Bayesian analyses of multiple random change points in survival models with applications to clinical trials.

Single and multiple random change points (RCPs) in survival analysis have arisen naturally in oncology trials, where the time to hazard rate change differs from one subject to another. Recently, Xu formulated and discovered important properties of these survival models using a frequentist approach, allowing us to estimate the hazard rates, rate parameters of the exponential distributions for the RCPs, expected survival and hazard functions. However, these methods did not provide an estimation of the uncertainty or the confidence intervals for the parameters and their differences or ratios. Therefore, statistical inferences were not able to be drawn on the parameters and their comparisons. To solve this issue, this article implements a Gibbs sampler method to estimate the above parameters and the differences or ratios alongside the 100(1 - α)% highest posterior density (HPD) intervals calculated from Chen-Shao's algorithm. The estimated rate parameters from the methods in Xu serve as empirical values in the Gibbs sampler method. Thus, formal statistical inferences can now be readily drawn. Simulation studies demonstrate that the proposed methods yield robust estimates, with the samples from the marginal posterior distributions converging rapidly and exhibiting favorable behavior. The 95% HPD intervals also demonstrate excellent coverage probabilities. This proposed method has a multitude of applications in clinical trials such as efficient clinical trial design and sample size adjustment based on the estimated parameter values at interim analyses.

The Spatiotemporal Link of Temporal Expectations: Contextual Temporal Expectation Is Independent of Spatial Attention.

Temporal expectation is the ability to construct predictions regarding the timing of events, based on previously experienced temporal regularities of different types. For example, cue-based expectations are constructed when a cue validly indicates when a target is expected to occur. However, in the absence of such cues, expectations can be constructed based on contextual temporal information, including the onset distribution of the event and recent prior experiences, both providing implicit probabilistic information regarding the timing of the event. It was previously suggested that cue-based temporal expectation is exerted via synchronization of spatially specific neural activity at a predictable time of a target, within receptive fields corresponding to the expected location of the target. Here, we tested whether the same theoretical model holds for contextual temporal effects. Participants (n = 40, 25 females) performed a speeded spatial-cuing detection task with two-thirds valid spatial cues. The hazard-rate function of the target was modulated by varying the foreperiod-the interval between the spatial cue and the target-among trials and was manipulated between groups by changing the interval distribution. Reaction times were analyzed using both frequentist and Bayesian generalized linear mixed models, accounting for hazard and sequential effects. Results showed that the effects of contextual temporal structures on reaction times were independent of spatial attention. This suggests that the spatiotemporal mechanisms, thought to account for cue-based expectation, cannot explain other sources of temporal expectations. We conclude that expectations based on contextual structures have different characteristics than cue-based temporal expectation, suggesting reliance on distinct neural mechanisms.SIGNIFICANCE STATEMENT Temporal expectation is the ability to predict an event onset based on temporal regularities. A neurophysiological model suggested that temporal expectation relies on the synchronization of spatially specific neurons whose receptive fields represent the attended location. This model predicts that temporal expectation would be evident solely within the locus of spatial attention. Existing evidence supported this model for expectation based on associations between a temporal cue and a target, but here we show that it cannot account for temporal expectation that is based on contextual information, that is, the distribution of intervals and recent priors. These findings reveal the existence of different predictive mechanisms for cued and contextual temporal predictions, with the former depending on spatial attention and the latter nonspatially specific.

P3-like signatures of temporal predictions: a computational EEG study.

Many cognitive processes, ranging from perception to action, depend on the ability to predict the timing of forthcoming events. Yet, how the brain uses predictive models in the temporal domain is still an unsolved question. In previous work, we began to explore the neural correlates of temporal predictions by using a computational approach in which an ideal Bayesian observer learned the temporal probabilities of target onsets in a simple reaction time task. Because the task was specifically designed to disambiguate updating of predictive models and surprise, changes in temporal probabilities were explicitly cued. However, in the real world, we are usually incidentally exposed to changes in the statistics of the environment. Here, we thus aimed to further investigate the electroencephalographic (EEG) correlates of Bayesian belief updating and surprise associated with incidental learning of temporal probabilities. In line with our previous EEG study, results showed distinct P3-like modulations for updating and surprise. While surprise was indexed by an early fronto-central P3-like modulation, updating was associated with a later and more posterior P3 modulation. Moreover, updating was associated with a P2-like potential at centro-parietal electrodes, likely capturing integration processes between prior beliefs and likelihood of the observed event. These findings support previous evidence of trial-by-trial variability of P3 amplitudes as an index of dissociable inferential processes. Coupled with our previous findings, the present study strongly bolsters the view of the P3 as a key brain signature of temporal Bayesian inference. Data and scripts are shared on OSF: osf.io/sdy8j/.

Nonparametric regression with right-censored covariate via conditional density function.

Censoring often occurs in data collection. This article, considers nonparametric regression when the covariate is censored under general settings. In contrast to censoring in the response variable in survival analysis, regression with censored covariates is more challenging but less studied in the literature, especially for dependent censoring. We propose to estimate the regression function using conditional hazard rates. The asymptotic normality of our proposed estimator is established. Both theoretical results and simulation studies demonstrate that the proposed method is more efficient than the estimation based on complete observations and other methods, especially when the censoring rate is high. We illustrate the usefulness of the proposed method using a data set from the Framingham heart study and a data set from a randomized placebo-controlled clinical trial of the drug D-penicillamine.

Estrogen receptor-negative/progesterone receptor-positive and her-2-negative breast cancer might no longer be classified as hormone receptor-positive breast cancer.

BACKGROUND: The single progesterone receptor (PR)-positive phenotype (estrogen receptor (ER)-/PR + , sPR positive) is an infrequent and independent biological entity. However, the prognosis of patients with sPR-positive and her-2-negative phenotype is still controversial, and it is not always easy to decide treatment strategies for them. METHODS: Patients during 2010-2014 were identified from Surveillance, Epidemiology, and End Results (SEER) database. The Kaplan-Meier method was used to evaluate cancer-specific survival (CSS). The propensity score matching (PSM) method was used to balance differences of characteristics in groups. The Life-Table method was used to calculate 5-year CSS rates and the annual hazard rate of death (HRD). RESULTS: A total of 97,527 patients were included, and only 745 (0.76%) patients were sPR-positive phenotype. The majority of sPR-positive breast cancer were basal-like subtype. Survival analysis showed that the sPR-positive breast cancer had similar prognosis comparing to double hormonal receptor-negative (ER-/PR-, dHoR-negative) breast cancer, and had the highest HRD during the initial 1-2 years of follow-up, then maintained the HRD of almost zero during the late years of follow-up. CONCLUSIONS: The patients with sPR-positive and her-2-negative breast cancer, similar to dHoR-negative breast cancer, had a worse survival, and could benefit from chemotherapy significantly. However, the escalating endocrine therapy was not recommended for sPR-positive patients. The patients with sPR positive should be excluded from future clinical trials concerning endocrine therapy.

How long should urologists observe patients with prostate cancer after radical prostatectomy? Weibull analysis.

OBJECTIVES: There is no recommended observation time for patients who have undergone radical prostatectomy for prostate cancer. This study was undertaken to determine the postoperative observation time by investigating the hazard rate for prostate-specific antigen failure and other-cause death using Weibull analysis. METHODS: We included 612 patients who underwent laparoscopic radical prostatectomy for localized prostate cancer between June 2002 and December 2017. Risk classification was categorized by the D'Amico risk classification, and the patients were divided into three age groups: <60, 60-69 and ≥70 years. The hazard rates at each point were derived using Weibull analysis. The optimal observation time after laparoscopic radical prostatectomy was determined as the intersection point at which the hazard rate of other-cause death overtakes the hazard rate of prostate-specific antigen failure. RESULTS: In all groups classified by age, the hazard rate of other-cause deaths increased over time. In contrast, the hazard rate of prostate-specific antigen failure decreased gradually. The ≥70 years age group showed the highest hazard rate. The hazard rate of prostate-specific antigen failure was highest in the high-risk group. The patients aged ≥70 and 60-69 years in the low-risk group were recommended 6 years 6 months and 14 years 8 months, respectively, for observation. The remaining patients were recommended >25 years of postsurgical observation. CONCLUSIONS: The observation time after laparoscopic radical prostatectomy could be estimated by comparing the estimated hazard rates of prostate-specific antigen failure and other-cause death based on Weibull analysis. Urologists should pay attention to age and risk classifications for optimal postoperative observation.

On the targets of inference with multivariate failure time data.

There are several different topics that can be addressed with multivariate failure time regression data. Data analysis methods are needed that are suited to each such topic. Specifically, marginal hazard rate models are well suited to the analysis of exposures or treatments in relation to individual failure time outcomes, when failure time dependencies are themselves of little or no interest. On the other hand semiparametric copula models are well suited to analyses where interest focuses primarily on the magnitude of dependencies between failure times. These models overlap with frailty models, that seem best suited to exploring the details of failure time clustering. Recently proposed multivariate marginal hazard methods, on the other hand, are well suited to the exploration of exposures or treatments in relation to single, pairwise, and higher dimensional hazard rates. Here these methods will be briefly described, and the final method will be illustrated using the Women's Health Initiative hormone therapy trial data.

Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual χ2 Divergence Measures.

In this work, we define cumulative residual q-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose q-hazard rate (QHR) function via q-logarithmic function as a new extension of hazard rate function. We show that CRQF information measure can be expressed in terms of the QHR function. We define further generalized cumulative residual χ2 divergence measures between two SFs. We then examine the cumulative residual q-Fisher information for two well-known mixture models, and the corresponding results reveal some interesting connections between the cumulative residual q-Fisher information and the generalized cumulative residual χ2 divergence measures. Further, we define Jensen-cumulative residual χ2 (JCR-χ2) measure and a parametric version of the Jensen-cumulative residual Fisher information measure and then discuss their properties and inter-connections. Finally, for illustrative purposes, we examine a real example of image processing and provide some numerical results in terms of the CRQF information measure.

Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach.

Noise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate ("escape noise"). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener-Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein-Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

Left-censored dementia incidences in estimating cohort effects.

We estimate the dementia incidence hazard in Germany for the birth cohorts 1900 until 1954 from a simple sample of Germany's largest health insurance company. Followed from 2004 to 2012, 36,000 uncensored dementia incidences are observed and further 200,000 right-censored insurants included. From a multiplicative hazard model we find a positive and linear trend in the dementia hazard over the cohorts. The main focus of the study is on 11,000 left-censored persons who have already suffered from the disease in 2004. After including the left-censored observations, the slope of the trend declines markedly due to Simpson's paradox, left-censored persons are imbalanced between the cohorts. When including left-censoring, the dementia hazard increases differently for different ages, we consider omitted covariates to be the reason. For the standard errors from large sample theory, left-censoring requires an adjustment to the conditional information matrix equality.

Further Results on the Proportional Vitalities Model.

In contrast to many survival models such as proportional hazard rates and proportional mean residual lives, the proportional vitalities model has also been introduced in the literature. In this paper, further stochastic ordering properties of a dynamic version of the model with a random vitality growth parameter are investigated. Examples are presented to illustrate different established properties of the model. Potentials for inference about the parameters in proportional vitalities model with possibly time-varying effects are also argued and discussed.

Maximum Entropy Approach to Reliability of Multi-Component Systems with Non-Repairable or Repairable Components.

The degradation and recovery processes are multi-scale phenomena in many physical, engineering, biological, and social systems, and determine the aging of the entire system. Therefore, understanding the interplay between the two processes at the component level is the key to evaluate the reliability of the system. Based on the principle of maximum entropy, an approach is proposed to model and infer the processes at the component level, and is applied to repairable and non-repairable systems. By incorporating the reliability block diagram, this approach allows for integrating the information of network connectivity and statistical moments to infer the hazard or recovery rates of the degradation or recovery processes. The overall approach is demonstrated with numerical examples.

Bayesian and Frequentist Inferences on a Type I Half-Logistic Odd Weibull Generator with Applications in Engineering.

In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability weighted moments, moments of (reversed) residual lifetime, entropy and order statistics. After producing the general class, two of the corresponding parametric statistical models are outlined. The hazard rate function of the sub-models can take a variety of shapes such as increasing, decreasing, unimodal, and Bathtub shaped, for different values of the parameters. Furthermore, the sub-models of the introduced family are also capable of modelling symmetric and skewed data. The parameter estimation of the special models are discussed by numerous methods, namely, the maximum likelihood, simple least squares, weighted least squares, Cramér-von Mises, and Bayesian estimation. Under the Bayesian framework, we have used informative and non-informative priors to obtain Bayes estimates of unknown parameters with the squared error and generalized entropy loss functions. An extensive Monte Carlo simulation is conducted to assess the effectiveness of these estimation techniques. The applicability of two sub-models of the proposed family is illustrated by means of two real data sets.

Size- and stage-dependence in cause-specific mortality of migratory brown trout.

Evidence-based management of natural populations under strong human influence frequently requires not only estimates of survival but also knowledge about how much mortality is due to anthropogenic vs. natural causes. This is the case particularly when individuals vary in their vulnerability to different causes of mortality due to traits, life history stages, or locations. Here, we estimated harvest and background (other cause) mortality of landlocked migratory salmonids over half a century. In doing so, we quantified among-individual variation in vulnerability to cause-specific mortality resulting from differences in body size and spawning location relative to a hydropower dam. We constructed a multistate mark-recapture model to estimate harvest and background mortality hazard rates as functions of a discrete state (spawning location) and an individual time-varying covariate (body size). We further accounted for among-year variation in mortality and migratory behaviour and fit the model to a unique 50-year time series of mark-recapture-recovery data on brown trout (Salmo trutta) in Norway. Harvest mortality was highest for intermediate-sized trout, and outweighed background mortality for most of the observed size range. Background mortality decreased with body size for trout spawning above the dam and increased for those spawning below. All vital rates varied substantially over time, but a trend was evident only in estimates of fishers' reporting rate, which decreased from over 50% to less than 10% throughout the study period. We highlight the importance of body size for cause-specific mortality and demonstrate how this can be estimated using a novel hazard rate parameterization for mark-recapture models. Our approach allows estimating effects of individual traits and environment on cause-specific mortality without confounding, and provides an intuitive way to estimate temporal patterns within and correlation among different mortality sources.

Lifetime risk of stroke in the general male population.

OBJECTIVES: Most previous studies of incidence rates of stroke are from register studies, while data from prospective cohort studies are limited. The aim of the present study was to describe hazard rates, prevalence and cumulative proportion free from stroke during a lifelong follow-up of a representative sample of middle-aged men sampled from the general population. METHODS: A population-based sample of 855 men, all born in 1913, was investigated at 50 years of age and followed up with repeated medical examinations at age 54, 60, 67, 75 and 80. Data from hospital records and the Cause of Death Register were collected, and all stroke events during 48 years of follow-up were registered. Medical records were scrutinized in order to confirm and validate the stroke diagnoses. RESULTS: One man was excluded because of stroke prior to baseline, while 176 of the remaining 854 men (20.7%) suffered a first-ever stroke during follow-up. The total 5-year stroke risk (hazard rate) increased with age, from 3.54 (95% CI: 0-7.55) per 1000 persons at risk at age 50 years, to 119.05 (95% CI: 45.39-192.70) at age 90 years. The stroke prevalence peaked at age 80 and older, with about 120 cases per 1000 years of observation. The survival rate (cumulative proportion free from stroke) at age 98 was 50.0%. CONCLUSION: One out of five men in this population sample suffered a stroke of any type during follow-up from 50 to 98 years of age and the cumulative incidence was close to 50%.

More powerful goodness-of-fit tests for uniform stochastic ordering.

The ordinal dominance curve (ODC) is a useful graphical tool to compare two population distributions. These distributions are said to satisfy uniform stochastic ordering (USO) if the ODC for them is star-shaped. A goodness-of-fit test for USO was recently proposed when both distributions are unknown. This test involves calculating the L p distance between an empirical estimator of the ODC and its least star-shaped majorant. The least favorable configuration of the two distributions was established so that proper critical values could be determined; i.e., to control the probability of type I error for all star-shaped ODCs. However, the use of these critical values can lead to a conservative test and minimal power to detect certain non-star-shaped alternatives. Two new methods for determining data-dependent critical values are proposed. Simulation is used to show both methods can provide substantial increases in power while still controlling the size of the distance-based test. The methods are also applied to a data set involving premature infants. An R package that implements all tests is provided.

Stochastic Comparisons of Weighted Distributions and Their Mixtures.

In this paper, various stochastic ordering properties of a parametric family of weighted distributions and the associated mixture model are developed. The effect of stochastic variation of the output random variable with respect to the parameter and/or the underlying random variable is specifically investigated. Special weighted distributions are considered to scrutinize the consistency as well as the usefulness of the results. Stochastic comparisons of coherent systems made of identical but dependent components are made and also a result for comparison of Shannon entropies of weighted distributions is developed.

Identification of modifiable factors associated with owner-reported equine laminitis in Britain using a web-based cohort study approach.

BACKGROUND: Equine laminitis is a complex disease that manifests as pain and lameness in the feet, often with debilitating consequences. There is a paucity of data that accounts for the multifactorial nature of laminitis and considers time-varying covariates that may be associated with disease development; particularly those that are modifiable and present potential interventions. A previous case-control study identified a number of novel, modifiable factors associated with laminitis which warranted further investigation and corroboration. The aim of this study was to identify factors associated with equine laminitis in horses/ponies in Great Britain (GB) using a prospective, web-based cohort study design, with particular interest in evaluating modifiable factors previously identified in the case-control study. RESULTS: Self-selected horse/pony owners in GB submitted initial baseline and follow-up health and management questionnaires for 1070 horses/ponies between August 2014 and December 2016. The enrolled horses/ponies contributed 1068 horse-years at risk with a median of 38 days between questionnaire submissions. Owners reported 123 owner-recognised and/or veterinary-diagnosed episodes of active laminitis using a previously-validated laminitis reporting form. Multivariable Cox regression modelling identified 16 risk/protective factors associated with laminitis development. In keeping with the previous case-control study, a prior history of laminitis (particularly non-veterinary-diagnosed episodes), soreness after shoeing/trimming and weight gain were associated with higher rates of laminitis. There is now strong evidence that these risk factors should be used to guide future recommendations in disease prevention. Factors with some prior evidence of association included breed, steroidal anti-inflammatory administration, transport and worming. The modifiable factors amongst these should be the focus of future laminitis studies. The remainder of the identified factors relating to health, turnout and grazing management and feeding are novel, and require further investigation to explore their relationship with laminitis and their applicability as potential interventions. CONCLUSIONS: This study has demonstrated a temporal relationship between a number of horse- and management-level factors and laminitis, identifying potential interventions and important risk groups for which these interventions would be of particular importance. These results serve as a sound evidence-base towards the development of strategic recommendations for the horse/pony-owning population to reduce the rate of laminitis in GB.

Nonparametric change point estimation for survival distributions with a partially constant hazard rate.

We present a new method for estimating a change point in the hazard function of a survival distribution assuming a constant hazard rate after the change point and a decreasing hazard rate before the change point. Our method is based on fitting a stump regression to p values for testing hazard rates in small time intervals. We present three real data examples describing survival patterns of severely ill patients, whose excess mortality rates are known to persist far beyond hospital discharge. For designing survival studies in these patients and for the definition of hospital performance metrics (e.g. mortality), it is essential to define adequate and objective end points. The reliable estimation of a change point will help researchers to identify such end points. By precisely knowing this change point, clinicians can distinguish between the acute phase with high hazard (time elapsed after admission and before the change point was reached), and the chronic phase (time elapsed after the change point) in which hazard is fairly constant. We show in an extensive simulation study that maximum likelihood estimation is not robust in this setting, and we evaluate our new estimation strategy including bootstrap confidence intervals and finite sample bias correction.

Toward an Application Guide for Safety Integrity Level Allocation in Railway Systems.

The work in the article presents the development of an application guide based on feedback and comments stemming from various railway actors on their practices of SIL allocation to railway safety-related functions. The initial generic methodology for SIL allocation has been updated to be applied to railway rolling stock safety-related functions in order to solve the SIL concept application issues. Various actors dealing with railway SIL allocation problems are the intended target of the methodology; its principles will be summarized in this article with a focus on modifications and precisions made in order to establish a practical guide for railway safety authorities. The methodology is based on the flowchart formalism used in CSM (common safety method) European regulation. It starts with the use of quantitative safety requirements, particularly tolerable hazard rates (THR). THR apportioning rules are applied. On the one hand, the rules are related to classical logical combinations of safety-related functions preventing hazard occurrence. On the other hand, to take into account technical conditions (last safety weak link, functional dependencies, technological complexity, etc.), specific rules implicitly used in existing practices are defined for readjusting some THR values. SIL allocation process based on apportioned and validated THR values is finally illustrated through the example of "emergency brake" subsystems. Some specific SIL allocation rules are also defined and illustrated.