The New England Journal of Statistics in Data Science

The crossover models and interference models are frequently used in clinical trials, agriculture studies, social studies, etc. While some theoretical optimality results are available, it is still challenging to apply these results in practice. The available theoretical results, due to the complexity of exact optimal designs, typically require some specific combinations of the number of treatments (t), periods (p), and subjects (n). A more flexible method is to build integer programming based on theories in approximate design theory, which can handle general cases of $(t,p,n)$. Nonetheless, those results are generally derived for specific models or design problems and new efforts are needed for new problems. These obstacles make the application of the theoretical results rather difficult. Here we propose a new algorithm, a revision of the optimal weight exchange algorithm by [1]. It provides efficient crossover designs quickly under various situations, for different optimality criteria, different parameters of interest, different configurations of $(t,p,n)$, as well as arbitrary dropout scenarios. To facilitate the usage of our algorithm, the corresponding R package and an R Shiny app as a more user-friendly interface has been developed.

Variable selection is widely used in all application areas of data analytics, ranging from optimal selection of genes in large scale micro-array studies, to optimal selection of biomarkers for targeted therapy in cancer genomics to selection of optimal predictors in business analytics. A formal way to perform this selection under the Bayesian approach is to select the model with highest posterior probability. The problem may be thought as an optimization problem over the model space where the objective function is the posterior probability of model. We propose to carry out this optimization using simulated annealing and we illustrate its feasibility in high dimensional problems. By means of various simulation studies, this new approach has been shown to be efficient. Theoretical justifications are provided and applications to high dimensional datasets are discussed. The proposed method is implemented in an R package sahpm for general use and is made available on R CRAN.

Tail probability plays an important part in the extreme value theory. Sometimes the conclusions from two approaches for estimating the tail probability of extreme events, the Bayesian and the frequentist methods, can differ a lot. In 1999, a rainfall that caused more than 30,000 deaths in Venezuela was not captured by the simple frequentist extreme value techniques. However, this catastrophic rainfall was not surprising if the Bayesian inference was used to allow for parameter uncertainty and the full available data was exploited [4].

Double generalized linear models provide a flexible framework for modeling data by allowing the mean and the dispersion to vary across observations. Common members of the exponential dispersion family including the Gaussian, Poisson, compound Poisson-gamma (CP-g), Gamma and inverse-Gaussian are known to admit such models. The lack of their use can be attributed to ambiguities that exist in model specification under a large number of covariates and complications that arise when data display complex spatial dependence. In this work we consider a hierarchical specification for the CP-g model with a spatial random effect. The spatial effect is targeted at performing uncertainty quantification by modeling dependence within the data arising from location based indexing of the response. We focus on a Gaussian process specification for the spatial effect. Simultaneously, we tackle the problem of model specification for such models using Bayesian variable selection. It is effected through a continuous spike and slab prior on the model parameters, specifically the fixed effects. The novelty of our contribution lies in the Bayesian frameworks developed for such models. We perform various synthetic experiments to showcase the accuracy of our frameworks. They are then applied to analyze automobile insurance premiums in Connecticut, for the year of 2008.

Subdata selection from big data is an active area of research that facilitates inferences based on big data with limited computational expense. For linear regression models, the optimal design-inspired Information-Based Optimal Subdata Selection (IBOSS) method is a computationally efficient method for selecting subdata that has excellent statistical properties. But the method can only be used if the subdata size, k, is at last twice the number of regression variables, p. In addition, even when $k\ge 2p$, under the assumption of effect sparsity, one can expect to obtain subdata with better statistical properties by trying to focus on active variables. Inspired by recent efforts to extend the IBOSS method to situations with a large number of variables p, we introduce a method called Combining Lasso And Subdata Selection (CLASS) that, as shown, improves on other proposed methods in terms of variable selection and building a predictive model based on subdata when the full data size n is very large and the number of variables p is large. In terms of computational expense, CLASS is more expensive than recent competitors for moderately large values of n, but the roles reverse under effect sparsity for extremely large values of n.

The supersaturated design is often used to discover important factors in an experiment with a large number of factors and a small number of runs. We propose a method for constructing supersaturated designs with small coherence. Such designs are useful for variable selection methods such as the Lasso. Examples are provided to illustrate the proposed method.

Traditionally, research in nutritional epidemiology has focused on specific foods/food groups or single nutrients in their relation with disease outcomes, including cancer. Dietary pattern analysis have been introduced to examine potential cumulative and interactive effects of individual dietary components of the overall diet, in which foods are consumed in combination. Dietary patterns can be identified by using evidence-based investigator-defined approaches or by using data-driven approaches, which rely on either response independent (also named “a posteriori” dietary patterns) or response dependent (also named “mixed-type” dietary patterns) multivariate statistical methods. Within the open methodological challenges related to study design, dietary assessment, identification of dietary patterns, confounding phenomena, and cancer risk assessment, the current paper provides an updated landscape review of novel methodological developments in the statistical analysis of a posteriori/mixed-type dietary patterns and cancer risk. The review starts from standard a posteriori dietary patterns from principal component, factor, and cluster analyses, including mixture models, and examines mixed-type dietary patterns from reduced rank regression, partial least squares, classification and regression tree analysis, and least absolute shrinkage and selection operator. Novel statistical approaches reviewed include Bayesian factor analysis with modeling of sparsity through shrinkage and sparse priors and frequentist focused principal component analysis. Most novelties relate to the reproducibility of dietary patterns across studies where potentialities of the Bayesian approach to factor and cluster analysis work at best.

In online experimentation, appropriate metrics (e.g., purchase) provide strong evidence to support hypotheses and enhance the decision-making process. However, incomplete metrics are frequently occurred in the online experimentation, making the available data to be much fewer than the planned online experiments (e.g., A/B testing). In this work, we introduce the concept of dropout buyers and categorize users with incomplete metric values into two groups: visitors and dropout buyers. For the analysis of incomplete metrics, we propose a clustering-based imputation method using k-nearest neighbors. Our proposed imputation method considers both the experiment-specific features and users’ activities along their shopping paths, allowing different imputation values for different users. To facilitate efficient imputation of large-scale data sets in online experimentation, the proposed method uses a combination of stratification and clustering. The performance of the proposed method is compared to several conventional methods in both simulation studies and a real online experiment at eBay.

Master protocol is a type of trial designs where multiple therapies and/or multiple disease populations can be investigated in the same trial. A shared control can be used for multiple therapies to gain operational efficiency and gain attraction to patients. To balance between controlling for false positive rate and having adequate power for detecting true signals, the impact of False Discovery Rate (FDR) is evaluated when multiple investigational drugs are studied in the master protocol. With the shared control group, the “random high” or “random low” in the control group can potentially impact all hypotheses testing that compare each of the test regimens and the control group in terms of probability of having at least one positive hypothesis outcome, or multiple positive outcomes. When regulatory agencies make the decision of approving or declining one or more regimens based on the master protocol design, this introduces a different type of error: simultaneous false-decision error. In this manuscript, we examine in detail the derivations and properties of the simultaneous false-decision error in the master protocol with shared control under the framework of FDR. The simultaneous false-decision error consists of two parts: simultaneous false-discovery rate (SFDR) and simultaneous false non-discovery rate (SFNR). Based on our analytical evaluation and simulations, the magnitude of SFDR and SFNR inflation is small. Therefore, the multiple error rate controls are generally adequate, further adjustment to a pre-specified level on SFDR or SFNR or reduce the alpha allocated to each individual treatment comparison to the shared control is deemed unnecessary.