Search for: All records

ABSTRACT Breast cancer patients may experience relapse or death after surgery during the follow‐up period, leading to dependent censoring of relapse. This phenomenon, known as semi‐competing risk, imposes challenges in analyzing treatment effects on breast cancer and necessitates advanced statistical tools for unbiased analysis. Despite progress in estimation and inference within semi‐competing risks regression, its application to causal inference is still in its early stages. This article aims to propose a frequentist and semi‐parametric framework based on copula models that can facilitate valid causal inference, net quantity estimation and interpretation, and sensitivity analysis for unmeasured factors under right‐censored semi‐competing risks data. We also propose novel procedures to enhance parameter estimation and its applicability in practice. After that, we apply the proposed framework to a breast cancer study and detect the time‐varying causal effects of hormone‐ and radio‐treatments on patients' relapse and overall survival. Moreover, extensive numerical evaluations demonstrate the method's feasibility, highlighting minimal estimation bias and reliable statistical inference. 

Abstract This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models extend tensor factor models by incorporating auxiliary covariates in the loading matrices. We propose an algorithm of iteratively projected singular value decomposition (IP-SVD) for the semi-parametric estimation. It iteratively projects tensor data onto the linear space spanned by the basis functions of covariates and applies singular value decomposition on matricized tensors over each mode. We establish the convergence rates of the loading matrices and the core tensor factor. The theoretical results only require a sub-exponential noise distribution, which is weaker than the assumption of sub-Gaussian tail of noise in the literature. Compared with the Tucker decomposition, IP-SVD yields more accurate estimators with a faster convergence rate. Besides estimation, we propose several prediction methods with new covariates based on the STEFA model. On both synthetic and real tensor data, we demonstrate the efficacy of the STEFA model and the IP-SVD algorithm on both the estimation and prediction tasks. 

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.