer, which is typical of many multicentre redox proteins, and, where present, fast proton exchange, ensure that only N rate constants can be measured for a protein with N redox centres. The equations that relate the observable macroscopic rate constants to the microscopic rate constants of individual centres depend on a set of parameters that can be approximated by using the Marcus theory of electron transfer together with a set of reasonable assumptions. The results are tested by fitting experimental data for the reduction of cytochrome c(3) by sodium dithionite, including its pH dependence.     

Stereochemistry and Circular Dichroism of Chiral Internal Olefin-Platinum(II) Complexes

A series of cis- and trans-dichloro(benzylamine) (chiral olefin) platinum(II) complexes, containing (Z) and (E) isomers of the internal chiral olefins R-CH=CH-R', has been prepared by ethylene displacement from the corresponding ethylene containing complexes. The particular stereochemical features of the complexes allow one to interpret the CD on the basis of the individual contributions coming from the chiral centres already present in the free olefin and from the chiral centres formed in the complexation of the double bond. Evidence is reported showing that the aforementioned contributions are additive and that the chiral centre(s) bound to the metal dominates the CD at about 400 nm, its chirality type being reflected in the sign and its chirality prevalence in the Δϵ value.     

Modelling risks in disease mapping

In this article, we propose a strategy of analysis of mortality data with the aim of providing a guideline for epidemiologists and public health researchers to choose a reasonable model for estimating mortality (or incidence) risks. Maps displaying the crude mortality rates or ratios are usually misleading because of the instability of the estimators in low populated areas. As an alternative, many smoothing methods have been presented in the literature based on Poisson inference. They account for the extra-Poisson variation (overdispersion), frequently present in the homogeneous Poisson model, by incorporating random effects. Here, we recommend to test for the potential sources of extra-Poisson variation because, depending on them, the models which fit better the data may be different. Overdispersion can be mainly due to spatial autocorrelation, unstructured heterogeneity or to a combination of these two, and also, when studying very rare diseases, it can be due to an excess of zeros in the data. In this article, different situations the analyst may encounter are detailed and appropriate procedures for each case are presented. The alternative models are illustrated using mortality data provided by the Statistical Institute of Navarra, Spain.     

Individually randomized intervention trials for disease prevention and control

It is argued that randomized, controlled trials should fulfil a critical role in the identification of practical approaches to the prevention and control of chronic diseases. Because of the great public health potential of chemopreventive and behavioural approaches to chronic disease prevention there is need for a major interdisciplinary scientific effort aimed at intervention development. Because of the cost and duration of controlled trials to evaluate specific interventions there is a need for well-conducted feasibility, pilot and intermediate outcome trials, to inform and to justify corresponding full-scale trials having clinical disease outcomes. Compared to therapeutic trials, prevention trials need to have a greater emphasis on overall benefit versus risk assessment. Such trials need to be large enough, and of sufficient duration, to yield powerful tests of key hypotheses, and informative benefit versus risk summary statements. These requirements have a range of implications for intervention trial design, conduct, monitoring and reporting, which are reviewed and discussed. The clinical trial component of the ongoing Women's Health Initiative provides illustration throughout this discussion.     

Some statistical issues in the design of HIV-1 vaccine and treatment trials

This article summarizes material on statistical issues in the design of HIV-1 preventive vaccine trials and antiretroviral HIV-1 treatment trials that was presented at the first school on Modern Statistical Methods in Medical Research, held at the International Centre for Theoretical Physics in Trieste, in September 1999. Design issues for the two trial types are discussed separately and are compared, which highlights the relative complexity of vaccine trials. Vaccine trial designs for assessing various vaccine effects are considered, including classical double-blind individual-randomized designs for evaluating biological vaccine effects on susceptibility to infection, and augmented partners, cluster-randomized, and infant designs for evaluating biological vaccine effects on infectiousness as well as on susceptibility. Within these designs, covered topics include surrogate endpoints for measuring vaccine effects on secondary transmission and on HIV-1 disease progression, and exploratory and confirmatory methods for assessing host immune and viral genotypic or phenotypic correlates of vaccine protection against infection or disease. For antiretroviral trials, covered topics include endpoint selection and structured designs such as fractional factorial and Latin square designs for rapidly screening combination drug regimens and for identifying patterns of HIV-1 genomic evolution that predict loss of drug efficacy.     

Random effects and latent processes approaches for analyzing binary longitudinal data with missingness: a comparison of approaches using opiate clinical trial data

The analysis of longitudinal data with non-ignorable missingness remains an active area in biostatistics research. This article discusses various random effects and latent process models which have been proposed for analyzing longitudinal binary data subject to both non-ignorable intermittent missing data and dropout. These models account for non-ignorable missingness by introducing random effects or a latent process which is shared between the response model and the model for the missing-data mechanism. We discuss various random effects and latent processes approaches and compare these approaches with analyses from an opiate clinical trial data set, which had high proportion of intermittent missingness and dropout. We also compare these random effect and latent process approaches with other methods for accounting for non-ignorable missingness using this data set.     

Development of a 3D model to predict curing dimensions and conversion rates of curable ceramic systems during stereolithography 3D printing process

To meet industry’s expectations for manufacturing ceramic parts by stereolithography, a better comprehension of the process, in particular laser scattering through the ceramic slurry is mandatory. This knowledge makes it possible to define adapted printing conditions to control the dimensions, homogeneity of the conversion and mechanical properties of the green parts, in order to achieve better resolutions and optimize the properties of sintered parts. This approach is focused on the development of a 3D polymerization modeling for stereolithography process able to predict curing and associated thermal phenomena. First, a design of experiments is carried out to identify material-dependent parameters, calibrate and validate the model, then able to predict monomer conversion rates and dimensions after curing depending on manufacturing parameters. Finally, temperature variation and exposure homogeneity have been evaluated. These results will allow, in future studies, to interpret the differences of deformations and mechanical properties of green parts.     

Intra-particle coating variability: Analysis and Monte-Carlo simulations

An analytical model is presented that describes the intra-particle coating variability of a single particle by a uniform spray. For uniformly random orientations, the film thickness coefficient of variation is proportional to the number of coating trials raised to the ?1/2 power, and thus the coefficient of variation asymptotes to zero as the number of coating trials increases. However, if the particle has a preferred orientation while in the spray zone, the limiting value of the coefficient of variation is non-zero. Monte-Carlo simulations of a single particle subject to a coating spray are also presented and verify the theoretical model. Finally, analysis of discrete element method (DEM) computer simulations of spheres in a rotating, circular drum without baffles show that a sphere passing through the “spray zone” has an orientation corresponding to a preferred rotation from the sphere's orientation during its last past through the spray zone. Although the intra-particle coefficient of variation for orientations exhibiting this effect still asymptote to zero over time, the rate at which this occurs is smaller than that for uniformly random orientations.     

Research on automatic spraying of single-walled carbon nanotubes and detection of spraying effects

Single-walled carbon nanotubes (SWNTs) have been introduced as compliant electrodes for dielectric elastomers (DEs) due to fault tolerance. To acquire a better electrostrictive strain and longer lifetime, it is essential to obtain a certain and uniform width of the SWNT electrode. To ensure uniform width manually, a small flux and longer time are necessary. Moreover, it is difficult to control the width of the electrode for the randomness of manual spraying. Therefore, a new type of automatic spraying process is presented in this paper. The width and homogeneity of the electrode can be easily controlled by certain parameters of the process. Two methods for detecting the homogeneity of the electrode are introduced in this paper: Measurement of surface resistance and luminosity. The coefficient of variation (CV) values detected by the two methods are virtually equal and less than 8%, which shows the feasibility of the detection method and homogeneity of automatic spraying. The speed of automatic spraying is 102 mm²/s, which is higher than that of manual spraying. The spraying process and the method used to detect homogeneity in this paper provide a reference for the relevant processes.     

Galvanomagnetic effects in graphite

A summary is given of recent work on galvanomagnetic effects in highly oriented pyrolytic graphite with current flow in the basal planes and magnetic field parallel to the c-axis. Experimental studies over a wide range of field are considered (0.001–23T) including the effect of fast neutron irradiation (0-2.9×10¹⁷ nvt (E > 1 MeV)). Theoretically, the effects of the variation of carrier properties along the zone edge, and trigonal warping of the constant energy surfaces are considered, and comparison made with predictions of the simple two band model usually used to describe galvanomagnetic properties.