Utilizing non-concurrent controls in the analysis of late-entering experimental arms in platform trials has recently received considerable attention, both on academic and regulatory levels. While incorporating this data can lead to increased power and lower required sample sizes, it might also introduce bias to the effect estimators if temporal drifts are present in the trial. Aiming to mitigate the potential calendar time bias, we propose various frequentist model-based approaches that leverage the non-concurrent control data, while adjusting for time trends. One of the currently available frequentist models incorporates time as a categorical fixed effect, separating the duration of the trial into periods, defined as time intervals bounded by any treatment arm entering or leaving the platform. In this work, we propose two extensions of this model. First, we consider an alternative definition of the time covariate by dividing the trial into fixed-length calendar time intervals. Second, we propose alternative methods to adjust for time trends. In particular, we investigate adjusting for autocorrelated random effects to account for dependency between closer time intervals and employing spline regression to model time with a smooth polynomial function. We evaluate the performance of the proposed approaches in a simulation study and illustrate their use by means of a case study.
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We propose an abstract conceptual framework for analysing complex security systems using a new notion of modes and mode transitions. A mode is an independent component of a system with its own objectives, monitoring data, algorithms, and scope and limits. The behaviour of a mode, including its transitions to other modes, is determined by interpretations of the mode's monitoring data in the light of its objectives and capabilities -- these interpretations we call beliefs. We formalise the conceptual framework mathematically and, by quantifying and visualising beliefs in higher-dimensional geometric spaces, we argue our models may help both design, analyse and explain systems. The mathematical models are based on simplicial complexes.
We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where no structural assumption is made on the system matrix $A^* \in \mathbb{R}^{n \times n}$, and have consequently analyzed the ordinary least squares (OLS) estimator in detail. We assume prior structural information on $A^*$ is available, which can be captured in the form of a convex set $\mathcal{K}$ containing $A^*$. For the solution of the ensuing constrained least squares estimator, we derive non-asymptotic error bounds in the Frobenius norm that depend on the local size of $\mathcal{K}$ at $A^*$. To illustrate the usefulness of these results, we instantiate them for four examples, namely when (i) $A^*$ is sparse and $\mathcal{K}$ is a suitably scaled $\ell_1$ ball; (ii) $\mathcal{K}$ is a subspace; (iii) $\mathcal{K}$ consists of matrices each of which is formed by sampling a bivariate convex function on a uniform $n \times n$ grid (convex regression); (iv) $\mathcal{K}$ consists of matrices each row of which is formed by uniform sampling (with step size $1/T$) of a univariate Lipschitz function. In all these situations, we show that $A^*$ can be reliably estimated for values of $T$ much smaller than what is needed for the unconstrained setting.
This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation error of the best linear coefficients for two widely-used policy evaluation algorithms: the temporal difference (TD) learning algorithm and the two-timescale linear TD with gradient correction (TDC) algorithm. In both the on-policy setting, where observations are generated from the target policy, and the off-policy setting, where samples are drawn from a behavior policy potentially different from the target policy, we establish the first sample complexity bound with high-probability convergence guarantee that attains the optimal dependence on the tolerance level. We also exhihit an explicit dependence on problem-related quantities, and show in the on-policy setting that our upper bound matches the minimax lower bound on crucial problem parameters, including the choice of the feature maps and the problem dimension.
A common problem in numerous research areas, particularly in clinical trials, is to test whether the effect of an explanatory variable on an outcome variable is equivalent across different groups. In practice, these tests are frequently used to compare the effect between patient groups, e.g. based on gender, age or treatments. Equivalence is usually assessed by testing whether the difference between the groups does not exceed a pre-specified equivalence threshold. Classical approaches are based on testing the equivalence of single quantities, e.g. the mean, the area under the curve (AUC) or other values of interest. However, when differences depending on a particular covariate are observed, these approaches can turn out to be not very accurate. Instead, whole regression curves over the entire covariate range, describing for instance the time window or a dose range, are considered and tests are based on a suitable distance measure of two such curves, as, for example, the maximum absolute distance between them. In this regard, a key assumption is that the true underlying regression models are known, which is rarely the case in practice. However, misspecification can lead to severe problems as inflated type I errors or, on the other hand, conservative test procedures. In this paper, we propose a solution to this problem by introducing a flexible extension of such an equivalence test using model averaging in order to overcome this assumption and making the test applicable under model uncertainty. Precisely, we introduce model averaging based on smooth AIC weights and we propose a testing procedure which makes use of the duality between confidence intervals and hypothesis testing. We demonstrate the validity of our approach by means of a simulation study and demonstrate the practical relevance of the approach considering a time-response case study with toxicological gene expression data.
Single-particle entangled states (SPES) can offer a more secure way of encoding and processing quantum information than their multi-particle counterparts. The SPES generated via a 2D alternate quantum-walk setup from initially separable states can be either 3-way or 2-way entangled. This letter shows that the generated genuine three-way and nonlocal two-way SPES can be used as cryptographic keys to securely encode two distinct messages simultaneously. We detail the message encryption-decryption steps and show the resilience of the 3-way and 2-way SPES-based cryptographic protocols against eavesdropper attacks like intercept-and-resend and man-in-the-middle. We also detail how these protocols can be experimentally realized using single photons, with the three degrees of freedom being OAM, path, and polarization. These have unparalleled security for quantum communication tasks. The ability to simultaneously encode two distinct messages using the generated SPES showcases the versatility and efficiency of the proposed cryptographic protocol. This capability could significantly improve the throughput of quantum communication systems.
In the era of fast-paced precision medicine, observational studies play a major role in properly evaluating new treatments in clinical practice. Yet, unobserved confounding can significantly compromise causal conclusions drawn from non-randomized data. We propose a novel strategy that leverages randomized trials to quantify unobserved confounding. First, we design a statistical test to detect unobserved confounding with strength above a given threshold. Then, we use the test to estimate an asymptotically valid lower bound on the unobserved confounding strength. We evaluate the power and validity of our statistical test on several synthetic and semi-synthetic datasets. Further, we show how our lower bound can correctly identify the absence and presence of unobserved confounding in a real-world setting.
Computing is still under a significant threat from ransomware, which necessitates prompt action to prevent it. Ransomware attacks can have a negative impact on how smart grids, particularly digital substations. In addition to examining a ransomware detection method using artificial intelligence (AI), this paper offers a ransomware attack modeling technique that targets the disrupted operation of a digital substation. The first, binary data is transformed into image data and fed into the convolution neural network model using federated learning. The experimental findings demonstrate that the suggested technique detects ransomware with a high accuracy rate.
Capturing the extremal behaviour of data often requires bespoke marginal and dependence models which are grounded in rigorous asymptotic theory, and hence provide reliable extrapolation into the upper tails of the data-generating distribution. We present a toolbox of four methodological frameworks, motivated by modern extreme value theory, that can be used to accurately estimate extreme exceedance probabilities or the corresponding level in either a univariate or multivariate setting. Our frameworks were used to facilitate the winning contribution of Team Yalla to the EVA (2023) Conference Data Challenge, which was organised for the 13$^\text{th}$ International Conference on Extreme Value Analysis. This competition comprised seven teams competing across four separate sub-challenges, with each requiring the modelling of data simulated from known, yet highly complex, statistical distributions, and extrapolation far beyond the range of the available samples in order to predict probabilities of extreme events. Data were constructed to be representative of real environmental data, sampled from the fantasy country of "Utopia"
We develop an inferential toolkit for analyzing object-valued responses, which correspond to data situated in general metric spaces, paired with Euclidean predictors within the conformal framework. To this end we introduce conditional profile average transport costs, where we compare distance profiles that correspond to one-dimensional distributions of probability mass falling into balls of increasing radius through the optimal transport cost when moving from one distance profile to another. The average transport cost to transport a given distance profile to all others is crucial for statistical inference in metric spaces and underpins the proposed conditional profile scores. A key feature of the proposed approach is to utilize the distribution of conditional profile average transport costs as conformity score for general metric space-valued responses, which facilitates the construction of prediction sets by the split conformal algorithm. We derive the uniform convergence rate of the proposed conformity score estimators and establish asymptotic conditional validity for the prediction sets. The finite sample performance for synthetic data in various metric spaces demonstrates that the proposed conditional profile score outperforms existing methods in terms of both coverage level and size of the resulting prediction sets, even in the special case of scalar and thus Euclidean responses. We also demonstrate the practical utility of conditional profile scores for network data from New York taxi trips and for compositional data reflecting energy sourcing of U.S. states.
Adaptive interventions, aka dynamic treatment regimens, are sequences of pre-specified decision rules that guide the provision of treatment for an individual given information about their baseline and evolving needs, including in response to prior intervention. Clustered adaptive interventions (cAIs) extend this idea by guiding the provision of intervention at the level of clusters (e.g., clinics), but with the goal of improving outcomes at the level of individuals within the cluster (e.g., clinicians or patients within clinics). A clustered, sequential multiple-assignment randomized trials (cSMARTs) is a multistage, multilevel randomized trial design used to construct high-quality cAIs. In a cSMART, clusters are randomized at multiple intervention decision points; at each decision point, the randomization probability can depend on response to prior data. A challenge in cluster-randomized trials, including cSMARTs, is the deleterious effect of small samples of clusters on statistical inference, particularly via estimation of standard errors. \par This manuscript develops finite-sample adjustment (FSA) methods for making improved statistical inference about the causal effects of cAIs in a cSMART. The paper develops FSA methods that (i) scale variance estimators using a degree-of-freedom adjustment, (ii) reference a t distribution (instead of a normal), and (iii) employ a ``bias corrected" variance estimator. Method (iii) requires extensions that are unique to the analysis of cSMARTs. Extensive simulation experiments are used to test the performance of the methods. The methods are illustrated using the Adaptive School-based Implementation of CBT (ASIC) study, a cSMART designed to construct a cAI for improving the delivery of cognitive behavioral therapy (CBT) by school mental health professionals within high schools in Michigan.
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