The New England Journal of Statistics in Data Science

Categorical data are prevalent in almost all research fields and business applications. Their statistical analysis and inference often rely on probit/logistic regression models. For these common models, however, there is no universally adopted measure for performing goodness-of-fit analysis. To this end, [26] proposed a so-called surrogate ${R^{2}}$ that resembles the ordinary least square (OLS) ${R^{2}}$ for linear regression models. The surrogate ${R^{2}}$ used the notion of surrogacy, namely, generating a continuous response S and using it as a surrogate of the original categorical response Y [24, 25, 8]. In this paper, we develop an R package $\mathbf{SurrogateRsq}$ to implement the surrogate ${R^{2}}$ method [43]. The package is compatible with existing model fitting functions (e.g., glm(), polr(), clm(), and vglm()), and its features are exhibited in a wine rating analysis. Our package can be used jointly with other R packages developed for variable selection and model diagnostics so as to form a complete model development process. This process is summarized and demonstrated in a categorical-data-modeling workflow that practitioners can follow. To exemplify an extended utility of the surrogate-${R^{2}}$-based goodness-of-fit analysis, we also use this package to illustrate how to compare different empirical models trained from different samples in the wine rating analysis. The result suggests that the package allows us to evaluate comparability across multiple samples/models/studies that address the same or similar scientific or business questions.

Meta-analysis is a powerful tool for assessing drug safety by combining treatment-related toxicological findings across multiple studies, as clinical trials are typically underpowered for detecting adverse drug effects. However, incomplete reporting of adverse events (AEs) in published clinical studies is frequently encountered, especially if the observed number of AEs is below a pre-specified study-dependent threshold. Ignoring the censored AE information, often found in lower frequency, can significantly bias the estimated incidence rate of AEs. Despite its importance, this prevalent issue in meta-analysis has received little statistical or analytic attention in the literature. To address this challenge, we propose a Bayesian approach to accommodating the censored and possibly rare AEs for meta-analysis of safety data. Through simulation studies, we demonstrate that the proposed method can improve accuracy in point and interval estimation of incidence probabilities, particularly in the presence of censored data. Overall, the proposed method provides a practical solution that can facilitate better-informed decisions regarding drug safety.

Multivariate testing is a popular method to improve the effectiveness of digital marketing in industry. Online campaigns are often conducted across multiple platforms, such as desktops, tablets, smart phones, and smart watches. We propose minimum sliced aberration designs to accommodate online experiments with four platforms. This approach provides important insights into how different sets of design factors work differently across the four platforms, which can be used by industry for optimizing many forms of digital marketing. The effectiveness of the proposed approach is illustrated by an industrial email campaign with four platforms.

We introduce the anytime-valid (AV) logrank test, a version of the logrank test that provides type-I error guarantees under optional stopping and optional continuation. The test is sequential without the need to specify a maximum sample size or stopping rule, and allows for cumulative meta-analysis with type-I error control. The method can be extended to define anytime-valid confidence intervals. The logrank test is an instance of the martingale tests based on E-variables that have been recently developed. We demonstrate type-I error guarantees for the test in a semiparametric setting of proportional hazards, show explicitly how to extend it to ties and confidence sequences and indicate further extensions to the full Cox regression model. Using a Gaussian approximation on the logrank statistic, we show that the AV logrank test (which itself is always exact) has a similar rejection region to O’Brien-Fleming α-spending but with the potential to achieve $100\% $ power by optional continuation. Although our approach to study design requires a larger sample size, the expected sample size is competitive by optional stopping.

We consider the problem of sequential multiple hypothesis testing with nontrivial data collection costs. This problem appears, for example, when conducting biological experiments to identify differentially expressed genes of a disease process. This work builds on the generalized α-investing framework which enables control of the marginal false discovery rate in a sequential testing setting. We make a theoretical analysis of the long term asymptotic behavior of α-wealth which motivates a consideration of sample size in the α-investing decision rule. Posing the testing process as a game with nature, we construct a decision rule that optimizes the expected α-wealth reward (ERO) and provides an optimal sample size for each test. Empirical results show that a cost-aware ERO decision rule correctly rejects more false null hypotheses than other methods for $n=1$ where n is the sample size. When the sample size is not fixed cost-aware ERO uses a prior on the null hypothesis to adaptively allocate of the sample budget to each test. We extend cost-aware ERO investing to finite-horizon testing which enables the decision rule to allocate samples in a non-myopic manner. Finally, empirical tests on real data sets from biological experiments show that cost-aware ERO balances the allocation of samples to an individual test against the allocation of samples across multiple tests.

Analyzing health effects associated with exposure to environmental chemical mixtures is a challenging problem in epidemiology, toxicology, and exposure science. In particular, when there are a large number of chemicals under consideration it is difficult to estimate the interactive effects without incorporating reasonable prior information. Based on substantive considerations, researchers believe that true interactions between chemicals need to incorporate their corresponding main effects. In this paper, we use this prior knowledge through a shrinkage prior that a priori assumes an interaction term can only occur when the corresponding main effects exist. Our initial development is for logistic regression with linear chemical effects. We extend this formulation to include non-linear exposure effects and to account for exposure subject to detection limit. We develop an MCMC algorithm using a shrinkage prior that shrinks the interaction terms closer to zero as the main effects get closer to zero. We examine the performance of our methodology through simulation studies and illustrate an analysis of chemical interactions in a case-control study in cancer.

We consider a formal statistical design that allows simultaneous enrollment of a main cohort and a backfill cohort of patients in a dose-finding trial. The goal is to accumulate more information at various doses to facilitate dose optimization. The proposed design, called Bi3+3, combines the simple dose-escalation algorithm in the i3+3 design and a model-based inference under the framework of probability of decisions (POD), both previously published. As a result, Bi3+3 provides a simple algorithm for backfilling patients to lower doses in a dose-finding trial once these doses exhibit safety profile in patients. The POD framework allows dosing decisions to be made when some backfill patients are still being followed with incomplete toxicity outcomes, thereby potentially expediting the clinical trial. At the end of the trial, Bi3+3 uses both toxicity and efficacy outcomes to estimate an optimal biological dose (OBD). The proposed inference is based on a dose-response model that takes into account either a monotone or plateau dose-efficacy relationship, which are frequently encountered in modern oncology drug development. Simulation studies show promising operating characteristics of the Bi3+3 design in comparison to existing designs.

The notion of an e-value has been recently proposed as a possible alternative to critical regions and p-values in statistical hypothesis testing. In this paper we consider testing the nonparametric hypothesis of symmetry, introduce analogues for e-values of three popular nonparametric tests, define an analogue for e-values of Pitman’s asymptotic relative efficiency, and apply it to the three nonparametric tests. We discuss limitations of our simple definition of asymptotic relative efficiency and list directions of further research.