The New England Journal of Statistics in Data Science

While randomized trials may be the gold standard for evaluating the effectiveness of the treatment intervention, in some special circumstances, single-arm clinical trials utilizing external control may be considered. The causal treatment effect of interest for single-arm trials is usually the average treatment effect on the treated (ATT) rather than the average treatment effect (ATE). Although methods have been developed to estimate the ATT, the selection and use of these methods require a thorough comparison and in-depth understanding of the advantages and disadvantages of these methods. In this study, we conducted simulations under different identifiability assumptions to compare the performance metrics (e.g., bias, standard deviation (SD), mean squared error (MSE), type I error rate) for a variety of methods, including the regression model, propensity score matching (PSM), Mahalanobis distance matching (MDM), coarsened exact matching, inverse probability weighting, augmented inverse probability weighting (AIPW), AIPW with SuperLearner, and targeted maximum likelihood estimator (TMLE) with SuperLearner.

The evolving focus in statistics and data science education highlights the growing importance of computing. This paper presents the Data Jamboree, a live event that combines computational methods with traditional statistical techniques to address real-world data science problems. Participants, ranging from novices to experienced users, followed workshop leaders in using open-source tools like Julia, Python, and R to perform tasks such as data cleaning, manipulation, and predictive modeling. The Jamboree showcased the educational benefits of working with open data, providing participants with practical, hands-on experience. We compared the tools in terms of efficiency, flexibility, and statistical power, with Julia excelling in performance, Python in versatility, and R in statistical analysis and visualization. The paper concludes with recommendations for designing similar events to encourage collaborative learning and critical thinking in data science.

Observations of groundwater pollutants, such as arsenic or Perfluorooctane sulfonate (PFOS), are riddled with left censoring. These measurements have an impact on the health and lifestyle of the populace. Left censoring of these spatially correlated observations is usually addressed by applying Gaussian processes (GPs), which have theoretical advantages. However, this comes with a challenging computational complexity of $\mathcal{O}({n^{3}})$, impractical for large datasets. Additionally, a sizable proportion of the left-censored data creates further bottlenecks since the likelihood computation now involves an intractable high-dimensional integral of the multivariate Gaussian density. In this article, we tackle these two problems simultaneously by approximating the GP with a Gaussian Markov random field (GMRF) approach that exploits an explicit link between a GP with Matérn correlation function and a GMRF using stochastic partial differential equations (SPDEs). We introduce a GMRF-based measurement error into the model, which alleviates the likelihood computation for the censored data, drastically improving the computational speed while maintaining admirable accuracy. Our approach demonstrates robustness and substantial computational scalability compared to state-of-the-art methods for censored spatial responses across various simulation settings. Finally, the fit of this fully Bayesian model to the concentration of PFOS in groundwater available at 24,959 sites across California, where 46.62% responses are censored, produces prediction surface and uncertainty quantification in real-time, thereby substantiating the applicability and scalability of the proposed method. Code for implementation is made available via GitHub.

In cancer research, leveraging patient-derived xenografts (PDXs) in pre-clinical experiments is a crucial approach for assessing innovative therapeutic strategies. Addressing the inherent variability in treatment response among and within individual PDX lines is essential. However, the current literature lacks a user-friendly statistical power analysis tool capable of concurrently determining the required number of PDX lines and animals per line per treatment group in this context. In this paper, we present a simulation-based R package for sample size determination, named ‘PDXpower’, which is publicly available at The Comprehensive R Archive Network (https://CRAN.R-project.org/package=PDXpower). The package is designed to estimate the necessary number of both PDX lines and animals per line per treatment group for the design of a PDX experiment, whether for an uncensored outcome, or a censored time-to-event outcome. Our sample size considerations rely on two widely used analytical frameworks: the mixed effects ANOVA model for uncensored outcomes and Cox’s frailty model for censored data outcomes, which effectively account for both inter-PDX variability and intra-PDX correlation in treatment response. Step-by-step illustrations for utilizing the developed package are provided, catering to scenarios with or without preliminary data.

Up-and-Down designs (UDDs) are ubiquitous for dose-finding in a wide variety of scientific, engineering, and clinical fields. They are defined by a few simple rules that generate a random walk around the target percentile. UDDs’ combination of robust, tractable behavior, straightforward usage, and good dose-finding performance, has won the trust of practitioners and their consulting analysts across fields and continents. In contrast, in recent decades the statistical dose-finding design field has turned a cold shoulder towards UDDs, and it is quite possible that many younger dose-finding methods researchers are not even aware of this design approach.

In the last two decades, single-arm trials (SATs) have been effectively used to study anticancer therapies in well-defined patient populations using durable response rates as an objective and interpretable study endpoints. With a growing trend of regulatory accelerated approval (AA) requiring randomized controlled trials (RCTs), some confusions have arisen about the roles of SATs in AA. This review is intended to elucidate necessary and desirable conditions under which an SAT may be considered appropriate for AA. Specifically, the paper describes (1) two necessary conditions for designing an SAT, (2) eight desirable conditions that help either optimize the study design and doses or interpret the study results, and (3) three additional considerations for construction of estimands, adaptive designs, and timely communication with relevant regulatory agencies. Three examples are presented to demonstrate how SATs can or cannot provide sufficient evidence to support regulatory decision. Conditions and considerations presented in this review may serve as a set of references for sponsors considering SATs to support regulatory approval of anticancer drugs.

Supervised dimension reduction (SDR) has been a topic of growing interest in data science, as it enables the reduction of high-dimensional covariates while preserving the functional relation with certain response variables of interest. However, existing SDR methods are not suitable for analyzing datasets collected from case-control studies. In this setting, the goal is to learn and exploit the low-dimensional structure unique to or enriched by the case group, also known as the foreground group. While some unsupervised techniques such as the contrastive latent variable model and its variants have been developed for this purpose, they fail to preserve the functional relationship between the dimension-reduced covariates and the response variable. In this paper, we propose a supervised dimension reduction method called contrastive inverse regression (CIR) specifically designed for the contrastive setting. CIR introduces an optimization problem defined on the Stiefel manifold with a non-standard loss function. We prove the convergence of CIR to a local optimum using a gradient descent-based algorithm, and our numerical study empirically demonstrates the improved performance over competing methods for high-dimensional data.

Fair Machine Learning endeavors to prevent unfairness arising in the context of machine learning applications embedded in society. To this end, several mathematical fairness notions have been proposed. The most known and used notions turn out to be expressed in terms of statistical independence, which is taken to be a primitive and unambiguous notion. However, two choices remain (and are largely unexamined to date): what exactly is the meaning of statistical independence and what are the groups to which we ought to be fair? We answer both questions by leveraging Richard Von Mises’ theory of probability, which starts with data, and then builds the machinery of probability from the ground up. In particular, his theory places a relative definition of randomness as statistical independence at the center of statistical modelling. Much in contrast to the classically used, absolute i.i.d.-randomness, which turns out to be “orthogonal” to his conception. We show how Von Mises’ frequential modeling approach fits well to the problem of fair machine learning and show how his theory (suitably interpreted) demonstrates the equivalence between the contestability of the choice of groups in the fairness criterion and the contestability of the choice of relative randomness. We thus conclude that the problem of being fair in machine learning is precisely as hard as the problem of defining what is meant by being random. In both cases there is a consequential choice, yet there is no universal “right” choice possible.

Variable rate irrigation (VRI) seeks to increase the efficiency of irrigation by spatially adjusting water output within an agricultural field. Central to the success of VRI technology is establishing homogeneous irrigation zones. In this research, we propose a fusion of statistical modeling and deep learning by using artificial neural networks to map irrigation zones from simple-to-measure predictors. We further couple our neural network model with spatial correlation to capture smooth variations in the irrigation zones. We demonstrate the effectiveness of our model to define irrigation zones for a farm of winter wheat crop in Rexburg, Idaho.

Growth curve analysis (GCA) has a wide range of applications in various fields where growth trajectories need to be modeled. Heteroscedasticity is often present in the error term, which can not be handled with sufficient flexibility by standard linear fixed or mixed-effects models. One situation that has been addressed is where the error variance is characterized by a linear predictor with certain covariates. A frequently encountered scenario in GCA, however, is one in which the variance is a smooth function of the mean with known shape restrictions. A naive application of standard linear mixed-effects models would underestimate the variance of the fixed effects estimators and, consequently, the uncertainty of the estimated growth curve. We propose to model the variance of the response variable as a shape-restricted (increasing/decreasing; convex/concave) function of the marginal or conditional mean using shape-restricted splines. A simple iteratively reweighted fitting algorithm that takes advantage of existing software for linear mixed-effects models is developed. For inference, a parametric bootstrap procedure is recommended. Our simulation study shows that the proposed method gives satisfactory inference with moderate sample sizes. The utility of the method is demonstrated using two real-world applications.