The estimands framework outlined in ICH E9 (R1) describes the components needed to precisely define the effects to be estimated in clinical trials, which includes how post-baseline "intercurrent" events (IEs) are to be handled. In late-stage clinical trials, it is common to handle intercurrent events like "treatment discontinuation" using the treatment policy strategy and target the treatment effect on all outcomes regardless of treatment discontinuation. For continuous repeated measures, this type of effect is often estimated using all observed data before and after discontinuation using either a mixed model for repeated measures (MMRM) or multiple imputation (MI) to handle any missing data. In basic form, both of these estimation methods ignore treatment discontinuation in the analysis and therefore may be biased if there are differences in patient outcomes after treatment discontinuation compared to patients still assigned to treatment, and missing data being more common for patients who have discontinued treatment. We therefore propose and evaluate a set of MI models that can accommodate differences between outcomes before and after treatment discontinuation. The models are evaluated in the context of planning a phase 3 trial for a respiratory disease. We show that analyses ignoring treatment discontinuation can introduce substantial bias and can sometimes underestimate variability. We also show that some of the MI models proposed can successfully correct the bias but inevitably lead to increases in variance. We conclude that some of the proposed MI models are preferable to the traditional analysis ignoring treatment discontinuation, but the precise choice of MI model will likely depend on the trial design, disease of interest and amount of observed and missing data following treatment discontinuation.
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There has been significant progress in the study of sampling discretization of integral norms for both a designated finite-dimensional function space and a finite collection of such function spaces (universal discretization). Sampling discretization results turn out to be very useful in various applications, particularly in sampling recovery. Recent sampling discretization results typically provide existence of good sampling points for discretization. In this paper, we show that independent and identically distributed random points provide good universal discretization with high probability. Furthermore, we demonstrate that a simple greedy algorithm based on those points that are good for universal discretization provides excellent sparse recovery results in the square norm.
Recurrent neural networks (RNNs) have yielded promising results for both recognizing objects in challenging conditions and modeling aspects of primate vision. However, the representational dynamics of recurrent computations remain poorly understood, especially in large-scale visual models. Here, we studied such dynamics in RNNs trained for object classification on MiniEcoset, a novel subset of ecoset. We report two main insights. First, upon inference, representations continued to evolve after correct classification, suggesting a lack of the notion of being ``done with classification''. Second, focusing on ``readout zones'' as a way to characterize the activation trajectories, we observe that misclassified representations exhibit activation patterns with lower L2 norm, and are positioned more peripherally in the readout zones. Such arrangements help the misclassified representations move into the correct zones as time progresses. Our findings generalize to networks with lateral and top-down connections, and include both additive and multiplicative interactions with the bottom-up sweep. The results therefore contribute to a general understanding of RNN dynamics in naturalistic tasks. We hope that the analysis framework will aid future investigations of other types of RNNs, including understanding of representational dynamics in primate vision.
Prognostic Health Management aims to predict the Remaining Useful Life (RUL) of degrading components/systems utilizing monitoring data. These RUL predictions form the basis for optimizing maintenance planning in a Predictive Maintenance (PdM) paradigm. We here propose a metric for assessing data-driven prognostic algorithms based on their impact on downstream PdM decisions. The metric is defined in association with a decision setting and a corresponding PdM policy. We consider two typical PdM decision settings, namely component ordering and/or replacement planning, for which we investigate and improve PdM policies that are commonly utilized in the literature. All policies are evaluated via the data-based estimation of the long-run expected maintenance cost per unit time, using monitored run-to-failure experiments. The policy evaluation enables the estimation of the proposed metric. We employ the metric as an objective function for optimizing heuristic PdM policies and algorithms' hyperparameters. The effect of different PdM policies on the metric is initially investigated through a theoretical numerical example. Subsequently, we employ four data-driven prognostic algorithms on a simulated turbofan engine degradation problem, and investigate the joint effect of prognostic algorithm and PdM policy on the metric, resulting in a decision-oriented performance assessment of these algorithms.
We tackle the extension to the vector-valued case of consistency results for Stepwise Uncertainty Reduction sequential experimental design strategies established in [Bect et al., A supermartingale approach to Gaussian process based sequential design of experiments, Bernoulli 25, 2019]. This lead us in the first place to clarify, assuming a compact index set, how the connection between continuous Gaussian processes and Gaussian measures on the Banach space of continuous functions carries over to vector-valued settings. From there, a number of concepts and properties from the aforementioned paper can be readily extended. However, vector-valued settings do complicate things for some results, mainly due to the lack of continuity for the pseudo-inverse mapping that affects the conditional mean and covariance function given finitely many pointwise observations. We apply obtained results to the Integrated Bernoulli Variance and the Expected Measure Variance uncertainty functionals employed in [Fossum et al., Learning excursion sets of vector-valued Gaussian random fields for autonomous ocean sampling, The Annals of Applied Statistics 15, 2021] for the estimation for excursion sets of vector-valued functions.
Bayesian cross-validation (CV) is a popular method for predictive model assessment that is simple to implement and broadly applicable. A wide range of CV schemes is available for time series applications, including generic leave-one-out (LOO) and K-fold methods, as well as specialized approaches intended to deal with serial dependence such as leave-future-out (LFO), h-block, and hv-block. Existing large-sample results show that both specialized and generic methods are applicable to models of serially-dependent data. However, large sample consistency results overlook the impact of sampling variability on accuracy in finite samples. Moreover, the accuracy of a CV scheme depends on many aspects of the procedure. We show that poor design choices can lead to elevated rates of adverse selection. In this paper, we consider the problem of identifying the regression component of an important class of models of data with serial dependence, autoregressions of order p with q exogenous regressors (ARX(p,q)), under the logarithmic scoring rule. We show that when serial dependence is present, scores computed using the joint (multivariate) density have lower variance and better model selection accuracy than the popular pointwise estimator. In addition, we present a detailed case study of the special case of ARX models with fixed autoregressive structure and variance. For this class, we derive the finite-sample distribution of the CV estimators and the model selection statistic. We conclude with recommendations for practitioners.
Sociodemographic inequalities in student achievement are a persistent concern for education systems and are increasingly recognized to be intersectional. Intersectionality considers the multidimensional nature of disadvantage, appreciating the interlocking social determinants which shape individual experience. Intersectional multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) is a new approach developed in population health but with limited application in educational research. In this study, we introduce and apply this approach to study sociodemographic inequalities in student achievement across two cohorts of students in London, England. We define 144 intersectional strata arising from combinations of student age, gender, free school meal status, special educational needs, and ethnicity. We find substantial strata-level variation in achievement composed primarily by additive rather than interactive effects with results stubbornly consistent across the cohorts. We conclude that policymakers should pay greater attention to multiply marginalized students and intersectional MAIHDA provides a useful approach to study their experiences.
Introduction: The amount of data generated by original research is growing exponentially. Publicly releasing them is recommended to comply with the Open Science principles. However, data collected from human participants cannot be released as-is without raising privacy concerns. Fully synthetic data represent a promising answer to this challenge. This approach is explored by the French Centre de Recherche en {\'E}pid{\'e}miologie et Sant{\'e} des Populations in the form of a synthetic data generation framework based on Classification and Regression Trees and an original distance-based filtering. The goal of this work was to develop a refined version of this framework and to assess its risk-utility profile with empirical and formal tools, including novel ones developed for the purpose of this evaluation.Materials and Methods: Our synthesis framework consists of four successive steps, each of which is designed to prevent specific risks of disclosure. We assessed its performance by applying two or more of these steps to a rich epidemiological dataset. Privacy and utility metrics were computed for each of the resulting synthetic datasets, which were further assessed using machine learning approaches.Results: Computed metrics showed a satisfactory level of protection against attribute disclosure attacks for each synthetic dataset, especially when the full framework was used. Membership disclosure attacks were formally prevented without significantly altering the data. Machine learning approaches showed a low risk of success for simulated singling out and linkability attacks. Distributional and inferential similarity with the original data were high with all datasets.Discussion: This work showed the technical feasibility of generating publicly releasable synthetic data using a multi-step framework. Formal and empirical tools specifically developed for this demonstration are a valuable contribution to this field. Further research should focus on the extension and validation of these tools, in an effort to specify the intrinsic qualities of alternative data synthesis methods.Conclusion: By successfully assessing the quality of data produced using a novel multi-step synthetic data generation framework, we showed the technical and conceptual soundness of the Open-CESP initiative, which seems ripe for full-scale implementation.
In the field of semi-supervised medical image segmentation, the shortage of labeled data is the fundamental problem. How to effectively learn image features from unlabeled images to improve segmentation accuracy is the main research direction in this field. Traditional self-training methods can partially solve the problem of insufficient labeled data by generating pseudo labels for iterative training. However, noise generated due to the model's uncertainty during training directly affects the segmentation results. Therefore, we added sample-level and pixel-level uncertainty to stabilize the training process based on the self-training framework. Specifically, we saved several moments of the model during pre-training, and used the difference between their predictions on unlabeled samples as the sample-level uncertainty estimate for that sample. Then, we gradually add unlabeled samples from easy to hard during training. At the same time, we added a decoder with different upsampling methods to the segmentation network and used the difference between the outputs of the two decoders as pixel-level uncertainty. In short, we selectively retrained unlabeled samples and assigned pixel-level uncertainty to pseudo labels to optimize the self-training process. We compared the segmentation results of our model with five semi-supervised approaches on the public 2017 ACDC dataset and 2018 Prostate dataset. Our proposed method achieves better segmentation performance on both datasets under the same settings, demonstrating its effectiveness, robustness, and potential transferability to other medical image segmentation tasks. Keywords: Medical image segmentation, semi-supervised learning, self-training, uncertainty estimation
Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for multivariate functions of a Markov chain, it is important to estimate not only the auto-correlation for each component but also to estimate cross-correlations, in order to better assess sample quality, improve estimates of effective sample size, and use more effective stopping rules. Berg and Song [2022] introduced the moment least squares (momentLS) estimator, a shape-constrained estimator for the autocovariance sequence from a reversible Markov chain, for univariate functions of the Markov chain. Based on this sequence estimator, they proposed an estimator of the asymptotic variance of the sample mean from MCMC samples. In this study, we propose novel autocovariance sequence and asymptotic variance estimators for Markov chain functions with multiple components, based on the univariate momentLS estimators from Berg and Song [2022]. We demonstrate strong consistency of the proposed auto(cross)-covariance sequence and asymptotic variance matrix estimators. We conduct empirical comparisons of our method with other state-of-the-art approaches on simulated and real-data examples, using popular samplers including the random-walk Metropolis sampler and the No-U-Turn sampler from STAN.
In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first consider the application of the proximal ADMM to solve well-posed linearly constrained two-block separable convex minimization problems in Hilbert spaces and obtain new and improved non-ergodic convergence rate results, including linear and sublinear rates under certain regularity conditions. We next consider proximal ADMM as a regularization method for solving linear ill-posed inverse problems in Hilbert spaces. When the data is corrupted by additive noise, we establish, under a benchmark source condition, a convergence rate result in terms of the noise level when the number of iteration is properly chosen.
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