The New England Journal of Statistics in Data Science

Estimating nonlinear exposure effects in Cox regression models is essential for accurately characterizing exposure–disease relationships, yet the presence of measurement error in exposures poses major challenges. While regression calibration has been widely applied under rare disease assumptions with linear exposure effects, recent work has extended the approach to accommodate quadratic and quantile effects. We generalize this framework to handle arbitrary polynomial and spline-based representations of the exposure effect, thereby enabling flexible modelling of complex nonlinear associations. Our method combines regression calibration with Monte Carlo integration to evaluate the conditional expectation of the hazard function when analytical solutions are unavailable. Furthermore, by stacking the estimating functions from both the Cox regression and measurement error models, we construct a sandwich variance estimator that avoids computationally intensive bootstrap procedures. To facilitate practical use, we implement our approach in the R package NonLinearRC.

Prompted by social upheaval in 2019, Chile initiated its first foray into entirely online education. Subsequently, owing to the global pandemic in 2020, all activities underwent an unavoidable shift to digital platforms, both on a global scale and within the university context. In response to this novel distance-learning system, the university encountered and surmounted new challenges during the four semesters that were conducted in this modality. This paper examines from a spatial statistics perspective the academic performance of first-year students enrolled in basic science courses across all engineering majors at Universidad Técnica Federico Santa María (USM) in Chile. This article emphasizes students’ performance as a georeferenced variable in space and compares it with a regular semester in which lectures are conducted in a face-to-face format. In particular, we discuss (a) the spatial patterns observed in the two largest cities, (b) the social variables that are pertinent for the study, and (c) the quality and performance of conditionally autoregressive (CAR)-type processes in modeling multivariate lattice data. We also reflect on the opportunity to enhance the learning experience linked to the retention rate of freshman engineering students.

The MiniPDX model is a cost-effective preclinical platform that replicates human tumor microenvironments in mice, enabling rapid drug response evaluation in precision oncology. In contrast, the patient-derived xenograft (PDX) model offers a more comprehensive but slower and costlier approach by engrafting human tumors into immunodeficient mice to evaluate efficacy in a physiologically relevant context. In this study, we present an integrated Bayesian framework that supports both separate and joint analyses of MiniPDX and PDX data. Our models borrow information across biomarker-defined subgroups and between assays, improving the efficiency and precision of drug effect estimation. Furthermore, we implement an adaptive sample size re-estimation procedure for MiniPDX experiments, allowing for more flexible designs and optimized resource utilization. Together, these methods provide a Bayesian framework that improves estimation efficiency for small-sample MiniPDX and PDX experiments and offers a principled adaptive sample-size rule, helping to identify biomarker-defined subpopulations with distinct predictive profiles for treatment response.

Phase I oncology trials aim to identify a safe dose—often the maximum tolerated dose (MTD)—for subsequent studies. Conventional designs focus on population-level toxicity modeling, with recent attention on leveraging pharmacokinetic (PK) data to improve dose selection. We propose the Precision Dose-Finding (PDF) design, a novel Bayesian phase I framework that integrates individual patient PK profiles into the dose-finding process. By incorporating patient-specific PK parameters (such as volume of distribution ${V_{i}}$ and elimination rate ${k_{i}}$), PDF models toxicity risk at the individual level, in contrast to traditional methods that ignore inter-patient variability. The trial is structured in two stages: an initial training stage to update model parameters using cohort-based dose escalation, and a subsequent test stage in which doses for new patients are chosen based on each patient’s own PK-predicted toxicity probability. This two-stage approach enables truly personalized dose assignment while maintaining rigorous safety oversight. Extensive simulation studies demonstrate the feasibility of PDF and suggest that it provides improved safety and dosing precision relative to the continual reassessment method (CRM). The PDF design thus offers a refined dose-finding strategy that tailors the MTD to individual patients, aligning phase I trials with the ideals of precision medicine.

Disease registries often involve cohorts of patients seen repeatedly at tertiary care centers with biospecimens collected at periodic clinic visits. With such registries it is possible to study the association between time-dependent biomarkers and a failure time of interest through Cox regression. However it can be prohibitively expensive or labor-intensive to assay all biospecimens for all members of the registry and in practice it is common to select a single biosample to assay for each individual. We derive the asymptotic bias of estimators obtained from the Cox model based on common strategies. We investigate the nature of this bias from a joint multistate model for the marker and failure processes. Alternative selection methods are then developed for consistent and efficient sub-sampling under budgetary constraints. The asymptotic relative efficiency of regression coefficients obtained from the Fisher information is then explored and an optimal design is identified within a class of designs. The proposed selection method is illustrated in a registry of patients with psoriatic arthritis where we investigate the association between a time-dependent biomarker (ESR_CRP) and the risk of developing arthritis mutilans.

Severe event class imbalance is observed in many fields, such as insurance fraud, severe weather, traffic safety, and rare disease, and has far-reaching significance when the generalization of minority event classes is of primary interest. While existing solutions mostly focus on differential sampling or sample re-weighting approaches to alleviate the imbalance issue, we take a novel alternative view on promoting generalization. Our proposal is formulated under the generative Bayesian framework, positing that predictors are the stochastic proxies of latent causes with limited samples, whose exceedance leads to extreme events. To accurately capture the extended tail, our solution adopts the Gumbel distribution as prior and is modeled with a variational inference framework. Following the assertion that exceedance leads to extremes, we devise a disentangled additive monotonic neural architecture to predict the risk. The proposed model acknowledges representation uncertainties while embracing improved interpretability, generalization, and robustness. We provide theoretical insights to show the merits of the proposed approach. To verify the effectiveness in empirical settings, we conducted studies on various real-world data against the state-of-the-art counterparts, with encouraging results reported.

Modern Statistics is made of the sensible combination of direct evidence (the data directly relevant or the “individual data”) and indirect evidence (the data and knowledge indirectly relevant or the “group data”). The admissible procedures combine the two sources of information, and technology advances make indirect evidence more substantial and ubiquitous. It has been pointed out, however, that an important problem of Statistics when “borrowing strength” is to treat in a fundamentally different way exceptional cases that do not adapt to the central “aurea mediocritas”. This is what has been coined as “the Clemente problem” in honor of R. Clemente, an exceptional batter [6]. In this article, we argue that the problem is caused by the simultaneous use of square loss function and conjugate (light-tailed) priors, which is the usual procedure. We propose in their place to use robust penalties, in the form of losses that penalize more severely huge errors, or (equivalently) priors of heavy tails which make the exceptional more probable. Using heavy-tailed priors, we can reproduce, in a Bayesian structured way, Efron and Morris’ “limited translated estimators” (with Double Exponential Priors) and “discarding priors estimators” (with Cauchy-like priors), which discard the prior in the presence of prior-likelihood conflict. We show that both Empirical Bayes and Full Bayes approaches can alleviate the Clemente problem and beat the James-Stein estimator in terms of smaller square errors, for sensible Robust Bayes priors. We model in parallel Empirical Bayes and Fully Bayesian hierarchical models, illustrating that the differences among sensible versions of both are relatively small, as compared with the effect due to the robust assumptions. We follow [16] in using a heavy-tailed (scaled) Beta2 distribution for (squared) scales that arise naturally as an alternative to the usual Inverted-Gamma distribution. The combination of a Cauchy Prior for location and Scaled Beta2 for square scales yields a novel closed-form prior for location, extremely suitable for Objective Robust Bayesian Analysis. Finally, we calculate the predictive intervals and the Robust models covers the Clemente average at $80\% $ of probability, which the conjugate do not. Our approach has connections with [25], which employs a completely different methodology. This is an instance of the convergence of the best frequentist and Bayesian analyses [see 3].

Natural language processing (NLP) algorithms have demonstrated significant capabilities in understanding responses to open-ended questions in survey data. However, the reliability and uncertainty of these methods on this task still need to be thoroughly investigated. To address this issue, this paper presents a comprehensive comparative analysis of various NLP methods for detecting fine-grained emotions in student responses about their mental health during the COVID-19 pandemic. The evaluated models include a Lexicon-based approach, the bag-of-words (BoW) model, Term Frequency-Inverse Document Frequency (TF-IDF), a pre-trained Bidirectional Encoder Representations from Transformers (BERT) model, MentalBERT, and OpenAI’s GPT-3.5. We carefully assess the efficacy of these models in accurately classifying emotions into predetermined categories using performance metrics such as accuracy and F1 score. Furthermore, model stability and distinguishing ability were quantified through repetitive cross-validation and the Area Under the Receiver Operating Characteristic Curve (AUC). The consistency of emotion detection across different models is also evaluated. The study highlights that the effectiveness of employing NLP methods for mental health analysis may vary depending on the emotions being analyzed, and their stability and uncertainty require thorough examination. Our work can provide valuable guidance for data scientists on applying NLP methods to survey data, particularly for understanding survey respondents’ emotions.

We consider the class of inverse probability weight (IPW) estimators, including the popular Horvitz–Thompson and Hájek estimators used routinely in survey sampling, causal inference and for Bayesian computation. We focus on the ‘weak paradoxes’ for these estimators due to two counterexamples by Basu (1988) and Wasserman (2004) and investigate the two natural Bayesian answers to this problem: one based on binning and smoothing: a ‘Bayesian sieve’ and the other based on a conjugate hierarchical model that allows borrowing information via exchangeability. We compare the mean squared errors for the two Bayesian estimators with the IPW estimators for Wasserman’s example via simulation studies on a broad range of parameter configurations. We also prove posterior consistency for the Bayes estimators under missing-completely-at-random assumption and show that it requires fewer assumptions on the inclusion probabilities. We also revisit the connection between the different problems where improved or adaptive IPW estimators will be useful, including survey sampling, evidence estimation strategies such as Conditional Monte Carlo, Riemannian sum, Trapezoidal rules and vertical likelihood, as well as average treatment effect estimation in causal inference.