Rates Of Rare Events Research Articles

Longitudinal Multinomial Relative Entropy-Based Discrete Relative Risk Models for Integrated Prediction of Competing Risk

Prognosis prediction is a pivotal aspect of survival analysis, particularly when considering competing risks. The contemporary landscape is enriched with an abundance of biobank data encompassing diverse risk factors like genetics, transcriptomics, and electronic health records, fueling efforts to enhance prognostic predictions. However, the resulting predictive models suffer from rare event rates, limited sample sizes, high dimensionality, and low signal-to-noise ratios. To address these challenges and amplify predictive capabilities, the integration of historical prediction models has emerged as a promising approach. Yet, prevailing integration methods often rest upon the premise of comparable underlying distributions across disparate data sources—a presumption that frequently diverges from reality. Disregarding the inherent heterogeneity among these information sources can inadvertently introduce substantial bias, underscoring the urgency of integrated competing risk analyses that systematically accommodate cohort heterogeneity. In response, we propose an original solution: a longitudinal multinomial relative entropy-based integration framework. This methodology incorporates the established prediction models from the literature, yielding refined prognostic predictions for newly acquired datasets.

Derivation of Sample Size Formula for Cluster Randomized Trials with Binary Responses Using a General Continuity Correction Factor and Identification of Optimal Settings for Small Event Rates

Trials for comparing interventions where cluster of subjects, rather than individuals, are randomized, are commonly called cluster randomized trials (CRTs). For comparison of binary outcomes in a CRT, although there are a few published formulations for sample size computation, the most commonly used is the one developed by Donner, Birkett, and Buck (Am J Epidemiol, 1981) probably due to its incorporation in the text book by Fleiss, Levin, and Paik (Wiley, 2003). In this paper, we derive a new χ 2 approximation formula with a general continuity correction factor (c) and show that specially for the scenarios of small event rates (< 0.01), the new formulation recommends lower number of clusters than the Donner et al. formulation thereby providing better efficiency. All known formulations can be shown to be special cases at specific value of the general correction factor (e.g., Donner formulation is equivalent to the new formulation for c = 1). Statistical simulation is presented with data on comparative efficacy of the available methods identifying correction factors that are optimal for rare event rates. Table of sample size recommendation for variety of rare event rates along with code in“R” language for easy computation of sample size in other settings is also provided. Sample size calculations for a published CRT (“Pathways to Health study” that evaluates the value of intervention for smoking cessation) are computed for various correction factors to illustrate that with an optimal choice of the correction factor, the study could have maintained the same power with a 20% less sample size.

ISOKANN: Invariant subspaces of Koopman operators learned by a neural network

The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural network.

Noise-induced switching from a symmetry-protected shallow metastable state

We consider escape from a metastable state of a nonlinear oscillator driven close to triple its eigenfrequency. The oscillator can have three stable states of period-3 vibrations and a zero-amplitude state. Because of the symmetry of period-tripling, the zero-amplitude state remains stable as the driving increases. However, it becomes shallow in the sense that the rate of escape from this state exponentially increases, while the system still lacks detailed balance. We find the escape rate and show how it scales with the parameters of the oscillator and the driving. The results facilitate using nanomechanical, Josephson-junction based, and other mesoscopic vibrational systems for studying, in a well-controlled setting, the rates of rare events in systems lacking detailed balance. They also describe how fluctuations spontaneously break the time-translation symmetry of a driven oscillator.

Degree Dispersion Increases the Rate of Rare Events in Population Networks.

There is great interest in predicting rare and extreme events in complex systems, and in particular, understanding the role of network topology in facilitating such events. In this Letter, we show that degree dispersion—the fact that the number of local connections in networks varies broadly—increases the probability of large, rare fluctuations in population networks generically. We perform explicit calculations for two canonical and distinct classes of rare events: network extinction and switching. When the distance to threshold is held constant, and hence stochastic effects are fairly compared among networks, we show that there is a universal, exponential increase in the rate of rare events proportional to the variance of a network’s degree distribution over its mean squared.

Simulation of diblock copolymer surfactants. II. Micelle kinetics.

Molecular dynamics (MD) simulations are used to measure dynamical properties of a simple bead-spring model of A-B diblock copolymer molecules, and to characterize rates and mechanisms of several dynamical processes. Dynamical properties are analyzed within the context of a kinetic population model that allows for both stepwise insertion and expulsion of individual free molecules and occasional fission and fusion of micelles. Kinetic coefficients for stepwise processes and micelle fission have been extracted from MD simulations of individual micelles. Insertion of a free surfactant molecule into a preexisting micelle is shown to be a completely diffusion-controlled process for the model studied here. Estimates are given for rates of rare events that create and destroy entire micelles by competing mechanisms involving stepwise association and dissociation or fission and fusion. Both mechanisms are shown to be relevant over the range of parameters studied here, with association and dissociation dominating in systems with more soluble surfactants and fission and fusion dominating in systems with less soluble surfactants.

Use of propensity score and disease risk score for multiple treatments with time-to-event outcome: a simulation study

ABSTRACTPropensity score (PS) and disease risk score (DRS) are often used in pharmacoepidemiologic safety studies. Methods of applying these two balancing scores are extensively studied in binary treatment settings. However, the use of PS and DRS is not well understood in the case of non-ordinal multiple treatments. Some PS methods of multiple treatments have been implemented since the theoretical establishment. Nevertheless, most of the work applies to continuous or binary outcomes. Little work has been done for time-to-event outcomes. In this study, we extend the application of the PS and DRS methods to time-to-event outcomes in multiple treatment settings. The analytical approaches include weighing, matching, stratification, and regression. Simulation studies with rare event rates are conducted to evaluate the performances of different methods. Different treatment-covariates and outcome-covariates strength of associations are considered. Additionally, the impacts of imbalanced designs and large or limited PS overlaps are investigated on various analytical approaches. We found that the inverse probability treatment weighting with bootstrap variance estimator, the generalized PS matching, and the Cox regression estimated DRS in full cohort generally performed well in multiple treatment settings. This study aims to provide additional guidance for researchers on PS and DRS analyses in pharmacoepidemiologic observational studies.

An Analysis of Scalp Thickness and Other Novel Risk Factors for Deep Brain Stimulator Infections

Introduction: Deep brain stimulator (DBS) infections are a persistent problem for patients undergoing this procedure. They may require further surgery, treatment with antibiotics, or even removal of the device. To date, no consensus exists on the best practices to avoid DBS infections or what factors predispose patients to an eventual infection. The goal of this study was to examine several patient factors for association with DBS infection.Methods: A single-center, single-surgeon quality improvement database was queried. All patients who experienced an infection were identified. The primary variable analyzed was scalp thickness. Other pre-specified, secondary variables included routine intraoperative cultures, operative time, diagnosis, and age.Results: None of the independent variables examined were significantly associated with DBS infections. Only two of the 46 infections qualified as surgical site infections as defined by the Centers for Disease Control.Conclusion: DBS infections are independent of all of the predictor variables analyzed. Surgical site infections, according to traditional definitions, are not the optimal definition for evaluating DBS infections/erosions. New studies must examine new variables that are not routinely gathered in this population. Also, because of the rare event rates and difficulty in randomizing patients to exposures, a large, multicenter registry may be the optimal study design to solve this clinical problem.

An Evaluation of Wheeler's Method for Monitoring the Rate of Rare Events

Its wide application in practice makes the monitoring of the rate of rare events a popular research topic. Recently a researcher proposed plotting the counts between events on an individuals X‐chart with an upper control limit to detect process improvement and plotting the reciprocals of the counts on an X‐chart to detect process deterioration. He also used the median as the center line and the median moving range to obtain control limits in both control charts to address the problem of the standard deviation estimate inflation caused by extreme values. In our paper, we investigated the statistical performance of the four proposed approaches using simulation. We find using the mean results in a high proportion of ineffective control limits, while using the median avoids the issue of ineffective control limits but produces an unacceptably high proportion of false alarms. Copyright © 2016 John Wiley & Sons, Ltd.

Rejoinder to ‘Estimating rates of rare events through a multidimensional dynamic hierarchical Bayesian framework’

Rejoinder to ‘Estimating rates of rare events through a multidimensional dynamic hierarchical Bayesian framework’

Discussion of ‘Estimating rates of rare events through a multidimensional dynamic hierarchical Bayesian framework’

Discussion of ‘Estimating rates of rare events through a multidimensional dynamic hierarchical Bayesian framework’

Discussion of ‘Estimating rates of rare events through a multidimensional dynamic hierarchical Bayesian framework’

Discussion of ‘Estimating rates of rare events through a multidimensional dynamic hierarchical Bayesian framework’

Estimating rates of rare events through a multidimensional dynamic hierarchical Bayesian framework

We consider the problem of estimating occurrence rates of rare events for extremely sparse data using pre‐existing hierarchies and selected features to perform inference along multiple dimensions. In particular, we focus on the problem of estimating click rates for {Advertiser, Publisher, and User} tuples where both the Advertisers and the Publishers are organized as hierarchies that capture broad contextual information at different levels of granularities. Typically, the click rates are low, and the coverage of the hierarchies and dimensions is sparse. To overcome these difficulties, we decompose the joint prior of the three‐dimensional click‐through rate using tensor decomposition and propose a multidimensional hierarchical Bayesian framework (abbreviated as MadHab). We set up a specific framework of each dimension to model dimension‐specific characteristics. More specifically, we consider the hierarchical beta process prior for the Advertiser dimension and for the Publisher dimension respectively and a feature‐dependent mixture model for the User dimension. Besides the centralized implementation, we propose two distributed algorithms through MapReduce and Spark for inferences, which make the model highly scalable and suited for large scale data mining applications. We demonstrate that on a real world ads campaign platform, our framework can effectively discriminate extremely rare events in terms of their click propensity. Copyright © 2016 John Wiley & Sons, Ltd.

Using Bayes formula to estimate rates of rare events in transition path sampling simulations.

Transition path sampling is a method for estimating the rates of rare events in molecular systems based on the gradual transformation of a path distribution containing a small fraction of reactive trajectories into a biased distribution in which these rare trajectories have become frequent. Then, a multistate reweighting scheme is implemented to postprocess data collected from the staged simulations. Herein, we show how Bayes formula allows to directly construct a biased sample containing an enhanced fraction of reactive trajectories and to concomitantly estimate the transition rate from this sample. The approach can remediate the convergence issues encountered in free energy perturbation or umbrella sampling simulations when the transformed distribution insufficiently overlaps with the reference distribution.

Exponential CUSUM Charts with Estimated Control Limits

Exponential CUSUM charts are used in monitoring the occurrence rate of rare events because the interarrival times of events for homogeneous Poisson processes are independent and identically distributed exponential random variables. In these applications, it is assumed that the exponential parameter, i.e. the mean, is known or has been accurately estimated. However, in practice, the in‐control mean is typically unknown and must be estimated to construct the limits for the exponential CUSUM chart. In this article, we investigate the effect of parameter estimation on the run length properties of one‐sided lower exponential CUSUM charts. In addition, analyzing conditional performance measures shows that the effect of estimation error can be significant, affecting both the in‐control average run length and the quick detection of process deterioration. We also provide recommendations regarding phase I sample sizes. This sample size must be quite large for the in‐control chart performance to be close to that for the known parameter case. Finally, we provide an industrial example to highlight the practical implications of estimation error, and to offer advice to practitioners when constructing/analyzing a phase I sample. Copyright © 2013 John Wiley & Sons, Ltd.

Pricing Options with Credit Risk in Markovian Regime-Switching Markets

This paper investigates the valuation of European option with credit risk in a reduced form model when the stock price is driven by the so-called Markov-modulated jump-diffusion process, in which the arrival rate of rare events and the volatility rate of stock are controlled by a continuous-time Markov chain. We also assume that the interest rate and the default intensity follow the Vasicek models whose parameters are governed by the same Markov chain. We study the pricing of European option and present numerical illustrations.

Control of rare events in reaction and population systems by deterministically imposed transitions

We consider control of reaction and population systems by imposing transitions between states with different numbers of particles or individuals. The transitions take place at predetermined instants of time. Even where they are significantly less frequent than spontaneous transitions, they can exponentially strongly modify the rates of rare events, including switching between metastable states or population extinction. We also study optimal control of rare events. Specifically, we are interested in the optimal control of disease extinction for a limited vaccine supply. A comparison is made with control of rare events by modulating the rates of elementary transitions rather than imposing transitions deterministically. It is found that, unexpectedly, for the same mean control parameters, controlling the transitions rates can be more efficient.

The barrier method: A technique for calculating very long transition times

In many dynamical systems, there is a large separation of time scales between typical events and "rare" events which can be the cases of interest. Rare-event rates are quite difficult to compute numerically, but they are of considerable practical importance in many fields, for example, transition times in chemical physics and extinction times in epidemiology can be very long, but are quite important. We present a very fast numerical technique that can be used to find long transition times (very small rates) in low-dimensional systems, even if they lack detailed balance. We illustrate the method for a bistable nonequilibrium system introduced by Maier and Stein and a two-dimensional (in parameter space) epidemiology model.

A spline for your saddle

Pinpointing extrema on a multidimensional hypersurface is an important generic problem with a broad scope of application in statistical mechanics, biophysics, chemical reaction dynamics, and quantum chemistry. Local minima of the hypersurface correspond to metastable structures and are usually the most important points to look for. They are relatively easy to find using standard minimizing algorithms. A considerably more difficult task is the location of saddle points. The saddle points most sought for are those which form the lowest barriers between given minima and are usually required for determining rates of rare events. We formulate a path functional minimum principle for the saddle point. We then develop a cubic spline method for applying this principle and locating the saddle point(s) separating two local minima on a potential hypersurface. A quasi-Newton algorithm is used for minimization. The algorithm does not involve second derivatives of the hypersurface and the number of potential gradients evaluated is usually less than 10% of the number of potential evaluations. We demonstrate the performance of the method on several standard examples and on a concerted exchange mechanism for self-diffusion in diamond. Finally, we show that the method may be used for solving large constrained minimization problems which are relevant for self-consistent field iterations in large systems.

Response to commentary by Dixon and Silman on the systematic review and meta-analysis by Bongartz et al.

Dixon and Silman [1] provide an insightful review of the methodology and results of our meta-analysis of harmful events among patients with rheumatoid arthritis treated with anti-tumour necrosis factor (TNF) antibody agents [2]. Meta-analyses of valid randomized trials of like agents ensure that, in the absence of a treatment effect, patients with rheumatoid arthritis in the intervention and placebo groups should share the same risk for developing serious infections or malignancy. Etanercept, although it needs study, was not included in our analysis because it is dissimilar from the anti-TNF agents. A particular advantage of such trials is that there is almost complete follow up of each treatment arm, with patients maintained in the assigned groups for intent-to-treat analysis at least for the randomized portion of the trial, even if drug exposure is discontinued for whatever reason. The appropriate statistical analysis of such comparator groups in the trial context of equivalent follow up in each arm is an odds ratio rather than incidence rate ratio. Dixon and Silman raise the possibility of bias in our analysis because of the greater dropout rate in the placebo arm, potentially leading to a lower detection threshold for malignancies in the placebo compared with the treatment arm. We found no evidence for a difference in detection thresholds in the placebo follow-up period, which was equivalent to the treatment arm in duration for the controlled phase of the studies on which we performed the analysis. Dixon and Silman also note a classification or detection bias for serious infections because of the greater likelihood of placebo patients being hospitalized. In this case our analysis would underestimate the true risk for serious infection in treated compared with control patients. In practice, lack of efficacy with the standard dose of 3 mg/kg of infliximab results in many patients using higher doses; as many as 61% of patients with rheumatoid arthritis after 1 year of use receive, on average, 4.9 mg/kg of infliximab [3]. The manufacturer's product label for infliximab allows doses up to 10 mg/kg of infliximab for partial responders [4]. Thus, not only are our findings applicable to clinical practice and biologically plausible, but they also fulfill the dose-effect criterion for causality. The low risk in the comparison group may be real, the result of chance, or due to an as yet unclear systematic design or analysis flaw of all included randomized controlled trials. We are wary of the interpretation of lower risk being due to chance or some other drug effect, which may give a false sense of security about the drug in question [5]. Long-term observation of large, unselected case cohorts, using methods such as treatment registries will provide widely generalizable information about the treatment response. However, it is even more difficult to compose the appropriate comparator group and control for all potential confounding factors in a registry than in a well conducted randomized clinical trial. Early conduct of meta-analyses with methods, such as those we put forward, to estimate the rate of rare events [2] can yield data that manufacturers and regulatory bodies, and patients and clinicians should consider when making policy and clinical decisions, respectively.