Optimal sufficient dimension reduction for the conditional mean in multivariate regression

The aim of this article is to develop optimal sufficient dimensionreduction methodology for the conditional mean in multivariateregression. The context is roughly the same as that of a relatedmethod by Cook & Setodji (2003), but the new method hasseveral advantages. It is asymptotically optimal in the sensedescribed herein and its test statistic for dimension alwayshas a chi-squared distribution asymptotically under the nullhypothesis. Additionally, the optimal method allows tests ofpredictor effects. A comparison of the two methods is provided.     

Permutation inference methods for multivariate meta-analysis

Multivariate meta-analysis is gaining prominence in evidence synthesis research because it enables simultaneous synthesis of multiple correlated outcome data, and random-effects models have generally been used for addressing between-studies heterogeneities. However, coverage probabilities of confidence regions or intervals for standard inference methods for random-effects models (eg, restricted maximum likelihood estimation) cannot retain their nominal confidence levels in general, especially when the number of synthesized studies is small because their validities depend on large sample approximations. In this article, we provide permutation-based inference methods that enable exact joint inferences for average outcome measures without large sample approximations. We also provide accurate marginal inference methods under general settings of multivariate meta-analyses. We propose effective approaches for permutation inferences using optimal weighting based on the efficient score statistic. The effectiveness of the proposed methods is illustrated via applications to bivariate meta-analyses of diagnostic accuracy studies for airway eosinophilia in asthma and a network meta-analysis for antihypertensive drugs on incident diabetes, as well as through simulation experiments. In numerical evaluations performed via simulations, our methods generally provided accurate confidence regions or intervals under a broad range of settings, whereas the current standard inference methods exhibited serious undercoverage properties.     

昆虫区系多元相似性分析方法

由植物学领域首先提出的相似性概念已广泛应用于动植物区系地理研究以及生物学、生态学等诸多自然学科乃至社会科学领域.根据Jacard提出的二元相似性系数公式SI=C/(A B-C)和Sprensen提出的二元相似性系数公式SI=2C/(A B),分别推导出2个计算多元相似性系数的数学表达式,SIJab…n=[(∑Hij)2/n (∑Hijk)3/n … Hab…n]/[∑Si-∑Hij-2∑Hijk-…-(n-1)Hab…n]和 SISab…n=[2(∑Hij)2/n (3∑Hijk)3/n … nHab…n]/ ∑Si,并用中国夜蛾广布种类在中国7个动物地理区的分布资料为例进行验证,从而可以直接从整体角度和宏观规模上简便、快捷地考量多个系统间的亲疏程度和相似关系.建议在以相似性为基础的聚类分析中,不必再先把2个系统合并成一个新系统后,再和第3个系统比较,而可直接计算多个系统的相似性系数,以避免由于合并带来的信息损失.还讨论了应该提高Sprensen公式0.5的显著性标准,以使同一组数据的两种计算结果趋向一致.     

世界蜘蛛的分布格局及其多元相似性聚类分析

蜘蛛是一类种类繁多、数量巨大、分布广泛的捕食性生物。至2012年底,全世界共有蜘蛛43678种（包括亚种）,隶属于112科3898属。科、属、种3个分类阶元的分布域非常悬殊,90%的种分布在一个界内,90%的科是跨界分布或全球分布。按行政区域,亚洲种类较多,欧洲较少,南极洲没有蜘蛛记录;按动物地理区域,古北界和新热带界较多,新北界较少。根据地理条件、生态条件和蜘蛛的分布状况,将全球陆地分为53个基础地理单元,用申效诚等新近提出的相似性通用公式和据此创立的多元相似性聚类分析方法,分别对属、种两级的分布进行分析,得到两个聚类结构相同、聚类关系合理的支序图,而且属级的支序图层次更为分明,在相似性水平为0.32时,53个基础地理单元聚为17个小单元群,在0,22水平上,又聚为8个大单元群。这些大、小单元群的组成单元地域相邻相连,生态条件相对一致,可以作为蜘蛛地理区划的界、亚界两个层级。和华莱士主要以哺乳动物建立的世界动物地理区划相比,主要差异是：1、古北界东、西两部分差异显著,可分设两界;2、新西兰和澳洲大陆相似性较低,可单独设界;3、新几内亚和太平洋岛屿与澳洲大陆的关系远于和东洋界的关系,华莱士线在两界间的作用似乎不存在; 4、新热带界的中美地区似乎属于新北界更为合适,并由此产生了南北美洲间的紧密联系;5、新北界与古北界的相似性关系弱于与新热带界的关系,全北界的概念几近消失。前两点差异可以从地球板块构造的变动得到解释,第3、5个差异已在植物和其它生物类群得到佐证,第4个差异尚不稳定,需要更多类群的比较与分析。使用多元相似性聚类分析方法对于如此典型的点状分布的生物类群和如此海量的数据,能够得到如此精细的,既符合地理学、统计学的逻辑,又符合生物学、生态学逻辑的定量分析结果,这在国内外都是首次成功尝试,其简便性和合理性将会促使在其它类群中的应用。     

Causal effect estimation for multivariate continuous treatments

Causal inference is widely used in various fields, such as biology, psychology, and economics, etc. In observational studies, balancing the covariates is an important step in estimating the causal effect. This study extends the one-dimensional entropy balancing method to multiple dimensions to balance the covariates. Both parametric and nonparametric methods are proposed to estimate the causal effect of multivariate continuous treatments and theoretical properties of the two estimations are provided. Furthermore, the simulation results show that the proposed method is better than other methods in various cases. Finally, the proposed method is applied to analyze the impact of the duration and frequency of smoking on medical expenditure. The results from the parametric method indicate that the frequency of smoking increases medical expenditure while the duration of smoking does not. The results from the nonparametric method indicate that there is a short-term downward trend and then a long-term upward trend as the duration and frequency of smoking increase.     

Application of multivariate statistical techniques in microbial ecology

Recent advances in high‐throughput methods of molecular analyses have led to an explosion of studies generating large‐scale ecological data sets. In particular, noticeable effect has been attained in the field of microbial ecology, where new experimental approaches provided in‐depth assessments of the composition, functions and dynamic changes of complex microbial communities. Because even a single high‐throughput experiment produces large amount of data, powerful statistical techniques of multivariate analysis are well suited to analyse and interpret these data sets. Many different multivariate techniques are available, and often it is not clear which method should be applied to a particular data set. In this review, we describe and compare the most widely used multivariate statistical techniques including exploratory, interpretive and discriminatory procedures. We consider several important limitations and assumptions of these methods, and we present examples of how these approaches have been utilized in recent studies to provide insight into the ecology of the microbial world. Finally, we offer suggestions for the selection of appropriate methods based on the research question and data set structure.     

Diagnosis of rheumatoid arthritis: multivariate analysis of biomarkers

Objective. To test if a combination of biomarkers can increase the classification power of autoantibodies to cyclic citrullinated peptides (anti-CCP) in the diagnosis of rheumatoid arthritis (RA) depending on the diagnostic situation. Methods. Biomarkers were subject to three inclusion/exclusion criteria (discrimination between RA patients and healthy blood donors, ability to identify anti-CCP-negative RA patients, specificity in a panel with major non-rheumatological diseases) before univariate ranking and multivariate analysis was carried out using a modelling panel (n=906). To enable the evaluation of the classification power in different diagnostic settings the disease controls (n=542) were weighted according to the admission rates in rheumatology clinics modelling a clinic panel or according to the relative prevalences of musculoskeletal disorders in the general population seen by general practitioners modelling a GP panel. Results. Out of 131 biomarkers considered originally, we evaluated 32 biomarkers in this study, of which only seven passed the three inclusion/exclusion criteria and were combined by multivariate analysis using four different mathematical models. In the modelled clinic panel, anti-CCP was the lead marker with a sensitivity of 75.8% and a specificity of 94.0%. Due to the lack in specificity of the markers other than anti-CCP in this diagnostic setting, any gain in sensitivity by any marker combination is off-set by a corresponding loss in specificity. In the modelled GP panel, the best marker combination of anti-CCP and interleukin (IL)-6 resulted in a sensitivity gain of 7.6% (85.9% vs. 78.3%) at a minor loss in specificity of 1.6% (90.3% vs. 91.9%) compared with anti-CCP as the best single marker. Conclusions. Depending on the composition of the sample panel, anti-CCP alone or anti-CCP in combination with IL-6 has the highest classification power for the diagnosis of established RA.     

The distribution of zooplankton in the Sanyati Bay,Lake Kariba; A multivariate analysis

A principal component and discriminant function analysis of zooplankton from the Sanyati Bay, Lake Kariba, indicated that the distribution of plankton was associated with the riverine in-flow into the lake.     

Anatomy of Brazilian Eriocaulaceae: correlation with taxonomy and habitat using multivariate analyses

In this study we present a survey on vegetative anatomy in species of Actinocephalus, Blastocaulon, Eriocaulon, Leiothrix, Paepalanthus, Philodice, Syngonanthus, and Tonina (Eriocaulaceae). Multivariate analyses were used to correlate anatomical characters to taxa and the habitats where the species occur. Root and stem anatomical characters seem to be more affected by environmental factors where these species occur, and seem of little value for delimiting major taxonomic groups within the family. Other characters in the leaves, such as epidermis with thickened wall cells, compartmented substomatal chambers, mesophyll with hypodermis, compact chlorenchyma, collenchymatous bundle sheath extensions, and numerous vascular bundles, were shown to be important for defining species clusters in Leiothrix, Syngonanthus, and Paepalanthus subg. Platycaulon. Similarly, loosely aggregated chlorenchyma caused Blastocaulon, Eriocaulon, Philodice, Syngonanthus sect. Carpocephalus, S. sect. Syngonanthus, and Tonina, genera from humid environments, to cluster. Scape characters appear to be more informative in discriminating groups. This situation probably reflects lower selection pressures determining anatomical characters of this organ.     

A multivariate approach to the selection of biological reserves

Multivariate analysis provides an effective context for the examination of some significant aspects of biodiversity and conservation. The framework is a multidimensional space that integrates sample sites, taxa and environments. This approach enables terms such as representativeness, complementarity and irreplaceability to be integrated within an intuitive and practical framework for reserve design. Cluster analysis is proposed to determine what is there by defining a set of complementary clusters. These clusters are sampled in a representative manner; from the core outward. The degree of irreplaceability of a site is defined as the multivariate distance of each potential reserve site to its nearest neighbour.     

Exploring the relationship between entheseal changes and physical activity: A multivariate study

Analyses of entheseal changes (EC) in identified skeletal samples employ a common research strategy based on the comparison between occupations grouped on the basis of shared biomechanical and/or social characteristics. Results from this approach are often ambiguous, with some studies that point to differences in EC between occupational samples and others failing to provide evidence of behavioral effects on EC. Here we investigate patterns of EC among documented occupations by means of a multivariate analysis of robusticity scores in nine postcranial entheses from a large (N = 372) contemporary skeletal sample including specimens from one Italian and two Portuguese identified collections. Data on entheseal robusticity, analyzed by pooled sides as well by separated sides and levels of asymmetry, are converted in binary scores and then analyzed through nonlinear principal component analysis and hierarchical cluster analysis. Results of these analyses are then used for the classification of occupations. Differences between occupational classes are tested by MANOVA and pairwise Hotelling's test. Results evidence three classes which separate occupations related to farming, physically demanding but generalized occupation, and physically undemanding occupations, with the more consistent differences between the first and the last classes. Our results are consistent with differences in biomechanical behavior between the occupations included in each class, and point to the physical and social specificity of farming activities. On the other hand, our study exemplifies the usefulness of alternative analytical protocols for the investigation of EC, and the value of research designs devoid of a priori assumptions for the test of biocultural hypotheses. Am J Phys Anthropol 156:215–223, 2015. © 2014 Wiley Periodicals, Inc.     

Guidance for performing multivariate data analysis of bioprocessing data: Pitfalls and recommendations

Biotech unit operations are often characterized by a large number of inputs (operational parameters) and outputs (performance parameters) along with complex correlations among them. A typical biotech process starts with the vial of the cell bank, ends with the final product, and has anywhere from 15 to 30 such unit operations in series. Besides the above‐mentioned operational parameters, raw material attributes can also impact process performance and product quality as well as interact among each other. Multivariate data analysis (MVDA) offers an effective approach to gather process understanding from such complex datasets. Review of literature suggests that the use of MVDA is rapidly increasing, fuelled by the gradual acceptance of quality by design (QbD) and process analytical technology (PAT) among the regulators and the biotech industry. Implementation of QbD and PAT requires enhanced process and product understanding. In this article, we first discuss the most critical issues that a practitioner needs to be aware of while performing MVDA of bioprocessing data. Next, we present a step by step procedure for performing such analysis. Industrial case studies are used to elucidate the various underlying concepts. With the increasing usage of MVDA, we hope that this article would be a useful resource for present and future practitioners of MVDA. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:967–973, 2014