The New England Journal of Statistics in Data Science

As a prominent dimension reduction method for multivariate linear regression, the envelope model has received increased attention over the past decade due to its modeling flexibility and success in enhancing estimation and prediction efficiencies. Several enveloping approaches have been proposed in the literature; among these, the partial response envelope model [57] that focuses on only enveloping the coefficients for predictors of interest, and the simultaneous envelope model [14] that combines the predictor and the response envelope models within a unified modeling framework, are noteworthy. In this article we incorporate these two approaches within a Bayesian framework, and propose a novel Bayesian simultaneous partial envelope model that generalizes and addresses some limitations of the two approaches. Our method offers the flexibility of incorporating prior information if available, and aids coherent quantification of all modeling uncertainty through the posterior distribution of model parameters. A block Metropolis-within-Gibbs algorithm for Markov chain Monte Carlo (MCMC) sampling from the posterior is developed. The utility of our model is corroborated by theoretical results, comprehensive simulations, and a real imaging genetics data application for the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study.

Clinical trials usually involve sequential patient entry. When designing a clinical trial, it is often desirable to include a provision for interim analyses of accumulating data with the potential for stopping the trial early. We review Bayesian sequential clinical trial designs based on posterior probabilities, posterior predictive probabilities, and decision-theoretic frameworks. A pertinent question is whether Bayesian sequential designs need to be adjusted for the planning of interim analyses. We answer this question from three perspectives: a frequentist-oriented perspective, a calibrated Bayesian perspective, and a subjective Bayesian perspective. We also provide new insights into the likelihood principle, which is commonly tied to statistical inference and decision making in sequential clinical trials. Some theoretical results are derived, and numerical studies are conducted to illustrate and assess these designs.

Controlled experiments are widely applied in many areas such as clinical trials or user behavior studies in IT companies. Recently, it is popular to study experimental design problems to facilitate personalized decision making. In this paper, we investigate the problem of optimal design of multiple treatment allocation for personalized decision making in the presence of observational covariates associated with experimental units (often, patients or users). We assume that the response of a subject assigned to a treatment follows a linear model which includes the interaction between covariates and treatments to facilitate precision decision making. We define the optimal objective as the maximum variance of estimated personalized treatment effects over different treatments and different covariates values. The optimal design is obtained by minimizing this objective. Under a semi-definite program reformulation of the original optimization problem, we use a YALMIP and MOSEK based optimization solver to provide the optimal design. Numerical studies are provided to assess the quality of the optimal design.

Anomaly detection plays an important role in traffic operations and control. Missingness in spatial-temporal datasets prohibits anomaly detection algorithms from learning characteristic rules and patterns due to the lack of large amounts of data. This paper proposes an anomaly detection scheme for the 2021 Algorithms for Threat Detection (ATD) challenge based on Gaussian process models that generate features used in a logistic regression model which leads to high prediction accuracy for sparse traffic flow data with a large proportion of missingness. The dataset is provided by the National Science Foundation (NSF) in conjunction with the National Geospatial-Intelligence Agency (NGA), and it consists of thousands of labeled traffic flow records for 400 sensors from 2011 to 2020. Each sensor is purposely downsampled by NSF and NGA in order to simulate missing completely at random, and the missing rates are 99%, 98%, 95%, and 90%. Hence, it is challenging to detect anomalies from the sparse traffic flow data. The proposed scheme makes use of traffic patterns at different times of day and on different days of week to recover the complete data. The proposed anomaly detection scheme is computationally efficient by allowing parallel computation on different sensors. The proposed method is one of the two top performing algorithms in the 2021 ATD challenge.

Discussion of “Four types of frequentism and their interplay with Bayesianism” by Jim Berger.

Platform trials are multiarm clinical studies that allow the addition of new experimental arms after the activation of the trial. Statistical issues concerning “adding new arms”, however, have not been thoroughly discussed. This work was motivated by a “two-period” pediatric osteosarcoma study, starting with two experimental arms and one control arm and later adding two more pre-planned experimental arms. The common control arm will be shared among experimental arms across the trial. In this paper, we provide a principled approach, including how to modify the critical boundaries to control the family-wise error rate as new arms are added, how to re-estimate the sample sizes and provide the optimal control-to-experimental arms allocation ratio, in terms of minimizing the total sample size to achieve a desirable marginal power level. We examined the influence of the timing of adding new arms on the design’s operating characteristics, which provides a practical guide for deciding the timing. Other various numerical evaluations have also been conducted. A method for controlling the pair-wise error rate (PWER) has also been developed. We have published an R package, PlatformDesign, on CRAN for practitioners to easily implement this platform trial approach. A detailed step-by-step tutorial is provided in Appendix A.2.