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Indolent cancers are characterized by long overall survival (OS) times. Therefore, powering a clinical trial to provide definitive assessment of the effects of an experimental intervention on OS in a reasonable timeframe is generally infeasible. Instead, the primary outcome in many pivotal trials is an intermediate clinical response such as progression-free survival (PFS). In several recently reported pivotal trials of interventions for indolent cancers that yielded promising results on an intermediate outcome, however, more mature data or post-approval trials showed concerning OS trends. These problematic results have prompted a keen interest in quantitative approaches for monitoring OS that can support regulatory decision-making related to the risk of an unacceptably large detrimental effect on OS. For example, the US Food and Drug Administration, the American Association for Cancer Research, and the American Statistical Association recently organized a one-day multi-stakeholder workshop entitled 'Overall Survival in Oncology Clinical Trials'. In this paper, we propose OS monitoring guidelines tailored for the setting of indolent cancers. Our pragmatic approach is modeled, in part, on the monitoring guidelines the FDA has used in cardiovascular safety trials conducted in Type 2 Diabetes Mellitus. We illustrate proposals through application to several examples informed by actual case studies.

The reverse engineering of a complex mixture, regardless of its nature, has become significant today. Being able to quickly assess the potential toxicity of new commercial products in relation to the environment presents a genuine analytical challenge. The development of digital tools (databases, chemometrics, machine learning, etc.) and analytical techniques (Raman spectroscopy, NIR spectroscopy, mass spectrometry, etc.) will allow for the identification of potential toxic molecules. In this article, we use the example of detergent products, whose composition can prove dangerous to humans or the environment, necessitating precise identification and quantification for quality control and regulation purposes. The combination of various digital tools (spectral database, mixture database, experimental design, Chemometrics / Machine Learning algorithm{\ldots}) together with different sample preparation methods (raw sample, or several concentrated / diluted samples) Raman spectroscopy, has enabled the identification of the mixture's constituents and an estimation of its composition. Implementing such strategies across different analytical tools can result in time savings for pollutant identification and contamination assessment in various matrices. This strategy is also applicable in the industrial sector for product or raw material control, as well as for quality control purposes.

We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher dimensional topological features such as connected components and holes (cycles or loops) in the data. In other words, persistent homology is a multiscale version of homology that characterizes sets based on the connected components and holes. We use super-level sets of functions to extract geometric features via persistent homology. In particular, we explore structures in regression curves via the persistent homology of super-level sets of a function, where the function of interest is - the first derivative of the regression function. In the course of this study, we extend an existing procedure of estimating the persistent homology for the first derivative of a regression function and establish its consistency. Moreover, as an application of the proposed methodology, we demonstrate that the persistent homology of the derivative of a function can reveal hidden structures in the function that are not visible from the persistent homology of the function itself. In addition, we also illustrate that the proposed procedure can be used to compare the shapes of two or more regression curves which is not possible merely from the persistent homology of the function itself.

Accurately estimating the positions of multi-agent systems in indoor environments is challenging due to the lack of Global Navigation Satelite System (GNSS) signals. Noisy measurements of position and orientation can cause the integrated position estimate to drift without bound. Previous research has proposed using magnetic field simultaneous localization and mapping (SLAM) to compensate for position drift in a single agent. Here, we propose two novel algorithms that allow multiple agents to apply magnetic field SLAM using their own and other agents measurements. Our first algorithm is a centralized approach that uses all measurements collected by all agents in a single extended Kalman filter. This algorithm simultaneously estimates the agents position and orientation and the magnetic field norm in a central unit that can communicate with all agents at all times. In cases where a central unit is not available, and there are communication drop-outs between agents, our second algorithm is a distributed approach that can be employed. We tested both algorithms by estimating the position of magnetometers carried by three people in an optical motion capture lab with simulated odometry and simulated communication dropouts between agents. We show that both algorithms are able to compensate for drift in a case where single-agent SLAM is not. We also discuss the conditions for the estimate from our distributed algorithm to converge to the estimate from the centralized algorithm, both theoretically and experimentally. Our experiments show that, for a communication drop-out rate of 80 percent, our proposed distributed algorithm, on average, provides a more accurate position estimate than single-agent SLAM. Finally, we demonstrate the drift-compensating abilities of our centralized algorithm on a real-life pedestrian localization problem with multiple agents moving inside a building.

We consider certain large random matrices, called random inner-product kernel matrices, which are essentially given by a nonlinear function $f$ applied entrywise to a sample-covariance matrix, $f(X^TX)$, where $X \in \mathbb{R}^{d \times N}$ is random and normalized in such a way that $f$ typically has order-one arguments. We work in the polynomial regime, where $N \asymp d^\ell$ for some $\ell > 0$, not just the linear regime where $\ell = 1$. Earlier work by various authors showed that, when the columns of $X$ are either uniform on the sphere or standard Gaussian vectors, and when $\ell$ is an integer (the linear regime $\ell = 1$ is particularly well-studied), the bulk eigenvalues of such matrices behave in a simple way: They are asymptotically given by the free convolution of the semicircular and Mar\v{c}enko-Pastur distributions, with relative weights given by expanding $f$ in the Hermite basis. In this paper, we show that this phenomenon is universal, holding as soon as $X$ has i.i.d. entries with all finite moments. In the case of non-integer $\ell$, the Mar\v{c}enko-Pastur term disappears (its weight in the free convolution vanishes), and the spectrum is just semicircular.

Recently, due to the popularity of deep neural networks and other methods whose training typically relies on the optimization of an objective function, and due to concerns for data privacy, there is a lot of interest in differentially private gradient descent methods. To achieve differential privacy guarantees with a minimum amount of noise, it is important to be able to bound precisely the sensitivity of the information which the participants will observe. In this study, we present a novel approach that mitigates the bias arising from traditional gradient clipping. By leveraging public information concerning the current global model and its location within the search domain, we can achieve improved gradient bounds, leading to enhanced sensitivity determinations and refined noise level adjustments. We extend the state of the art algorithms, present improved differential privacy guarantees requiring less noise and present an empirical evaluation.

We introduce a convergent hierarchy of lower bounds on the minimum value of a real homogeneous polynomial over the sphere. The main practical advantage of our hierarchy over the sum-of-squares (SOS) hierarchy is that the lower bound at each level of our hierarchy is obtained by a minimum eigenvalue computation, as opposed to the full semidefinite program (SDP) required at each level of SOS. In practice, this allows us to go to much higher levels than are computationally feasible for the SOS hierarchy. For both hierarchies, the underlying space at the $k$-th level is the set of homogeneous polynomials of degree $2k$. We prove that our hierarchy converges as $O(1/k)$ in the level $k$, matching the best-known convergence of the SOS hierarchy when the number of variables $n$ is less than the half-degree $d$ (the best-known convergence of SOS when $n \geq d$ is $O(1/k^2)$). More generally, we introduce a convergent hierarchy of minimum eigenvalue computations for minimizing the inner product between a real tensor and an element of the spherical Segre-Veronese variety, with similar convergence guarantees. As examples, we obtain hierarchies for computing the (real) tensor spectral norm, and for minimizing biquadratic forms over the sphere. Hierarchies of eigencomputations for more general constrained polynomial optimization problems are discussed.

Difference-in-differences (DID) is a popular approach to identify the causal effects of treatments and policies in the presence of unmeasured confounding. DID identifies the sample average treatment effect in the treated (SATT). However, a goal of such research is often to inform decision-making in target populations outside the treated sample. Transportability methods have been developed to extend inferences from study samples to external target populations; these methods have primarily been developed and applied in settings where identification is based on conditional independence between the treatment and potential outcomes, such as in a randomized trial. This paper develops identification and estimators for effects in a target population, based on DID conducted in a study sample that differs from the target population. We present a range of assumptions under which one may identify causal effects in the target population and employ causal diagrams to illustrate these assumptions. In most realistic settings, results depend critically on the assumption that any unmeasured confounders are not effect measure modifiers on the scale of the effect of interest. We develop several estimators of transported effects, including a doubly robust estimator based on the efficient influence function. Simulation results support theoretical properties of the proposed estimators. We discuss the potential application of our approach to a study of the effects of a US federal smoke-free housing policy, where the original study was conducted in New York City alone and the goal is extend inferences to other US cities.

Statistical methods to study the association between a longitudinal biomarker and the risk of death are very relevant for the long-term care of subjects affected by chronic illnesses, such as potassium in heart failure patients. Particularly in the presence of comorbidities or pharmacological treatments, sudden crises can cause potassium to undergo very abrupt yet transient changes. In the context of the monitoring of potassium, there is a need for a dynamic model that can be used in clinical practice to assess the risk of death related to an observed patient's potassium trajectory. We considered different dynamic survival approaches, starting from the simple approach considering the most recent measurement, to the joint model. We then propose a novel method based on wavelet filtering and landmarking to retrieve the prognostic role of past short-term potassium shifts. We argue that while taking into account past information is important, not all past information is equally informative. State-of-the-art dynamic survival models are prone to give more importance to the mean long-term value of potassium. However, our findings suggest that it is essential to take into account also recent potassium instability to capture all the relevant prognostic information. The data used comes from over 2000 subjects, with a total of over 80 000 repeated potassium measurements collected through Administrative Health Records and Outpatient and Inpatient Clinic E-charts. A novel dynamic survival approach is proposed in this work for the monitoring of potassium in heart failure. The proposed wavelet landmark method shows promising results revealing the prognostic role of past short-term changes, according to their different duration, and achieving higher performances in predicting the survival probability of individuals.

Breast cancer remains a global challenge, causing over 1 million deaths globally in 2018. To achieve earlier breast cancer detection, screening x-ray mammography is recommended by health organizations worldwide and has been estimated to decrease breast cancer mortality by 20-40%. Nevertheless, significant false positive and false negative rates, as well as high interpretation costs, leave opportunities for improving quality and access. To address these limitations, there has been much recent interest in applying deep learning to mammography; however, obtaining large amounts of annotated data poses a challenge for training deep learning models for this purpose, as does ensuring generalization beyond the populations represented in the training dataset. Here, we present an annotation-efficient deep learning approach that 1) achieves state-of-the-art performance in mammogram classification, 2) successfully extends to digital breast tomosynthesis (DBT; "3D mammography"), 3) detects cancers in clinically-negative prior mammograms of cancer patients, 4) generalizes well to a population with low screening rates, and 5) outperforms five-out-of-five full-time breast imaging specialists by improving absolute sensitivity by an average of 14%. Our results demonstrate promise towards software that can improve the accuracy of and access to screening mammography worldwide.