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ABSTRACT It is of substantial scientific interest to detect mediators that lie in the causal pathway from an exposure to a survival outcome. However, with high‐dimensional mediators, as often encountered in modern genomic data settings, there is a lack of powerful methods that can provide valid post‐selection inference for the identified marginal mediation effect. To resolve this challenge, we develop a post‐selection inference procedure for the maximally selected natural indirect effect using a semiparametric efficient influence function approach. To this end, we establish the asymptotic normality of a stabilized one‐step estimator that takes the selection of the mediator into account. Simulation studies show that our proposed method has good empirical performance. We further apply our proposed approach to a lung cancer dataset and find multiple DNA methylation CpG sites that might mediate the effect of cigarette smoking on lung cancer survival. 

Abstract Functional data with non-smooth features (e.g., discontinuities in the functional mean and/or covariance) and monotonicity arise frequently in practice. This paper develops simultaneous inference for concurrent functional linear regression in this setting. We construct a simultaneous confidence band for a functional covariate effect of interest. Along with a Wald-type formulation, our approach is based on a powerful nonparametric likelihood ratio method. Our procedures are flexible enough to allow discontinuities in the coefficient functions and the covariance structure, while accounting for discretization of the observed trajectories under a fixed dense design. A simulation study shows that the proposed likelihood ratio-based procedure outperforms the Wald-type procedure in moderate sample sizes. We apply the proposed methods to studying the effect of age on the occupation time curve derived from wearable device data obtained in an NHANES study. 

Objective:Cognitive training may benefit older adults with mild cognitive impairment (MCI), but the prognostic factors are not well-established. Methods:This study analyzed data from a 78-week trial with 107 participants with MCI, comparing computerized cognitive training (CCT) and computerized crossword puzzle training (CPT). Outcomes were changes in cognitive and functional measures from baseline. Linear mixed-effect models were used to identify prognostic factors for each intervention. Results:Baseline neuropsychological composite z-score was positively associated with cognitive and functional improvements for both interventions in univariable models, retaining significance in the final multivariable model for functional outcome in CPT (P< 0.001). Apolipoprotein E e4 carriers had worse cognitive (P= 0.023) and functional (P= 0.001) outcomes than noncarriers for CPT but not CCT. African Americans showed greater functional improvements than non-African Americans in both CPT (P= 0.001) and CCT (P= 0.010). Better baseline odor identification was correlated with cognitive improvements in CPT (P= 0.006) and functional improvements in CCT (P< 0.001). Conclusion:Baseline cognitive test performance, African American background, and odor identification ability are potential prognostic factors for improved outcomes with cognitive interventions in older adults with MCI. Apolipoprotein E e4 is associated with poor outcomes. Replication of these findings may improve the selection of cognitive interventions for individuals with MCI. 

Abstract Stein’s method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representations model how quantum effects result from the interaction of finitely many classical ‘worlds’, with the role of sample size played by the number of worlds. Each approximation arises as the ground state of a Hamiltonian involving a particular interworld potential function. Our approach, framed in terms of spherical coordinates, provides the rate of convergence of the discrete approximation to the ground state in terms of Wasserstein distance. Applying a novel Stein’s method technique to the radial component of the ground state solution, the fastest rate of convergence to the ground state is found to occur in three dimensions. 

Functional data analysis (FDA) studies data that include infinite-dimensional functions or objects, generalizing traditional univariate or multivariate observations from each study unit. Among inferential approaches without parametric assumptions, empirical likelihood (EL) offers a principled method in that it extends the framework of parametric likelihood ratio–based inference via the nonparametric likelihood. There has been increasing use of EL in FDA due to its many favorable properties, including self-normalization and the data-driven shape of confidence regions. This article presents a review of EL approaches in FDA, starting with finite-dimensional features, then covering infinite-dimensional features. We contrast smooth and nonsmooth frameworks in FDA and show how EL has been incorporated into both of them. The article concludes with a discussion of some future research directions, including the possibility of applying EL to conformal inference. 

There has been a growing interest in incorporating auxiliary summary information from external studies into the analysis of internal individual‐level data. In this paper, we propose an adaptive estimation procedure for an additive risk model to integrate auxiliary subgroup survival information via a penalized method of moments technique. Our approach can accommodate information from heterogeneous data. Parameters to quantify the magnitude of potential incomparability between internal data and external auxiliary information are introduced in our framework while nonzero components of these parameters suggest a violation of the homogeneity assumption. We further develop an efficient computational algorithm to solve the numerical optimization problem by profiling out the nuisance parameters. In an asymptotic sense, our method can be as efficient as if all the incomparable auxiliary information is accurately acknowledged and has been automatically excluded from consideration. The asymptotic normality of the proposed estimator of the regression coefficients is established, with an explicit formula for the asymptotic variance‐covariance matrix that can be consistently estimated from the data. Simulation studies show that the proposed method yields a substantial gain in statistical efficiency over the conventional method using the internal data only, and reduces estimation biases when the given auxiliary survival information is incomparable. We illustrate the proposed method with a lung cancer survival study. 

Abstract This paper develops a nonparametric inference framework that is applicable to occupation time curves derived from wearable device data. These curves consider all activity levels within the range of device readings, which is preferable to the practice of classifying activity into discrete categories. Motivated by certain features of these curves, we introduce a powerful likelihood ratio approach to construct confidence bands and compare functional means. Notably, our approach allows discontinuities in the functional covariances while accommodating discretization of the observed trajectories. A simulation study shows that the proposed procedures outperform competing functional data procedures. We illustrate the proposed methods using wearable device data from an NHANES study.