Canadian Journal of Statistics-Revue Canadienne De Statistique最新文献

Precision medicine tailors treatments to individual patient characteristics, which is especially valuable for obstructive sleep apnea (OSA), where treatment responses vary widely. Traditional trials often overlook subgroup differences, leading to suboptimal recommendations. Current approaches rely on prespecified thresholds, which may be incorrectly specified. This case study compares prespecified thresholds to two Bayesian methods: the established FK-BMA (free-knot Bayesian model averaging) method, and its novel variant, FK. The FK approach retains the flexibility of free-knot splines but omits variable selection, providing stable, interpretable models. Using biomarker data from large studies, this design identifies subgroups dynamically, allowing early trial termination or enrollment adjustments. Simulation results—motivated by real-world biomarker distributions and clinical constraints—show that under conditions of limited signal-to-noise ratio and limited candidate biomarkers, FK improves efficiency and subgroup detection.

This article considers the receiver operating characteristic (ROC) curve analysis for medical data with non-ignorable missingness in the disease status. In the framework of the logistic regression models for both the disease status and the verification status, we first establish the identifiability of model parameters, and then propose a likelihood method to estimate the model parameters, the ROC curve, and the area under the ROC curve for the biomarker. The asymptotic distributions of these estimators are established. Via extensive simulation studies, we compare our method with competing methods of point estimation and assess the accuracy of confidence interval estimation under various scenarios. To illustrate the use of our proposed approach in a practical setting, we apply our method to the Alzheimer's disease dataset from the National Alzheimer's Coordinating Center.

When data from multiple tasks have outlier contamination, existing multitask learning methods perform less efficiently. To address this issue, we propose a robust multitask feature learning method by combining the adaptive Huber regression tasks with mixed regularization. The robustification parameters can be chosen to adapt to the sample size, model dimension, and moments of the error distribution while striking a balance between unbiasedness and robustness. We consider heavy-tailed distributions for multiple datasets that have bounded $��(�1�+�\omega �)�$th moment for any $��\omega �>�0�$. Our method can achieve estimation and sign recovery consistency. Additionally, we propose a robust information criterion to conduct joint inference on related tasks, which can be used for consistent model selection. Through different simulation studies and real data applications, we illustrate that the performance of the proposed model can provide smaller estimation errors and higher feature selection accuracy than the non robust multitask learning and robust single-task methods.

Many models require integrals of high-dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The LA is exact if the function is proportional to a normal density; its effectiveness therefore depends on the function's true shape. Here, we propose the use of the probabilistic numerical framework to develop a diagnostic for the LA and its underlying shape assumptions, modelling the function and its integral as a Gaussian process and devising a “test” by conditioning on a finite number of function values. The test is decidedly non asymptotic and is not intended as a full substitute for numerical integration - rather, it is simply intended to test the feasibility of the assumptions underpinning the LA with minimal computation. We discuss approaches to optimize and design the test, apply it to known sample functions, and highlight the challenges of high dimensions.

Both the Bayes factor and the relative belief ratio satisfy the principle of evidence and are therefore valid measures of statistical evidence. Which of these measures of evidence is more appropriate? We argue here that there are questions concerning the validity of a commonly used definition of the Bayes factor based on a mixture prior, and when all is considered, the relative belief ratio has better properties as a measure of evidence. We further show that, when a natural restriction on the mixture prior is imposed, the Bayes factor equals the relative belief ratio obtained without using the mixture prior. Even with this restriction, this still leaves open the question of how the strength of evidence is to be measured. We argue here that the current practice of using the size of the Bayes factor to measure strength is not correct and present a solution. We also discuss and address several general criticisms of these measures of evidence.

We propose a unified class of generalized structural equation models (GSEMs) with data of mixed types in mediation analysis, including continuous, categorical, and count variables. Such models extend substantially the classical linear structural equation model to accommodate many data types arising from the application of mediation analysis. Invoking the hierarchical modelling approach, we specify GSEMs by a copula joint distribution of outcome variable, mediator and exposure variable, in which marginal distributions are built upon generalized linear models (GLMs) with confounding factors. We discuss the identifiability conditions for the causal mediation effects in the counterfactual paradigm as well as the issue of mediation leakage, and develop an asymptotically efficient profile maximum likelihood estimation and inference for two key mediation estimands, namely natural direct effect and natural indirect effect, in different scenarios of mixed data types. The proposed new methodology is illustrated by a motivating epidemiological study that aims to investigate whether the tempo of reaching infancy BMI (body mass index) peak (delay or on time), an important early life growth milestone, mediates the association between prenatal exposure to phthalates and pubertal health outcomes.

As a widely carried out task in data-driven applications, clustering relies on good data representation. Since deep neural networks are powerful tools for the analysis of clustering-friendly representations, certain combinations of clustering and deep models have been explored in the literature. Yet, only limited improvement has been achieved for real data with complex structures such as positive and unlabelled (PU) data. In this article we propose an unsupervised clustering model, called the deep support vector clustering (dSVC). The method combines a deep autoencoder neural network with hinge loss, and is further extended to binary semi-supervised PU data learning. Theoretical results are established for label recovery and novelty detection using a large-margin classifier. Intensive numerical experiments on multiple datasets of both high and low dimension validate the efficiency of the proposed approach. We found that the proposed approach constructs clusters in a manner opposite to the popular generative adversarial network (GAN) model.

A distinctive functional of the Poisson point process is the negative binomial process for which the increments are not independent but are independent conditional on an underlying gamma variable. Using a new point process representation for the negative binomial process, we generalize the Poisson–Kingman distribution and its corresponding random discrete probability measure. This new proposed family of discrete random probability measures, which is defined by normalizing the points of the negative binomial process, provides a new set of useful priors for Bayesian nonparametric models with more flexibility than the random discrete probability measure which are obtained by normalizing the points of a Poisson point process. We illustrate how this family of random discrete probability measures contains the nonparametric Bayesian priors such as the Dirichlet process, the normalized positive $��\alpha �$-stable process, the Poisson–Dirichlet process (PDP), and others. With the same gamma Lévy measure, we derive an extension of the Dirichlet process and its almost sure approximation. Using our representation for the negative binomial process, we develop a new series representation for the PDP. We demonstrate through simulations how using priors from this family can enhance the accuracy of Bayesian nonparametric hierarchical models.

Modern longitudinal data from wearable devices consist of biological signals at high-frequency time points. Distributed statistical methods have emerged as a powerful tool to overcome the computational burden of estimation and inference with large data, but methodology for distributed functional regression remains limited. We propose a distributed estimation and inference procedure that efficiently estimates both functional and scalar parameters with intensively measured longitudinal outcomes. The procedure overcomes computational difficulties through a scalable divide-and-conquer algorithm that partitions the outcomes into smaller sets. We circumvent traditional basis selection problems by analyzing data using quadratic inference functions in smaller subsets such that the basis functions have a low dimension. To address the challenges of combining estimates from dependent subsets, we propose a statistically efficient one-step estimator derived from a constrained generalized method of moments objective function with a smoothing penalty. We show theoretically and numerically that the proposed estimator is as statistically efficient as non-distributed alternative approaches and more efficient computationally. We demonstrate the practicality of our approach with the analysis of accelerometer data from the National Health and Nutrition Examination Survey.

Multi-dimensional data frequently occur in many different fields, including risk management, insurance, biology, environmental sciences, and many more. In analyzing multivariate data, it is imperative that the underlying modelling assumptions adequately reflect both the marginal behaviour and the associations between components. This article focuses specifically on developing a new multivariate Poisson model appropriate for multi-dimensional count data. The proposed formulation is based on convolutions of comonotonic shock vectors with Poisson-distributed components and allows for flexibility in capturing different degrees of positive dependence. In this article, we will present the general model framework along with various distributional properties. Several estimation techniques will be explored and assessed both through simulations and in a real data application involving extreme rainfall events.