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.

A comprehensive meta-analysis of common genetic variants in autism spectrum conditions

Background Autism spectrum conditions (ASC) are a group of neurodevelopmental conditions characterized by difficulties in social interaction and communication alongside repetitive and stereotyped behaviours. ASC are heritable, and common genetic variants contribute substantial phenotypic variability. More than 600 genes have been implicated in ASC to date. However, a comprehensive investigation of candidate gene association studies in ASC is lacking. Methods In this study, we systematically reviewed the literature for association studies for 552 genes associated with ASC. We identified 58 common genetic variants in 27 genes that have been investigated in three or more independent cohorts and conducted a meta-analysis for 55 of these variants. We investigated publication bias and sensitivity and performed stratified analyses for a subset of these variants. Results We identified 15 variants nominally significant for the mean effect size, 8 of which had P values below a threshold of significance of 0.01. Of these 15 variants, 11 were re-investigated for effect sizes and significance in the larger Psychiatric Genomics Consortium dataset, and none of them were significant. Effect direction for 8 of the 11 variants were concordant between both the datasets, although the correlation between the effect sizes from the two datasets was poor and non-significant. Conclusions This is the first study to comprehensively examine common variants in candidate genes for ASC through meta-analysis. While for majority of the variants, the total sample size was above 500 cases and 500 controls, the total sample size was not large enough to accurately identify common variants that contribute to the aetiology of ASC.

Assessing species’ habitat associations from occurrence records, standardised monitoring data and expert opinion: a test with British butterflies

Accurate knowledge of species’ habitat associations is important for conservation planning and policy. Assessing habitat associations is a vital precursor to selecting appropriate indicator species for prioritising sites for conservation or assessing trends in habitat quality. However, much existing knowledge is based on qualitative expert opinion or local scale studies, and may not remain accurate across different spatial scales or geographic locations. Data from biological recording schemes have the potential to provide objective measures of habitat association, with the ability to account for spatial variation. We used data on 50 British butterfly species as a test case to investigate the correspondence of data-derived measures of habitat association with expert opinion, from two different butterfly recording schemes. One scheme collected large quantities of occurrence data (c. 3 million records) and the other, lower quantities of standardised monitoring data (c. 1400 sites). We used general linear mixed effects models to derive scores of association with broad-leaf woodland for both datasets and compared them with scores canvassed from experts. Scores derived from occurrence and abundance data both showed strongly positive correlations with expert opinion. However, only for occurrence data did these fell within the range of correlations between experts. Data-derived scores showed regional spatial variation in the strength of butterfly associations with broad-leaf woodland, with a significant latitudinal trend in 26% of species. Sub-sampling of the data suggested a mean sample size of 5000 occurrence records per species to gain an accurate estimation of habitat association, although habitat specialists are likely to be readily detected using several hundred records. Occurrence data from recording schemes can thus provide easily obtained, objective, quantitative measures of habitat association.

Rejection thresholds (RjT) of sweet likers and dislikers

Sweetness is generally a desirable taste, however consumers can be grouped into sweet likers and dislikers according to optimally preferred sucrose concentrations. Understanding the levels of sweetness in products that are acceptable and unacceptable to both consumer groups is important to product development and for influencing dietary habits. The concentrations at which sucrose decreases liking (the rejection threshold; RjT) in liquid and semi-solid matrices were investigated in this study. Thirty six consumers rated their liking of 5 sucrose aqueous solutions; this identified 36% sweet likers (SL) whose liking ratings increased with increasing sucrose and 64% sweet dislikers (SD) whose liking ratings decreased above 6% (w/v) sucrose. We hypothesized that SL and SD would have different RjT for sucrose in products. This was tested by preparing 8 levels of sucrose in orange juice and orange jelly and presenting each against the lowest level in forced choice preference tests. In orange juice, as sucrose increased from 33g/L to 75g/L the proportion of people preferring the sweeter sample increased in both groups. However, at higher sucrose levels, the proportion of consumers preferring the sweet sample decreased. For SD, a RjT was reached at 380 g/L, whereas a significant RjT for SL was not reached. RjT in jelly were not reached as the sweetness in orange jelly was significantly lower than for orange juice (p<0.001). Despite statistically significant differences in rated sweetness between SL and SD (p=0.019), the extent of difference between the two groups was minor. The results implied that sweet liker status was not substantially related to differences in sweetness perception. Self-reported dietary intake of carbohydrate, sugars and sucrose were not significantly affected by sweet liker status. However the failure to find an effect may be due to the small sample size and future studies within a larger, more representative population sample are justifiable from the results of this study.

Ecological niche similarities of Peponapis bees and non-domesticated Cucurbita species

Peponapis bees are considered specialized pollinators of Cucurbita flowers, a genus that presents several species of economic value (squashes and pumpkins). Both genera originated in the Americas, and their diversity dispersion center is in Mexico. Ten species of Peponapis and ten species of Cucurbita (only non-domesticated species) were analyzed considering the similarity of their ecological niche characteristics with respect to climatic conditions of their occurrence areas (abiotic variables) and interactions between species (biotic variables). The similarity of climatic conditions (temperature and precipitation) was estimated through cluster analyses. The areas of potential occurrence of the most similar species were obtained through ecological niche modeling and summed with geographic information system tools. Three main clusters were obtained: one with species that shared potential occurrence areas mainly in deserts (P. pruinosa, P. timberlakei, C. digitata, C. palmata, C. foetidissima), another in moist forests (P. limitaris, P. atrata, C. lundelliana, C. o. martinezii) and a third mainly in dry forests (C. a. sororia, C. radicans, C. pedatifolia, P. azteca, P. smithi, P. crassidentata, P. utahensis). Some species with similar ecological niche presented potential shared areas that are also similar to their geographical distribution, like those occurring predominantly on deserts. However, some clustered species presented larger geographical areas, such as P. pruinosa and C. foetidissima suggesting other drivers than climatic conditions to shape their distributions. The domestication of Cucurbita and also the natural history of both genera were considered also as important factors. (C) 2011 Elsevier B.V. All rights reserved.

Vivipary in the cactus family: A reply to Ortega-Baes` et al. evaluation of 25 species from northwestern Argentina

This is a reply to Ortega-Baes` et al. (2010) survey of 25 Argentinean species of cacti evaluated for vivipary. We argue that the sample size and geographic area of the species investigated is insufficient to totally exclude the putative commonness of this condition in the Cactaceae. We indicate possible reasons why they did not find viviparous fruits in their survey. Failure to detect vivipary in cacti of NW Argentina may be correlated with limited taxonomic sampling and geographic region in addition to intrinsic and extrinsic plant factors, including different stages of fruit and seed development and genetic, ecological, and edaphic aspects, which, individually or in concert, control precocious germination. We uphold that viviparity is putatively frequent in this family and list 16 new cases for a total of 53 viviparous cacti, which make up ca. 4% incidence of viviparism in the Cactaceae, a substantially higher percentage than most angiosperm families exhibiting this condition. The Cactaceae ranks fourth in frequency of viviparity after the aquatic families of mangroves and seagrasses. We suggest the re-evaluation of cactus vivipary, primarily as a reproductive adaptation to changing environments and physiological stress with a secondary role as a reproductive strategy with limited offspring dispersal/survival and fitness advantages. (C) 2011 Elsevier Ltd. All rights reserved.

The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

Performance Improvement of Tomographic Image Reconstruction Based on DSP Processors

This paper presents the use of a multiprocessor architecture for the performance improvement of tomographic image reconstruction. Image reconstruction in computed tomography (CT) is an intensive task for single-processor systems. We investigate the filtered image reconstruction suitability based on DSPs organized for parallel processing and its comparison with the Message Passing Interface (MPI) library. The experimental results show that the speedups observed for both platforms were increased in the same direction of the image resolution. In addition, the execution time to communication time ratios (Rt/Rc) as a function of the sample size have shown a narrow variation for the DSP platform in comparison with the MPI platform, which indicates its better performance for parallel image reconstruction.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Inferential Implications of Over-Parametrization: A Case Study in Incomplete Categorical Data

P>In the context of either Bayesian or classical sensitivity analyses of over-parametrized models for incomplete categorical data, it is well known that prior-dependence on posterior inferences of nonidentifiable parameters or that too parsimonious over-parametrized models may lead to erroneous conclusions. Nevertheless, some authors either pay no attention to which parameters are nonidentifiable or do not appropriately account for possible prior-dependence. We review the literature on this topic and consider simple examples to emphasize that in both inferential frameworks, the subjective components can influence results in nontrivial ways, irrespectively of the sample size. Specifically, we show that prior distributions commonly regarded as slightly informative or noninformative may actually be too informative for nonidentifiable parameters, and that the choice of over-parametrized models may drastically impact the results, suggesting that a careful examination of their effects should be considered before drawing conclusions.Resume Que ce soit dans un cadre Bayesien ou classique, il est bien connu que la surparametrisation, dans les modeles pour donnees categorielles incompletes, peut conduire a des conclusions erronees. Cependant, certains auteurs persistent a negliger les problemes lies a la presence de parametres non identifies. Nous passons en revue la litterature dans ce domaine, et considerons quelques exemples surparametres simples dans lesquels les elements subjectifs influencent de facon non negligeable les resultats, independamment de la taille des echantillons. Plus precisement, nous montrons comment des a priori consideres comme peu ou non-informatifs peuvent se reveler extremement informatifs en ce qui concerne les parametres non identifies, et que le recours a des modeles surparametres peut avoir sur les conclusions finales un impact considerable. Ceci suggere un examen tres attentif de l`impact potentiel des a priori.

Improved likelihood inference in Birnbaum-Saunders regressions

The Birnbaum-Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. Our simulation results suggest that the likelihood ratio test tends to be liberal when the sample size is small. We obtain a correction factor which reduces the size distortion of the test. Also, we consider a parametric bootstrap scheme to obtain improved critical values and improved p-values for the likelihood ratio test. The numerical results show that the modified tests are more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application. (C) 2009 Elsevier B.V. All rights reserved.

Asymptotic Skewness in Exponential Family Nonlinear Models

In this article, we give an asymptotic formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in exponencial family nonlinear models. We generalize the result by Cordeiro and Cordeiro ( 2001). The formula is given in matrix notation and is very suitable for computer implementation and to obtain closed form expressions for a great variety of models. Some special cases and two applications are discussed.

Methods for Equivalence and Noninferiority Testing

Classical hypothesis testing focuses on testing whether treatments have differential effects on outcome. However, sometimes clinicians may be more interested in determining whether treatments are equivalent or whether one has noninferior outcomes. We review the hypotheses for these noninferiority and equivalence research questions, consider power and sample size issues, and discuss how to perform such a test for both binary and survival outcomes. The methods are illustrated on 2 recent studies in hematopoietic cell transplantation.

Asymptotic skewness in Birnbaum-Saunders nonlinear regression models

The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in Birnbaum-Saunders nonlinear regression models, recently introduced by Lemonte and Cordeiro (2009). The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors, in order to obtain closed-form skewness in a wide range of nonlinear regression models. Empirical and real applications are analyzed and discussed. (C) 2010 Elsevier B.V. All rights reserved.

The Choice of STIGA Table Tennis Blades : Evidence from China

The purpose of this paper is to investigate how individuals with different characteristics make their choice-decisions when consuming STIGA table tennis blades, which are combinations of various attributes, such as price, control, attack, etc. It is expected that the general trend of choice behavior on this special commodity can be, at least to some extent, revealed. Data were collected using questionnaires sent to registered members of a table tennis club in China. The questionnaires included information and questions about individuals’ monthly income levels, ages, technique styles, etc. A multinomial logit model was then applied to analyze factors determining Chinese consumers’ choice behavior on STIGA table tennis blades. The results indicated that the main element influencing Chinese consumers’ choice of STIGA ping-pong blades was the technique style and other variables did not seem to influence the choice of table tennis blades. These results might be explained by the limited sample size as well as unmeasured and immeasurable factors. Thus, a more extensive research is needed to be conducted in the future.