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The flexibility and wide applicability of the Fisher randomization test (FRT) make it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. This paper provides a theoretical inferential framework for FRT by establishing its connection with confidence distributions. Such a connection leads to development’s of (i) an unambiguous procedure for inversion of FRTs to generate confidence intervals with guaranteed coverage, (ii) new insights on the effect of size of the Monte Carlo sample on the estimation of a p-value curve and (iii) generic and specific methods to combine FRTs from multiple independent experiments with theoretical guarantees. Our developments pertain to finite sample settings but have direct extensions to large samples. Simulations and a case example demonstrate the benefit of these new developments.

 

Many clinical endpoint measures, such as the number of standard drinks consumed per week or the number of days that patients stayed in the hospital, are count data with excessive zeros. However, the zero‐inflated nature of such outcomes is sometimes ignored in analyses of clinical trials. This leads to biased estimates of study‐level intervention effect and, consequently, a biased estimate of the overall intervention effect in a meta‐analysis. The current study proposes a novel statistical approach, the Zero‐inflation Bias Correction (ZIBC) method, that can account for the bias introduced when using the Poisson regression model, despite a high rate of inflated zeros in the outcome distribution of a randomized clinical trial. This correction method only requires summary information from individual studies to correct intervention effect estimates as if they were appropriately estimated using the zero‐inflated Poisson regression model, thus it is attractive for meta‐analysis when individual participant‐level data are not available in some studies. Simulation studies and real data analyses showed that the ZIBC method performed well in correcting zero‐inflation bias in most situations.

 

Multivariate failure time data are frequently analyzed using the marginal proportional hazards models and the frailty models. When the sample size is extraordinarily large, using either approach could face computational challenges. In this paper, we focus on the marginal model approach and propose a divide‐and‐combine method to analyze large‐scale multivariate failure time data. Our method is motivated by the Myocardial Infarction Data Acquisition System (MIDAS), a New Jersey statewide database that includes 73,725,160 admissions to nonfederal hospitals and emergency rooms (ERs) from 1995 to 2017. We propose to randomly divide the full data into multiple subsets and propose a weighted method to combine these estimators obtained from individual subsets using three weights. Under mild conditions, we show that the combined estimator is asymptotically equivalent to the estimator obtained from the full data as if the data were analyzed all at once. In addition, to screen out risk factors with weak signals, we propose to perform the regularized estimation on the combined estimator using its combined confidence distribution. Theoretical properties, such as consistency, oracle properties, and asymptotic equivalence between the divide‐and‐combine approach and the full data approach are studied. Performance of the proposed method is investigated using simulation studies. Our method is applied to the MIDAS data to identify risk factors related to multivariate cardiovascular‐related health outcomes.

 

Fusion learning methods, developed for the purpose of analyzing datasets from many different sources, have become a popular research topic in recent years. Individualized inference approaches through fusion learning extend fusion learning approaches to individualized inference problems over a heterogeneous population, where similar individuals are fused together to enhance the inference over the target individual. Both classical fusion learning and individualized inference approaches through fusion learning are established based on weighted aggregation of individual information, but the weight used in the latter is localized to thetargetindividual. This article provides a review on two individualized inference methods through fusion learning,iFusion andiGroup, that are developed under different asymptotic settings. Both procedures guarantee optimal asymptotic theoretical performance and computational scalability.

This article is categorized under:

Statistical Learning and Exploratory Methods of the Data Sciences > Manifold Learning

Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

Data: Types and Structure > Massive Data

 

International trade research plays an important role to inform trade policy and shed light on wider economic issues. With recent advances in information technology, economic agencies distribute an enormous amount of internationally comparable trading data, providing a gold mine for empirical analysis of international trade. International trading data can be viewed as a dynamic transport network because it emphasizes the amount of goods moving across network edges. Most literature on dynamic network analysis concentrates on parametric modeling of the connectivity network that focuses on link formation or deformation rather than the transport moving across the network. We take a different non-parametric perspective from the pervasive node-and-edge-level modeling: the dynamic transport network is modeled as a time series of relational matrices; variants of the matrix factor model of Wang et al. (2019) are applied to provide a specific interpretation for the dynamic transport network. Under the model, the observed surface network is assumed to be driven by a latent dynamic transport network with lower dimensions. Our method is able to unveil the latent dynamic structure and achieves the goal of dimension reduction. We applied the proposed method to a dataset of monthly trading volumes among 24 countries (and regions) from 1982 to 2015. Our findings shed light on trading hubs, centrality, trends, and patterns of international trade and show matching change points to trading policies. The dataset also provides a fertile ground for future research on international trade.

 

We consider the problem of matrix approximation and denoising induced by the Kronecker product decomposition. Specifically, we propose to approximate a given matrix by the sum of a few Kronecker products of matrices, which we refer to as the Kronecker product approximation (KoPA). Because the Kronecker product is an extensions of the outer product from vectors to matrices, KoPA extends the low rank matrix approximation, and includes it as a special case. Comparing with the latter, KoPA also offers a greater flexibility, since it allows the user to choose the configuration, which are the dimensions of the two smaller matrices forming the Kronecker product. On the other hand, the configuration to be used is usually unknown, and needs to be determined from the data in order to achieve the optimal balance between accuracy and parsimony. We propose to use extended information criteria to select the configuration. Under the paradigm of high dimensional analysis, we show that the proposed procedure is able to select the true configuration with probability tending to one, under suitable conditions on the signal-to-noise ratio. We demonstrate the superiority of KoPA over the low rank approximations through numerical studies, and several benchmark image examples.