Unknown Time Point Research Articles

Diabetic Nephropathy in Spontaneously Type 2 Diabetic Nonhuman Primates (Rhesus Monkeys Macaca mulatta): Comparator Validation of Angiotensin Receptor Blocker Valsartan

In patients, Type 2 Diabetes Mellitus (T2DM) and Diabetic Nephropathy (DN) have unknown initiation time points, likely well before their respective clinically‐defined features of elevated fasting glucose/HbA1c and reduced eGFR/microalbuminuria respectively, and have unknown preceding and/or causal mechanisms or events (genetic or otherwise). In part, this is due to animal models that do not fully reflect the human condition, do not show the same progressive processes preceding overt onset of clinically‐defined symptoms, and do not show similar associations of contributing factors including hypertension and cardiovascular disease (CVD)/metabolic syndrome (MetSyn). Nonhuman primates (NHPs, rhesus monkeys, Macaca mulatta) frequently, naturally and spontaneously develop obesity, MetSyn, T2DM and DN, with or without CVD, and in this study have been followed metabolically for diabetes‐related and cardiovascular disease features longitudinally from normal young adults to full expression of these diseases (colony N= 1198). We have identified the specific criteria for the identification of DN (eGFR CKD‐EPI 30–59 ml/min/1.73m2 or Iohexol clearance for direct GFR) and/or urine albumin/creatinine ratio (UACR ≥ 10 mg/g) and of CVD (cardiac function by ECHO HFpEF or HFrEF with LVEF <50%, e’<8 cm/s and E/e’ >10) in these animals and have examined these features in relation to the progression of DN and T2DM (using ADA DM diagnostic criteria as applied to patients). Of those with CKD (N=52), 58% also had CVD. In addition, we report here the responses of adult monkeys, selected for the presence of T2DM and diabetic nephropathy ((increased eGFR and decreased urine albumin/creatinine ratio (UACR)) to the validation drug, an angiotensin receptor blocker, Valsartan. Monkeys (N=8 with both CKD and CVD) were studied before and at 2‐week intervals during the 8 week treatment period for the effects on blood pressure, Creatinine, Cystatin C, BUN, and eGFR. Significant improvements compared to vehicle were observed in eGFR (‐increased 23%), UACR (decreased 76%) and SBP (decreased14%) (all p’s <0.05). There were no differences in cardiac ultrasound evaluations compared to vehicle. The similarities in all features and effects between the rhesus monkey and previous reports in humans in clinical settings are extraordinary. We have previously shown the histopathology of DN in monkeys to be “classical human glomerulopathy”, and show that these important similarities permit renal biopsies to be used at any desired intervals to follow changes in DN histopathology and molecular markers, and to evaluate their reversal or modification by therapeutic agents of direct relevance to human pathophysiology.Support or Funding InformationNIH National Institute on Aging: HHSN263200800022C; SCPrimed Shines Biotech Co., Ltd, Chengdu, Sichuan, China

On Optimal Quantized Non-Bayesian Quickest Change Detection With Energy Harvesting

In this paper, we consider a problem of decentralized non-Bayesian quickest change detection using a wireless sensor network where the sensor nodes are powered by harvested energy from the environment. The underlying random process being monitored by the sensors is subject to change in its distribution at an unknown but deterministic time point, and the sensors take samples (sensing) periodically, compute the likelihood ratio based on the distributions before and after the change, quantize it and send it to a remote fusion centre (FC) over fading channels for performing a sequential test to detect the change. Due to the unpredictable and intermittent nature of harvested energy arrivals, the sensors need to decide whether they want to sense, and at what rate they want to quantize their information before sending them to the FC, since higher quantization rates result in higher accuracy and better detection performance, at the cost of higher energy consumption. We formulate an optimal sensing and quantization rate allocation problem (in order to minimize the expected detection delay subject to false alarm rate constraint) based on the availability (at the FC) of non-causal and causal information of sensors’ energy state information, and channel state information between the sensors and the FC. Motivated by the asymptotically inverse relationship between the expected detection delay (under a vanishingly small probability of false alarm) and the Kullback-Leibler (KL) divergence measure at the FC, we maximize an expected sum of the KL divergence measure over a finite horizon to obtain the optimal sensing and quantization rate allocation policy, subject to energy causality constraints at each sensor. The optimal solution is obtained using a typical dynamic programming based technique, and based on the optimal quantization rate, the optimal quantization thresholds are found by maximizing the KL information measure per slot. We also provide suboptimal threshold design policies using uniform quantization and an asymptotically optimal quantization policy for higher number of quantization bits. We provide an asymptotic approximation for the loss due to quantization of the KL measure, and also consider an alternative optimization problem with minimizing the expected sum of the inverse the KL divergence measure as the cost per time slot. Numerical results are provided comparing the various optimal and suboptimal quantization strategies for both optimization problem formulations, illustrating the comparative performance of these strategies at different regimes of quantization rates.

CAM-ICU may not be the optimal screening tool for early delirium screening in older emergency department patients: a prospective cohort study.

Delirium is a frequent problem among older patients in the emergency department (ED) and early detection is important to prevent its associated adverse outcomes. Several screening tools for delirium have been proposed for the ED, such as the 6-Item Cognitive Impairment Test (6-CIT) and the Confusion Assessment Method-ICU (CAM-ICU). Previous validation of the CAM-ICU for use in the ED showed varying results, possibly because it was administered at different or unknown time points. The aim was to study the prevalence of delirium in older ( ≥ 70 years) ED patients using the CAM-ICU and 6-CIT. A prospective cohort study was carried out in one tertiary care and one secondary care hospital in the Netherlands. Patients aged 70 years and older attending the ED were included. Delirium screening was performed within 1 h after ED registration using the CAM-ICU. The 6-CIT was determined for comparison using a cut-off point of at least 14 points indicating possible delirium. A total of 997 patients were included in the study, with a median age of 78 years (interquartile range 74-84). Delirium as assessed with CAM-ICU was positive in only 13 (1.3%, 95% confidence interval: 0.8-2.2) patients. Ninety-five (9.5% 95% confidence interval: 7.9-11.5) patients had 6-CIT more than or equal to 14. We found a delirium prevalence of 1.3% using the CAM-ICU, which was much lower than the expected prevalence of around 10% as being frequently reported in the literature and what we found when using the 6-CIT. On the basis of these results, caution is warranted to use the CAM-ICU for early screening in the ED.

Detection and Measurement of the Unknown Moment and Magnitude of the Gaussian Random Process Energy Parameter Abrupt Change

Synthesis, analysis, and simulation of the algorithms for detecting and measuring the abrupt change in the unknown mathematical expectation and dispersion of a fast fluctuating Gaussian random process at an unknown point in time are carried out in this paper. These algorithms can be technically implemented in a simpler way than the ones obtained by means of the common approaches. New asymptotic expressions are proposed for the logarithm of the functional of the likelihood ratio and its adaptive versions obtained after maximization by the unknown regular parameters under various hypotheses. By applying the joint application of the small parameter method and the local Markov approximation method, the closed asymptotically exact expressions are found for the characteristics of the performance of the synthesized detector and measurer. Both the procedure for determining the distribution law and the error moments of the estimate of the discontinuous parameter (abrupt change point) are illustrated, with an allowance of anomalous effects. By means of the statistical computer simulation, a satisfactory agreement is established between the obtained theoretical results and the corresponding experimental data.

Comparing crossing hazard rate functions by joint modelling of survival and longitudinal data

It is one of the important issues in survival analysis to compare two hazard rate functions to evaluate treatment effect. It is quite common that the two hazard rate functions cross each other at one or more unknown time points, representing temporal changes of the treatment effect. In certain applications, besides survival data, we also have related longitudinal data available regarding some time-dependent covariates. In such cases, a joint model that accommodates both types of data can allow us to infer the association between the survival and longitudinal data and to assess the treatment effect better. In this paper, we propose a modelling approach for comparing two crossing hazard rate functions by joint modelling survival and longitudinal data. Maximum likelihood estimation is used in estimating the parameters of the proposed joint model using the EM algorithm. Asymptotic properties of the maximum likelihood estimators are studied. To illustrate the virtues of the proposed method, we compare the performance of the proposed method with several existing methods in a simulation study. Our proposed method is also demonstrated using a real dataset obtained from an HIV clinical trial.

Estimation in the single change-point hazard function for interval-censored data with a cure fraction

ABSTRACTIn reliability or survival analysis, the hazard function plays a significant part for it can display the instantaneous failure rate at any time point. In practice, the abrupt change in hazard function at an unknown time point may occur after a maintenance activity or major operation. Under these circumstances, identifying the change point and estimating the size of the change are meaningful. In this paper, we assume that the hazard function is piecewise constant with a single jump at an unknown time. We propose the single change-point model for interval-censored survival data with a cure fraction. Estimation methods for the proposed model are investigated, and large-sample properties of the estimators are established. Simulation studies are carried out to evaluate the performance of the estimating method. The liver cancer data and breast cancer data are analyzed as the applications.

Increasing the share of correct clustering of characteristic signal with random losses in self-organizing maps

Analysis of methods for optimizing algorithms of functioning of the Kohonen neural networks, self-organizing maps (SOM), in terms of training speed and percentage of correct clustering was made. Effective optimization of self-organizing maps was determined by the second criterion, the enhanced self-organizing incremental neural network (ESOINN). It was established that in the case of incomplete input signal, that is the signal with losses at unknown time points, the share of correct clustering is unacceptably low with any SOM algorithms, both basic and optimized. The incomplete signal was represented as the input vector of the neural network, the values of which are represented by a single array, that is without taking into consideration conformity of the moments of losses to the current values and without the possibility of determining these moments. A method for determining conformance of the incomplete input vector to the input layer of neurons to increase percentage of correct recognition was programmed and proposed. The method is based on finding the minimum distance between the current input vector and the vector of weights of each neuron. To reduce operating time of the algorithm, it was proposed to operate not with individual values of the input signal but their indivisible parts and the corresponding groups of input neurons. The proposed method was implemented for the SOM and ESOINN. To prove effectiveness of implementation of the basic algorithm of the SOM, its comparison with existing counterparts of other developers was made. A mathematical model was developed for formation of examples of complete signals of a training sample on the basis of reference curves of the second order and a training sample was generated. In accordance with the training sample, training of all neural networks implemented with and without the proposed method was made. A diagram of simulation of losses was developed and test samples were generated for computational experiments with incomplete signals. On the basis of experiments, efficiency of the proposed method for classification in terms of incomplete input signal on the basis of self-organizing maps was proved both for implementations of the basic algorithm of SOM and ESOINN

Properties of the weighted log-rank test in the design of confirmatory studies with delayed effects.

Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. This assumption not only affects the analysis part but also the sample size calculation. The presence of delayed effects causes a change in the hazard ratio while the trial is ongoing since at the beginning we do not observe any difference between treatment arms, and after some unknown time point, the differences between treatment arms will start to appear. Hence, the proportional hazards assumption no longer holds, and both sample size calculation and analysis methods to be used should be reconsidered. The weighted log-rank test allows a weighting for early, middle, and late differences through the Fleming and Harrington class of weights and is proven to be more efficient when the proportional hazards assumption does not hold. The Fleming and Harrington class of weights, along with the estimated delay, can be incorporated into the sample size calculation in order to maintain the desired power once the treatment arm differences start to appear. In this article, we explore the impact of delayed effects in group sequential and adaptive group sequential designs and make an empirical evaluation in terms of power and type-I error rate of the of the weighted log-rank test in a simulated scenario with fixed values of the Fleming and Harrington class of weights. We also give some practical recommendations regarding which methodology should be used in the presence of delayed effects depending on certain characteristics of the trial.

Optimal Detection and Error Exponents for Hidden Semi-Markov Models

We study detection of random signals corrupted by noise that over time switch their values (states) between a finite set of possible values, where the switchings occur at unknown points in time. We model such signals as hidden semi-Markov signals, which generalize classical Markov chains by introducing explicit (possibly nongeometric) distribution for the time spent in each state. Assuming two possible signal states and Gaussian noise, we derive optimal likelihood ratio test and show that it has a computationally tractable form of a matrix product, with the number of matrices involved in the product being the number of process observations. The product matrices are independent and identically distributed, constructed by a simple measurement modulation of the sparse semi-Markov model transition matrix that we define in the paper. Using this result, we show that the Neyman–Pearson error exponent is equal to the top Lyapunov exponent for the corresponding random matrices. Using theory of large deviations, we derive a lower bound on the error exponent. Finally, we show that this bound is tight by means of numerical simulations.

Detecting changes in a Poisson process monitored at uneven time intervals where the arrival rates are unknown

We look at a Poisson process where the arrival rate changes at some unknown time point. We monitor this process only at certain time points. At each time point, we count the number of arrivals that happened in that time interval. We assume that the times at which the process is observed is fixed but uneven. In previous papers, we assumed that the arrival rates both before after the change are known. In this article, we assume that the arrival rates both before the change and after the change are unknown. We only know that when the change happens, this results in an increasing arrival rate.

Statistical analysis of multi-dimensional, temporal gene expression of stem cells to elucidate colony size-dependent neural differentiation.

High throughput gene expression analysis using qPCR is commonly used to identify molecular markers of complex cellular processes. However, statistical analysis of multi-dimensional, temporal gene expression data is complicated by limited biological replicates and large number of measurements. Moreover, many available statistical tools for analysis of time series data assume that the data sequence is static and does not evolve over time. With this assumption, the parameters used to model the time series are fixed and thus, can be estimated by pooling data together. However, in many cases, dynamic processes of biological systems involve abrupt changes at unknown time points, making the assumption of stationary time series break down. We addressed this problem using a combination of statistical methods including hierarchical clustering, change point detection, and multiple testing. We applied this multi-step method to multi-dimensional, temporal gene expression data that resulted from our study of colony size-dependent neural cell differentiation of stem cells. The gene expression data were time series as the observations were recorded sequentially over time. Hierarchical clustering segregated the genes into three distinct clusters based on their temporal expression profiles; change point detection identified specific time points at which the entire dataset was divided into several homogenous subsets to allow a separate analysis of each subset; and multiple testing procedure identified the differentially expressed genes in each cluster within each subset of data. We established that our multi-step approach pinpoints specific sets of genes that underlie colony size-mediated neural differentiation of stem cells and demonstrated its advantages over conventional parametric and non-parametric tests that do not take into account temporal dynamics of the data. Importantly, our proposed approach is broadly applicable to any multivariate data sets of limited sample size from high throughput and high content screening such as in drug and biomarker discovery studies.

Abrupt change in mean using block bootstrap and avoiding variance estimation

We deal with sequences of weakly dependent observations that are naturally ordered in time. Their constant mean is possibly subject to change at most once at some unknown time point. The aim is to test whether such an unknown change has occurred or not. The change point methods presented here rely on ratio type test statistics based on maxima of the cumulative sums. These detection procedures for the abrupt change in mean are also robustified by considering a general score function. The main advantage of the proposed approach is that the variance of the observations neither has to be known nor estimated. The asymptotic distribution of the test statistic under the no change null hypothesis is derived. Moreover, we prove the consistency of the test under the alternatives. A block bootstrap method is developed in order to obtain better approximations for the test’s critical values. The validity of the bootstrap algorithm is shown. The results are illustrated through a simulation study, which demonstrates computational efficiency of the procedures. A practical application to real data is presented as well.

Developmental Shifts and the Australian-Peruvian Exchange Rate: A VECM Analysis

In this study we examine the fundamental linkages between a single currency pair. The studied pair is the Australia Dollar and Peru Nuevo Sol from the dates 1994 to 2017. We perform a cointegration analysis and test for structural breaks at an unknown point in time. The results show that during 2002 the pair of currencies become cointegrated. We then perform a fundamental analysis to ascertain what is driving this structural change. We suggest that the growing importance of the export sectors of both economies, particularly the increasing dependence on China as an export destination, is a fundamental driver of this relationship as well as deepening international development.

Quickest Detection of Parameter Changes in Stochastic Regression: Nonparametric CUSUM

We consider the problem of detecting abrupt parameter changes in a stochastic regression with unknown noise distribution. The process changes at some unknown point of time. Under general conditions on the regression function and unknown distributions of observations before and after the disruption, the paper develops a nonparametric cumulative sum procedure (CUSUM). Unlike likelihood-based CUSUM algorithms, constructed mostly on log-likelihood ratio statistics, we use a special system of basic statistics in Page's procedure. By applying a sequential sampling scheme, which measures time in terms of accumulated Kullback-Leibler (K-L) divergence, we come to a system of statistics with the martingale properties close to those of the log-likelihood ratios. The proposed approach suggests also an alternative performance criterion in the analysis of the procedure by replacing the expected detection delay by the corresponding K-L divergence. We show that, under the false alarm probability constraint, the nonparametric CUSUM rule is optimal in the sense that it ensures the logarithmic asymptotic for the detection delay.

Enrichment of Targetable Mutations in the Relapsed Neuroblastoma Genome.

Neuroblastoma is characterized by a relative paucity of recurrent somatic mutations at diagnosis. However, recent studies have shown that the mutational burden increases at relapse, likely as a result of clonal evolution of mutation-carrying cells during primary treatment. To inform the development of personalized therapies, we sought to further define the frequency of potentially actionable mutations in neuroblastoma, both at diagnosis and after chemotherapy. We performed a retrospective study to determine mutation frequency, the only inclusion criterion being availability of cancer gene panel sequencing data from Foundation Medicine. We analyzed 151 neuroblastoma tumor samples: 44 obtained at diagnosis, 42 at second look surgery or biopsy for stable disease after chemotherapy, and 59 at relapse (6 were obtained at unknown time points). Nine patients had multiple tumor biopsies. ALK was the most commonly mutated gene in this cohort, and we observed a higher frequency of suspected oncogenic ALK mutations in relapsed disease than at diagnosis. Patients with relapsed disease had, on average, a greater number of mutations reported to be recurrent in cancer, and a greater number of mutations in genes that are potentially targetable with available therapeutics. We also observed an enrichment of reported recurrent RAS/MAPK pathway mutations in tumors obtained after chemotherapy. Our data support recent evidence suggesting that neuroblastomas undergo substantial mutational evolution during therapy, and that relapsed disease is more likely to be driven by a targetable oncogenic pathway, highlighting that it is critical to base treatment decisions on the molecular profile of the tumor at the time of treatment. However, it will be necessary to conduct prospective clinical trials that match sequencing results to targeted therapeutic intervention to determine if cancer genomic profiling improves patient outcomes.

Utility Change Point Detection in Online Social Media: A Revealed Preference Framework

This paper deals with change detection of utility maximization behaviour in online social media. Such changes occur due to the effect of marketing, advertising, or changes in ground truth. First, we use the revealed preference framework to detect the unknown time point (change point) at which the utility function changed. We derive necessary and sufficient conditions for detecting the change point. Second, in the presence of noisy measurements, we propose a method to detect the change point and construct a decision test. Also, an optimization criteria is provided to recover the linear perturbation coefficients. Finally, to reduce the computational cost, a dimensionality reduction algorithm using Johnson-Lindenstrauss transform is presented. The results developed are illustrated on two real datasets: Yahoo! Tech Buzz dataset and Youstatanalyzer dataset. By using the results developed in the paper, several useful insights can be gleaned from these data sets. First, the changes in ground truth affecting the utility of the agent can be detected by utility maximization behaviour in online search. Second, the recovered utility functions satisfy the single crossing property indicating strategic substitute behaviour in online search. Third, due to the large number of videos in YouTube, the utility maximization behaviour was verified through the dimensionality reduction algorithm. Finally, using the utility function recovered in the lower dimension, we devise an algorithm to predict total traffic in YouTube.

Dating multiple change points in the correlation matrix

A nonparametric procedure for detecting and dating multiple change points in the correlation matrix of sequences of random variables is proposed. The procedure is based on a recently proposed test for changes in correlation matrices at an unknown point in time. Although the procedure requires constant expectations and variances, only mild assumptions on the serial dependence structure are assumed. The convergence rate of the change point estimators is derived and the asymptotic validity of the procedure is proved. Moreover, the performance of the proposed algorithm in finite samples is illustrated by means of a simulation study and the analysis of a real data example with financial returns. These examples show that the algorithm has large power in finite samples.

Dating Multiple Change Points in the Correlation Matrix

We propose a nonparametric procedure for detecting and dating multiple change points in the correlation matrix of a sequence of random variables. The procedure is based on a test for changes in correlation matrices at an unknown point in time recently proposed by Wied (2014). Although the procedure requires constant expectations and variances, only mild assumptions on the serial dependence structure are assumed. We show the validity of the procedure including the convergence rate of the change point estimators. Moreover, we illustrate its performance in finite samples by means of a simulation study and the analysis of a real data example with financial returns. These examples show that the proposed algorithm has large power in finite samples.

Detecting changes in a Poisson process monitored at random time intervals

ABSTRACTWe look at a Poisson process where the arrival rate changes at some unknown time point. We monitor this process only at certain time points. At each time point, we count the number of arrivals that happened in that time interval. In previous work, it was assumed that the time intervals were fixed in advance. We relax this assumption to assume that the time intervals in which the process are monitored is also random. For a loss function consisting of the cost of late detection and a penalty for early stopping, we develop, using dynamic programming, the one- and two-step look-ahead Bayesian stopping rules. We then compare various observation schemes to determine the best model. We provide some numerical results to illustrate the effectiveness of the detection procedures.

A simulation study to examine the sensitivity of the Pettitt test to detect abrupt changes in mean

The Pettitt test is a non-parametric test that has been used in a number of hydroclimatological studies to detect abrupt changes in the mean of the distribution of the variable of interest. This test is based on the Mann-Whitney two-sample test (rank-based test), and allows the detection of a single shift at an unknown point in time. This test is often used to detect shifts in extremes because of the lack of distributional assumptions. However, the downside of not specifying a distribution is that the Pettitt test may be inefficient in detecting breaks when dealing with extremes. Here we adopt a Monte Carlo approach to examine the sensitivity of the Pettitt test in detecting shifts in the mean under different conditions (location of the break within the series, magnitude of the shift, record length, level of variability in the data, extreme vs non-extreme records, and pre-assigned significance level). These simulation results show that the sensitivity of this test in detecting abrupt changes increases with the increase in the magnitude of the shift and record length. The number of detections is higher when the time series represents the central part of the distribution (e.g. changes in the time series of medians), while the skill decreases as we move toward either low or high extremes (e.g. changes in the time series of maxima). Furthermore, the number of detections decreases as the variability in the data increases. Finally, abrupt changes are more easily detected when they occur toward the center of the time series.Editor D. Koutsoyiannis Associate editor K. Hamed