Two‐stage estimation for multivariate recurrent event data with a dependent terminal event

Recurrent event data arise in longitudinal follow‐up studies, where each subject may experience the same type of events repeatedly. The work in this article is motivated by the data from a study of repeated peritonitis for patients on peritoneal dialysis. Due to the aspects of medicine and cost, the peritonitis cases were classified into two types: Gram‐positive and non‐Gram‐positive peritonitis. Further, since the death and hemodialysis therapy preclude the occurrence of recurrent events, we face multivariate recurrent event data with a dependent terminal event. We propose a flexible marginal model, which has three characteristics: first, we assume marginal proportional hazard and proportional rates models for terminal event time and recurrent event processes, respectively; second, the inter‐recurrences dependence and the correlation between the multivariate recurrent event processes and terminal event time are modeled through three multiplicative frailties corresponding to the specified marginal models; third, the rate model with frailties for recurrent events is specified only on the time before the terminal event. We propose a two‐stage estimation procedure for estimating unknown parameters. We also establish the consistency of the two‐stage estimator. Simulation studies show that the proposed approach is appropriate for practical use. The methodology is applied to the peritonitis cohort data that motivated this study.     

On the single event hypothesis in radiogenetics

It is shown that the assumption of a cumulative action of many independent random events as the primary cause of induction of a mutation fits the experimental data at least equally as well as the single event hypothesis. The theory is illustrated on the existing data of X-ray induced lethals in the X-chromosome ofDrosophila. Possible shortcomings of the single event theory in connection with these experimental data and alternative ways of its modification are indicated.     

Analysis of interval‐censored recurrent event processes subject to resolution

Interval‐censored recurrent event data arise when the event of interest is not readily observed but the cumulative event count can be recorded at periodic assessment times. In some settings, chronic disease processes may resolve, and individuals will cease to be at risk of events at the time of disease resolution. We develop an expectation‐maximization algorithm for fitting a dynamic mover‐stayer model to interval‐censored recurrent event data under a Markov model with a piecewise‐constant baseline rate function given a latent process. The model is motivated by settings in which the event times and the resolution time of the disease process are unobserved. The likelihood and algorithm are shown to yield estimators with small empirical bias in simulation studies. Data are analyzed on the cumulative number of damaged joints in patients with psoriatic arthritis where individuals experience disease remission.     

Computationally efficient marginal models for clustered recurrent event data

Large observational databases derived from disease registries and retrospective cohort studies have proven very useful for the study of health services utilization. However, the use of large databases may introduce computational difficulties, particularly when the event of interest is recurrent. In such settings, grouping the recurrent event data into prespecified intervals leads to a flexible event rate model and a data reduction that remedies the computational issues. We propose a possibly stratified marginal proportional rates model with a piecewise-constant baseline event rate for recurrent event data. Both the absence and the presence of a terminal event are considered. Large-sample distributions are derived for the proposed estimators. Simulation studies are conducted under various data configurations, including settings in which the model is misspecified. Guidelines for interval selection are provided and assessed using numerical studies. We then show that the proposed procedures can be carried out using standard statistical software (e.g., SAS, R). An application based on national hospitalization data for end-stage renal disease patients is provided.     

Growth-band counts from elephantfish Callorhinchus milii fin spines do not correspond with independently estimated ages

Fin spines from elephantfish Callorhinchus milii were sectioned and viewed with transmitted white light under a compound microscope. The sections displayed growth bands but their interpretation and significance were unclear. Three different methods were used for counting growth bands. The results were compared with reference growth curves based on length-at-age estimates for six juvenile year classes derived from length-frequency distributions, and tagging data that showed longevity is at least 20 years. None of the three ageing methods showed good correspondence with the reference curves and all methods departed markedly from the reference curves at ages above 2 years old. Therefore, growth bands present in C. milii spines are not useful for ageing, at least with the three methods tested here. Spine bands may not represent age marks, but instead may be layers of material deposited irregularly to strengthen the spine.     

Semi-supervised method for biomedical event extraction

Background

Biomedical extraction based on supervised machine learning still faces the problem that a limited labeled dataset does not saturate the learning method. Many supervised learning algorithms for bio-event extraction have been affected by the data sparseness.

Methods

In this study, a semi-supervised method for combining labeled data with large scale of unlabeled data is presented to improve the performance of biomedical event extraction. We propose a set of rich feature vector, including a variety of syntactic features and semantic features, such as N-gram features, walk subsequence features, predicate argument structure (PAS) features, especially some new features derived from a strategy named Event Feature Coupling Generalization (EFCG). The EFCG algorithm can create useful event recognition features by making use of the correlation between two sorts of original features explored from the labeled data, while the correlation is computed with the help of massive amounts of unlabeled data. This introduced EFCG approach aims to solve the data sparse problem caused by limited tagging corpus, and enables the new features to cover much more event related information with better generalization properties.

Results

The effectiveness of our event extraction system is evaluated on the datasets from the BioNLP Shared Task 2011 and PubMed. Experimental results demonstrate the state-of-the-art performance in the fine-grained biomedical information extraction task.

Conclusions

Limited labeled data could be combined with unlabeled data to tackle the data sparseness problem by means of our EFCG approach, and the classified capability of the model was enhanced through establishing a rich feature set by both labeled and unlabeled datasets. So this semi-supervised learning approach could go far towards improving the performance of the event extraction system. To the best of our knowledge, it was the first attempt at combining labeled and unlabeled data for tasks related biomedical event extraction.

     

Graphical procedures for evaluating overall and subject-specific incremental values from new predictors with censored event time data

Quantitative procedures for evaluating added values from new markers over a conventional risk scoring system for predicting event rates at specific time points have been extensively studied. However, a single summary statistic, for example, the area under the receiver operating characteristic curve or its derivatives, may not provide a clear picture about the relationship between the conventional and the new risk scoring systems. When there are no censored event time observations in the data, two simple scatterplots with individual conventional and new scores for "cases" and "controls" provide valuable information regarding the overall and the subject-specific level incremental values from the new markers. Unfortunately, in the presence of censoring, it is not clear how to construct such plots. In this article, we propose a nonparametric estimation procedure for the distributions of the differences between two risk scores conditional on the conventional score. The resulting quantile curves of these differences over the subject-specific conventional score provide extra information about the overall added value from the new marker. They also help us to identify a subgroup of future subjects who need the new predictors, especially when there is no unified utility function available for cost-risk-benefit decision making. The procedure is illustrated with two data sets. The first is from a well-known Mayo Clinic primary biliary cirrhosis liver study. The second is from a recent breast cancer study on evaluating the added value from a gene score, which is relatively expensive to measure compared with the routinely used clinical biomarkers for predicting the patient's survival after surgery.     

Life event classifications and the event-illness relationship.

Several theoretically important and distinct categories of life change are found in most life event scales. These categories can be organized in terms of at least three dimensions: the person's control over the event, the desirability of the event, and whether or not the independent variable of the event is confounded with the dependent variable of illness. It is important to separate conceptually and, to the extent possible, to distinguish empirically among events according to these dimensions, because several different models of the event-illness relationship are implied when events from several categories are combined. A secondary analysis of recently published data shows that the kinds of events associated with illness are undesirable events within the subject's control. It may not be necessary to consider these dimensions in predicting illness, but the prevention and understanding of illness are furthered by their consideration.     

Bayesian monitoring of event rates with censored data

A Bayesian approach to monitoring event rates with censored data is proposed. A Dirichlet prior for discrete time event probabilities is blended with discrete survival times to provide a posterior distribution that is a mixture of Dirichlets. Approximation of the posterior distribution via data augmentation is discussed. Practical issues involved in implementing the procedure are discussed and illustrated with a simulation of the single arm Cord Blood Transplantation Study where 6-month survival is monitored.     

Dynamic analysis of recurrent event data using the additive hazard model

We propose a method for analysis of recurrent event data using information on previous occurrences of the event as a time-dependent covariate. The focus is on understanding how to analyze the effect of such a dynamic covariate while at the same time ensuring that the effects of treatment and other fixed covariates are unbiasedly estimated. By applying an additive regression model for the intensity of the recurrent events, concepts like direct, indirect and total effects of the fixed covariates may be defined in an analogous way as for traditional path analysis. Theoretical considerations as well as simulations are presented, and a data set on recurrent bladder tumors is used to illustrate the methodology.     

Second-order analysis of semiparametric recurrent event processes

A typical recurrent event dataset consists of an often large number of recurrent event processes, each of which contains multiple event times observed from an individual during a follow-up period. Such data have become increasingly available in medical and epidemiological studies. In this article, we introduce novel procedures to conduct second-order analysis for a flexible class of semiparametric recurrent event processes. Such an analysis can provide useful information regarding the dependence structure within each recurrent event process. Specifically, we will use the proposed procedures to test whether the individual recurrent event processes are all Poisson processes and to suggest sensible alternative models for them if they are not. We apply these procedures to a well-known recurrent event dataset on chronic granulomatous disease and an epidemiological dataset on meningococcal disease cases in Merseyside, United Kingdom to illustrate their practical value.     

A hot-deck multiple imputation procedure for gaps in longitudinal recurrent event histories

We propose a regression-based hot-deck multiple imputation method for gaps of missing data in longitudinal studies, where subjects experience a recurrent event process and a terminal event. Examples are repeated asthma episodes and death, or menstrual periods and menopause, as in our motivating application. Research interest concerns the onset time of a marker event, defined by the recurrent event process, or the duration from this marker event to the final event. Gaps in the recorded event history make it difficult to determine the onset time of the marker event, and hence, the duration from onset to the final event. Simple approaches such as jumping gap times or dropping cases with gaps have obvious limitations. We propose a procedure for imputing information in the gaps by substituting information in the gap from a matched individual with a completely recorded history in the corresponding interval. Predictive mean matching is used to incorporate information on longitudinal characteristics of the repeated process and the final event time. Multiple imputation is used to propagate imputation uncertainty. The procedure is applied to an important data set for assessing the timing and duration of the menopausal transition. The performance of the proposed method is assessed by a simulation study.     

A random time interval approach for analysing the impact of a possible intermediate event on a terminal event

We consider the impact of a possible intermediate event on a terminal event in an illness-death model with states 'initial', 'intermediate' and 'terminal'. One aim is to unambiguously describe the occurrence of the intermediate event in terms of the observable data, the problem being that the intermediate event may not occur. We propose to consider a random time interval, whose length is the time spent in the intermediate state. We derive an estimator of the joint distribution of the left and right limit of the random time interval from the Aalen-Johansen estimator of the matrix of transition probabilities and study its asymptotic properties. We apply our approach to hospital infection data. Estimating the distribution of the random time interval will usually be only a first step of an analysis. We illustrate this by analysing change in length of hospital stay following an infection and derive the large sample properties of the respective estimator.     

A varying-coefficient Cox model for the effect of age at a marker event on age at menopause

It is of recent interest in reproductive health research to investigate the validity of a marker event for the onset of menopausal transition and to estimate age at menopause using age at the marker event. We propose a varying-coefficient Cox model to investigate the association between age at a marker event, defined as a specific bleeding pattern change, and age at menopause, where both events are subject to censoring and their association varies with age at the marker event. Estimation proceeds using the regression spline method. The proposed method is applied to the Tremin Trust data to evaluate the association between age at onset of the 60-day menstrual cycle and age at menopause. The performance of the proposed method is evaluated using a simulation study.     

江苏省典型干旱过程特征

为了研究江苏省重大干旱过程的生消和演变特征,选取2006年10-11月覆盖全省的一次严重秋旱事件作为典型个例,收集54个气象台站的逐日气象观测资料,计算逐日复合气象干旱指数CI值,以此为基础统计干旱发生的开始日期、结束日期、持续日数和逐日旱强,研究全省和各地区的旱情生消和演变特征;选用MODIS产品数据,利用植被供水指数法,反演干旱发展过程;利用实测土壤相对湿度数据,在ArcGIS9.3中采用反距离权重插值法,分析干旱事件中土壤湿度的空间变化特征.研究结果表明:(1)在这一典型秋旱事件中,由CI指数、VWSI指数和土壤相对湿度反映的大气、植被、土壤干旱的生消和演变过程基本一致.(2)干旱的发生是由西北到东南逐渐扩展蔓延,结束则由东南向西北逐渐收缩消失,持续天数从北向南递减.(3)旱情总体上北重南轻,但不同地区因大气背景和自然地理条件不同发展过程差异较大.(4)利用CI指数、VSWI指数和土壤湿度可以较全面而系统地监测干旱过程的生消、演变和强度变化.     

Variance estimation for statistics computed from single recurrent event processes

This article is concerned with variance estimation for statistics that are computed from single recurrent event processes. Such statistics are important in diagnosis for each individual recurrent event process. The proposed method only assumes a semiparametric form for the first-order structure of the processes but not for the second-order (i.e., dependence) structure. The new variance estimator is shown to be consistent for the target parameter under very mild conditions. The estimator can be used in many applications in semiparametric rate regression analysis of recurrent event data such as outlier detection, residual diagnosis, as well as robust regression. A simulation study and application to two real data examples are used to demonstrate the use of the proposed method.     

A simple nonparametric test for linkage with sib-pair censored event time observations

Consider the case that individual phenotype and genotype observations were collected from a large or moderate number of pedigrees. Some of the pedigrees have multi-generation nuclear families. For each nuclear family, the phenotype trait value of each sibling is the time to onset for a specific event (e.g., disease). Often, this event time may be right censored, that is, an individual is event-free at the study examination time point. In this article, we propose a purely nonparametric test for testing if the distribution of a Haseman-Elston distance measure between two siblings' event times is independent of their mean genetic sharing identical by descent at a genetic marker based on such incomplete observations from all the nuclear families. The new test can be implemented easily and is illustrated with a data set from the Genetic Analysis Workshop 12. The validity of the new test is examined via a simulation study.     

A measure of explained variation for event history data

Summary There is no shortage of proposed measures of prognostic value of survival models in the statistical literature. They come under different names, including explained variation, correlation, explained randomness, and information gain, but their goal is common: to define something analogous to the coefficient of determination R² in linear regression. None however have been uniformly accepted, none have been extended to general event history data, including recurrent events, and many cannot incorporate time‐varying effects or covariates. We present here a measure specifically tailored for use with general dynamic event history regression models. The measure is applicable and interpretable in discrete or continuous time; with tied data or otherwise; with time‐varying, time‐fixed, or dynamic covariates; with time‐varying or time‐constant effects; with single or multiple event times; with parametric or semiparametric models; and under general independent censoring/observation. For single‐event survival data with neither censoring nor time dependency it reduces to the concordance index. We give expressions for its population value and the variance of the estimator and explore its use in simulations and applications. A web link to R software is provided.     

Neuroimaging studies of autobiographical event memory

Commonalities and differences in findings across neuroimaging studies of autobiographical event memory are reviewed. In general terms, the overall pattern across studies is of medial and left-lateralized activations associated with retrieval of autobiographical event memories. It seems that the medial frontal cortex and left hippocampus in particular are responsive to such memories. However, there are also inconsistencies across studies, for example in the activation of the hippocampus and dorsolateral prefrontal cortex. It is likely that methodological differences between studies contribute to the disparate findings. Quantifying and assessing autobiographical event memories presents a challenge in many domains, including neuroimaging. Methodological factors that may be pertinent to the interpretation of the neuroimaging data and the design of future experiments are discussed. Consideration is also given to aspects of memory that functional neuroimaging might be uniquely disposed to examine. These include assessing the functionality of damaged tissue in patients and the estimation of inter-regional communication (effective connectivity) between relevant brain regions.     

Shared frailty models for recurrent events and a terminal event

There has been an increasing interest in the analysis of recurrent event data (Cook and Lawless, 2002, Statistical Methods in Medical Research 11, 141-166). In many situations, a terminating event such as death can happen during the follow-up period to preclude further occurrence of the recurrent events. Furthermore, the death time may be dependent on the recurrent event history. In this article we consider frailty proportional hazards models for the recurrent and terminal event processes. The dependence is modeled by conditioning on a shared frailty that is included in both hazard functions. Covariate effects can be taken into account in the model as well. Maximum likelihood estimation and inference are carried out through a Monte Carlo EM algorithm with Metropolis-Hastings sampler in the E-step. An analysis of hospitalization and death data for waitlisted dialysis patients is presented to illustrate the proposed methods. Methods to check the validity of the proposed model are also demonstrated. This model avoids the difficulties encountered in alternative approaches which attempt to specify a dependent joint distribution with marginal proportional hazards and yields an estimate of the degree of dependence.