多元匹配比例（Multivariate matched proportions, MMP）数据广泛存在于药物上市后不良事件监测、疾病分类、医疗服务提供者一致性评估等多种场景中，由同一受试者的多组成对二分类测量结果构成。尽管近期研究提出了非贝叶斯方法来处理MMP数据的复杂性，但稀疏响应问题（即一组或多组数据中记录的“是”响应为零或极少）尚未得到解决。稀疏响应组的存在会导致现有方法出现方差低估、置信区间覆盖率不足以及检验效能降低的问题。贝叶斯方法此前尚未被应用于MMP数据，但在存在稀疏响应的情况下能提供有效的分析框架，其中贝叶斯probit模型为方差低估问题提供了简洁的解决方案。我们研究了基于该模型的三种方法：采用平坦先验的朴素分析、对均值模型方差使用半柯西先验的惩罚化分析，以及结合贝叶斯函数主成分分析（functional principal component analysis, FPCA）对潜变量协方差建模的多元分析。结果表明，该多元分析在存在稀疏响应的MMP数据上表现优异，性能优于现有的非贝叶斯方法。在对一项针对精神与行为障碍儿童的照护体系（system of care, SOC）框架研究的数据进行再分析时，我们能够更完整地呈现数据中的关联关系，提供了此前单变量分析未能发现的关于SOC运行机制的额外洞见。
英文摘要：
Multivariate matched proportions (MMP) data appears in a variety of contexts including post-market surveillance of adverse events in pharmaceuticals, disease classification, and agreement between care providers. It consists of multiple sets of paired binary measurements taken on the same subject. While recent work proposes non-Bayesian methods to address the complexities of MMP data, the issue of sparse response, where no or very few "yes" responses are recorded for one or more sets, is unaddressed. The presence of sparse response sets results in underestimates of variance, loss of coverage, and lowered power in existing methods. Bayesian methods have not previously been considered for MMP data but provide a useful framework when sparse responses are present. In particular, the Bayesian probit model provides an elegant solution to the problem of variance underestimation. We examine three approaches built on that model: a naive analysis with flat priors, a penalized analysis using half-Cauchy priors on the mean model variances, and a multivariate analysis with a Bayesian functional principal component analysis (FPCA) to model the latent covariance. We show that the multivariate analysis performs well on MMP data with sparse responses and outperforms existing non-Bayesian methods. In a re-analysis of data from a study of the system of care (SOC) framework for children with mental and behavioral disorders, we are able to provide a more complete picture of the relationships in the data. Our analysis provides additional insights into the functioning on the SOC that a previous univariate analysis missed.
This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the suitable number of components used in the imputation step. We develop an efficient sampling algorithm for posterior computation and multiple imputation via Markov Chain Monte Carlo methods. The proposed method can be easily extended to the situation where the data contains not only continuous variables but also discrete variables such as binary and count value…
We propose new tests for assessing whether covariates in a treatment group and matched control group are balanced in observational studies. The tests exhibit high power under a wide range of multivariate alternatives, some of which existing tests have little power for. The asymptotic permutation null distributions of the proposed tests are studied and the p-values calculated through the asymptotic results work well in finite samples, facilitating the application of the test to large data sets. The tests are illustrated in a study of the effect of smoking on blood lead levels. The proposed test…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the Laplace, penalized quasi-likelihood, Gaussian variational, and expectation propagation methods. Unfortunately, these all ignore the potential skewness of the posterior distribution. We propose a modification that accounts for skewness, where key statistics of the posterior distribution are matched instead to a multivariate skew-normal distribution. A combination …
We present a multivariate one-sided sensitivity analysis for matched observational studies, appropriate when the researcher has specified that a given causal mechanism should manifest itself in effects on multiple outcome variables in a known direction. The test statistic can be thought of as the solution to an adversarial game, where the researcher determines the best linear combination of test statistics to combat nature's presentation of the worst-case pattern of hidden bias. The corresponding optimization problem is convex, and can be solved efficiently even for reasonably sized observatio…
The assessment of diversity and similarity is relevant in monitoring the status of ecosystems. The respective indicators are based on the taxonomic composition of biological communities of interest, currently estimated through the proportions computed from sampling multivariate counts. In this work we present a novel method able to work with only one sample to estimate the taxonomic composition when the data are affected by overdispersion. The presence of overdispersion in taxonomic counts may be the result of significant environmental factors which are often unobservable but influence communi…
In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as the detection of outliers in a multivariate functional data set. Due to the heterogeneity of this data set, the proposed contaminated mixture model both clusters the multivariate functional data into homogeneous groups and detects outliers. The main advantage of this procedure over its competitors is that it does not require to specify the proportion of outlie…
We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for a wide range of response distributions and flexible relationships between the additive predictor and mean response. The new class covers a broad range of interesting models including multi-resolution spatial processes, partial likelihood-based survival models, and multivariate measurement error models. Because computation of the exact posterior distribution is infeasible, we develop a fast, scalable approximate Bayesian inference methodology for this class based on nested Gaussian, Laplace, and a…
When is multivariate kriging worthwhile? Design geometry, parameter sharing and response coupling under heterotopic sampling
University of Edinburgh Business School（爱丁堡大学商学院）；Faculty of Science and Engineering, University of Nottingham Ningbo China（宁波诺丁汉大学理学院）；College of Data Science, Jiaxing University（嘉兴大学数据科学学院）
Arsenic (As) and other toxic elements contamination of groundwater in Bangladesh poses a major threat to millions of people on a daily basis. Understanding complex relationships between arsenic and other elements can provide useful insights for mitigating arsenic poisoning in drinking water and requires multivariate modeling of the elements. However, environmental monitoring of such contaminants often involves a substantial proportion of left-censored observations falling below a minimum detection limit (MDL). This problem motivates us to propose a multivariate spatial Bayesian model for left-…
As alternatives to the time-to-first-event analysis of composite endpoints, the {\it net benefit} (NB) and the {\it win ratio} (WR) -- which assess treatment effects using prioritized component outcomes based on clinical importance -- have been proposed. However, statistical inference of NB and WR relies on a large-sample assumptions, which can lead to an invalid test statistic and inadequate, unsatisfactory confidence intervals, especially when the sample size is small or the proportion of wins is near 0 or 1. In this paper, we develop a systematic approach to address these limitations in a p…
This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class covariance, which is proportional to the between-class covariance in the conjugate prior. The scalar proportionality constant is the only plugin parameter. All other model parameters are intergated out in closed form. An expression is given for the model evidence, which can be used to make plugin estimates for the proportionality constant. Pattern recognition is done …
A new non-parametric test for multivariate paired data from pair matching or paired designs
School of Data Science, Fudan University（复旦大学数据科学学院）；Department of Statistics, University of California, Davis（加州大学戴维斯分校统计系）；Beijing International Center for Mathematical Research and School of Public Health, Peking University（北京大学北京国际数学研究中心与公共卫生学院）
We propose a novel Bayesian model framework for discrete ordinal and count data based on conditional transformations of the responses. The conditional transformation function is estimated from the data in conjunction with an a priori chosen reference distribution. For count responses, the resulting transformation model is novel in the sense that it is a Bayesian fully parametric yet distribution-free approach that can additionally account for excess zeros with additive transformation function specifications. For ordinal categoric responses, our cumulative link transformation model allows the i…
Flow cytometry is a high-throughput technology used to quantify multiple surface and intracellular markers at the level of a single cell. This enables to identify cell sub-types, and to determine their relative proportions. Improvements of this technology allow to describe millions of individual cells from a blood sample using multiple markers. This results in high-dimensional datasets, whose manual analysis is highly time-consuming and poorly reproducible. While several methods have been developed to perform automatic recognition of cell populations, most of them treat and analyze each sample…
We consider the five classes of multivariate statistical problems identified by James (1964), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James' problems involves the eigenvalues of $E^{-1}H$ where $H$ and $E$ are proportional to high dimensional Wishart matrices. Under the null hypothesis, both Wisharts are central with identity covariance. Under the alternative, the non-centrality or the covariance parameter of $H$ has a single eigenvalue, a spike, that stands alone. When the spike is smaller than a case-spec…
We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure, statistical data, and a user's prior knowledge, and returns a score proportional to the posterior probability of the network structure given the data. The search procedure generates networks for evaluation by the scoring metric. Previous work has concentrated on metrics for domains containing only discrete variables, under the assumption that data represents a m…
We propose a new class of multivariate survival models based on archimedean copulas with margins modeled by the Yang and Prentice (YP) model. The Ali-Mikhail-Haq (AMH), Clayton, Frank, Gumbel-Hougaard (GH), and Joe copulas are employed to accommodate the dependency among marginal distributions. Baseline distributions are modeled semiparametrically by the piecewise exponential (PE) distribution and the Bernstein polynomials. The new class of models possesses some attractive features: i) the ability to take into account survival data with crossing survival curves; ii) the inclusion of the well-k…
An efficient monotone data augmentation (MDA) algorithm is proposed for missing data imputation for incomplete multivariate nonnormal data that may contain variables of different types, and are modeled by a sequence of regression models including the linear, binary logistic, multinomial logistic, proportional odds, Poisson, negative binomial, skew-normal, skew-t regressions or a mixture of these models. The MDA algorithm is applied to the sensitivity analyses of longitudinal trials with nonignorable dropout using the controlled pattern imputations that assume the treatment effect reduces or di…
We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding regression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. We highlight two models under which this parameterization ar…
We introduce a Bayesian approach for analyzing high-dimensional multinomial data that are referenced over space and time. In particular, the proportions associated with multinomial data are assumed to have a logit link to a latent spatio-temporal mixed effects model. This strategy allows for covariances that are nonstationarity in both space and time, asymmetric, and parsimonious. We also introduce the use of the conditional multivariate logit-beta distribution into the dependent multinomial data setting, which leads to conjugate full-conditional distributions for use in a collapsed Gibbs samp…
In his 1986 book, Aitchison explains that compositional data is regularly mishandled in statistical analyses, a pattern that continues to this day. The Dirichlet Type I distribution is a multivariate distribution commonly used to model a set of proportions that sum to one. Aitchinson goes on to lament the difficulties of Dirichlet modelling and the scarcity of alternatives. While he addresses the second of these issues, we address the first. The Dirichlet Type II distribution is a transformation of the Dirichlet Type I distribution and is a multivariate distribution on the positive real number…
This paper introduces the sparse functional boxplot and the intensity sparse functional boxplot as practical exploratory tools. Besides being available for complete functional data, they can be used in sparse univariate and multivariate functional data. The sparse functional boxplot, based on the functional boxplot, displays sparseness proportions within the 50\% central region. The intensity sparse functional boxplot indicates the relative intensity of fitted sparse point patterns in the central region. The two-stage functional boxplot, which derives from the functional boxplot to detect outl…
Envelope methods offer targeted dimension reduction for various models. The overarching goal is to improve efficiency in multivariate parameter estimation by projecting the data onto a lower-dimensional subspace known as the envelope. Envelope approaches have advantages in analyzing data with highly correlated variables, but their iterative Grassmannian optimization algorithms do not scale very well with ultra high-dimensional data. While the connections between envelopes and partial least squares in multivariate linear regression have promoted recent progress in high-dimensional studies of en…
A Linear Relationship between Correlation and Cohen's Kappa for Binary Data and Simulating Multivariate Nominal and Ordinal Data with Specified Kappa Matrix
George Mason University（乔治梅森大学）；Baidu Research（百度研究院）；U.S. Census Bureau（美国人口普查局）
A tacit assumption in linear regression is that (response, predictor)-pairs correspond to identical observational units. A series of recent works have studied scenarios in which this assumption is violated under terms such as ``Unlabeled Sensing and ``Regression with Unknown Permutation''. In this paper, we study the setup of multiple response variables and a notion of mismatches that generalizes permutations in order to allow for missing matches as well as for one-to-many matches. A two-stage method is proposed under the assumption that most pairs are correctly matched. In the first stage, th…
This work focuses on the characterization of the central tendency of a sample of compositional data. It provides new results about theoretical properties of means and covariance functions for compositional data, with an axiomatic perspective. Original results that shed new light on the geostatistical modeling of compositional data are presented. As a first result, it is shown that the weighted arithmetic mean is the only central tendency characteristic satisfying a small set of axioms, namely continuity, reflexivity and marginal stability. Moreover, this set of axioms also implies that the wei…
A Bayesian location-scale joint model for time-to-event and multivariate longitudinal data with association based on within-individual variability
MRC Biostatistics Unit, University of Cambridge（剑桥大学MRC生物统计单元）；Department of Medical Statistics, London School of Hygiene & Tropical Medicine（伦敦卫生与热带医学院医学统计学系）；Royal Brompton Hospital, part of Guy’s and St Thomas’ NHS Foundation Trust（皇家布龙普顿医院（盖伊和圣托马斯NHS基金会信托旗下））；National Heart and Lung Institute, Imperial College（帝国理工学院国家心肺研究所）；Divisions of Biostatistics and Epidemiology and Pulmonary Medicine, Cincinnati Children’s Hospital Medical Center（辛辛那提儿童医院医疗中心生物统计、流行病学和肺病科）；Department of Pediatrics, University of Cincinnati（辛辛那提大学儿科系）；Department of Public Health, Policy and Systems, University of Liverpool（利物浦大学公共卫生、政策和系统系）；Cardiovascular Epidemiology Unit, University of Cambridge（剑桥大学心血管流行病学单元）；Ohio University Heritage College of Osteopathic Medicine（俄亥俄大学遗产骨科医学院）；University of Edinburgh（爱丁堡大学）
Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., multivariate data in the form of probability vectors that contain relative proportions. In particular, there is considerable interest in modeling interactions among such relative proportions. To this end we propose a class of exponential family models that accommodate general patterns of pairwise interaction while being supported on the probability simplex. Special cases include the family of Dirichlet distributions as well as Aitchison's additive logistic norm…
Ecological studies involving counts of abundance, presence-absence or occupancy rates often produce data having a substantial proportion of zeros. Furthermore, these types of processes are typically multivariate and only adequately described by complex nonlinear relationships involving externally measured covariates. Ignoring these aspects of the data and implementing standard approaches can lead to models that fail to provide adequate scientific understanding of the underlying ecological processes, possibly resulting in a loss of inferential power. One method of dealing with data having exces…
University of Florida Informatics Institute（佛罗里达大学信息学研究所）；University of Florida（佛罗里达大学）
Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected over time, such as interactions between users of a social media platform on different days, or across multiple subjects, such as in multi-subject studies of brain connectivity. When analyzing multiple large networks, dimensionality reduction techniques are often used to embed networks in a more tractable low-dimensional space. To this end, we develop a framewor…
