A class of transformation rate models for recurrent event data

Recurrent event data frequently occur in longitudinal studies, and it is often of interest to estimate the effects of covariates on the recurrent event rate. This paper considers a class of semiparametric transformation rate models for recurrent event data, which uses an additive Aalen model as its covariate dependent baseline. The new models are flexible in that they allow for both additive and multiplicative covariate effects, and some covariate effects are allowed to be nonparametric and time-varying. An estimating procedure is proposed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. Simulation studies and a real data analysis demonstrate that the proposed method performs well and is appropriate for practical use.     

A general additive-multiplicative rates model for recurrent event data

In this article, we propose a general additive-multiplicative rates model for recurrent event data. The proposed model includes the additive rates and multiplicative rates models as special cases. For the inference on the model parameters, estimating equation approaches are developed, and asymptotic properties of the proposed estimators are established through modern empirical process theory. In addition, an illustration with multiple-infection data from a clinic study on chronic granulomatous disease is pr...     

A class of additive-accelerated means regression models for recurrent event data

In this article, we propose a class of additive-accelerated means regression models for analyzing recurrent event data. The class includes the proportional means model, the additive rates model, the accelerated failure time model, the accelerated rates model and the additive-accelerated rate model as special cases. The new model offers great flexibility in formulating the effects of covariates on the mean functions of counting processes while leaving the stochastic structure completely unspecified. For the inference on the model parameters, estimating equation approaches are derived and asymptotic properties of the proposed estimators are established. In addition, a technique is provided for model checking. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is illustrated.     

An additive-multiplicative rates model for multivariate recurrent events with event categories missing at random

Multivariate recurrent event data arises when study subjects may experience more than one type of recurrent events. In some situations, however, although event times are always observed, event categories may be partially missing. In this paper, an additive-multiplicative rates model is proposed for the analysis of multivariate recurrent event data when event categories are missing at random. A weighted estimating equations approach is developed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a model-checking technique is presented to assess the adequacy of the model. Simulation studies are conducted to evaluate the finite sample behavior of the proposed estimators, and an application to a platelet transfusion reaction study is provided.     

Partially time-varying coefficient linear rate model for the recurrent event data

In [13], Schaubel et al. proposed a semiparametric partially linear rate model for the statistical analysis of recurrent event data. But they only considered the model with time-independent covariate effects. In this paper, rate function of the recurrent event is modeled by a semipaxametric partially linear function which can include the time-varying effects. We propose the method of generalized estimating equations to make inferences about both the time-varying effects and time-independent effects. The large sample properties are established, while extensive simulation studies are carried out to examine the proposed procedures. At last, we apply the procedures to the well-known bladder cancer study.     

Bayesian MAP model selection of chain event graphs

Chain event graphs are graphical models that while retaining most of the structural advantages of Bayesian networks for model interrogation, propagation and learning, more naturally encode asymmetric state spaces and the order in which events happen than Bayesian networks do. In addition, the class of models that can be represented by chain event graphs for a finite set of discrete variables is a strict superset of the class that can be described by Bayesian networks. In this paper we demonstrate how with complete sampling, conjugate closed form model selection based on product Dirichlet priors is possible, and prove that suitable homogeneity assumptions characterise the product Dirichlet prior on this class of models. We demonstrate our techniques using two educational examples.     

Probability of a fuzzy event: An axiomatic approach

Axioms are proposed that could justify the natural definition of the probability of a fuzzy event initially given by Zadeh. They are based (1) on the postulate that the sum of the conditional probability of a fuzzy event and of its complement given any fuzzy event adds to one or (2) on soft independence for orthogonal sets with independent constitutive elements. A general postulate is also required concerning the complement of a fuzzy set. The classical definition of the operator representing the complement can also be deduced.     

Time-varying latent model for longitudinal data with informative observation and terminal event times

Longitudinal data often occur in follow-up studies, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. We propose a semiparametric mixed effect model with time-varying latent effects in the analysis of longitudinal data with informative observation times and a dependent terminal event. Estimating equation approaches are developed for parameter estimation, and asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is provided.     

A semiparametric additive rates model for clustered recurrent event data

Recurrent event data often arises in biomedical studies, and individuals within a cluster might not be independent. We propose a semiparametric additive rates model for clustered recurrent event data, wherein the covariates are assumed to add to the unspecified baseline rate. For the inference on the model parameters, estimating equation approaches are developed, and both large and finite sample properties of the proposed estimators are established.     

Analytical and numerical solutions of the expected number of occurrences for combinations of event sequences due to variability

This paper investigates variability in the occurrence of different event sequences on an annual basis during the operation of a proposed nuclear facility. During the operational period of a nuclear facility, the annual radiological dose received by workers or members of the public depends on the number of event sequence occurrences. Based on the facility design, some combinations of event sequences will be expected to occur at least once during the operational period, and some combinations will not. This paper provides analytical solutions for calculating the expected number of combinations of independent event sequences. These analytical solutions agree with numerical solutions for an example problem. Although uncertainties can be incorporated into the method, only point-estimate parameter values are used in the example problem presented. The main objectives of this paper are to present calculational approaches to (i) identify which combinations of event sequences within the same year are expected to occur at least once during the operational life of a proposed facility and (ii) determine the annual doses from those identified combinations. Facility performance based on some proposed design is evaluated against the operational dose limits. Because the operational dose limits tend to be annual quantities that may not be exceeded in any year of operation, calculation of the doses resulting from combinations of event sequences that are expected to occur at least once can provide insight on the maximum annual dose expected during the operation of a proposed facility.     

A real-time monitoring approach for bivariate event data

Early detection of changes in the frequency of events is an important task in many fields, such as disease surveillance, monitoring of high-quality processes, reliability monitoring, and public health. This article focuses on detecting changes in multivariate event data by monitoring the time-between-events (TBE). Existing multivariate TBE charts are limited because they only signal after an event occurred for each of the individual processes. This results in delays (i.e., long time-to-signal), especially when we are interested in detecting a change in one or a few processes with different rates. We propose a bivariate TBE chart, which can signal in real-time. We derive analytical expressions for the control limits and average time-to-signal performance, conduct a performance evaluation and compare our chart to an existing method. Our findings showed that our method is an effective approach for monitoring bivariate TBE data and has better detection ability than the existing method under transient shifts and is more generally applicable. A significant benefit of our method is that it signals in real-time and that the control limits are based on analytical expressions. The proposed method is implemented on two real-life datasets from reliability and health surveillance.     

An extended event graph-based modelling method for parallel and distributed discrete-event simulation

The developing logical process (LP)-based parallel and distributed discrete-event simulation (PDES) in the existing PDES programming environments is a difficult and time-consuming process. Event graph is a simple and powerful modelling formalism of discrete-event simulation, whereas this formalism does not support PDES. This article proposes an extension of the event graph to consider the communication of LPs via the events sent, which is called ‘extended event graph (EEG)’, and proposes an EEG-based modelling method for PDES. This modelling method shifts the focus of PDES development from writing code to building models, and the system implementation can be automatically and directly generated from EEG model. The experimental results show that EEG models can successfully execute in the parallel simulator, and this framework can effectively improve the PDES modelling activities.     

Evaluating the quality of online optimization algorithms by discrete event simulation

A key feature of dynamic problems which offer degrees of freedom to the decision maker is the necessity for a goal-oriented decision making routine which is employed every time the logic of the system requires a decision. In this paper, we look at optimization procedures which appear as subroutines in dynamic problems and show how discrete event simulation can be used to assess the quality of algorithms: after establishing a general link between online optimization and discrete event systems, we address performance measurement in dynamic settings and derive a corresponding tool kit. We then analyze several control strategies using the methodologies discussed previously in two real world examples of discrete event simulation models: a manual order picking system and a pickup and delivery service.     

Parallel discrete event simulation algorithm for manufacturing supply chains

Parallel discrete event simulation (PDES) is concerned with the distributed execution of large-scale system models on multiple processors. It is an enabler in the implementation of the virtual enterprise concept, integrating semi-autonomous models of production cells, factories, or units of a supply chain. The key issue in PDES is to maintain causality relationships between system events, while maximizing parallelism in their execution. Events can be executed conservatively only when it is safe to do so, sacrificing the extent to which potential parallelism of the system can be exploited. Alternatively, they can be processed optimistically without guarantee of correctness, but incurring the overhead of a rollback to an earlier saved state when causality error is detected. The paper proposes a modified optimistic scheme for distributed simulation of constituent models of a supply chain in manufacturing, which exploits the inherent operating characteristics of its domain.     

Regression analysis of multivariate recurrent event data with time-varying covariate effects

Recurrent event data occur in many fields and many approaches have been proposed for their analyses (Andersen et al. (1993) [1]; Cook and Lawless (2007) [3]). However, most of the available methods allow only time-independent covariate effects, and sometimes this may not be true. In this paper, we consider regression analysis of multivariate recurrent event data in which some covariate effects may be time-dependent. For the problem, we employ the marginal modeling approach and, especially, estimating equation-based inference procedures are developed. Both asymptotic and finite-sample properties of the proposed estimates are established and an illustrative example is provided.     

A Bayesian network model for spatial event surveillance

Methods for spatial cluster detection attempt to locate spatial subregions of some larger region where the count of some occurrences is higher than expected. Event surveillance consists of monitoring a region in order to detect emerging patterns that are indicative of some event of interest. In spatial event surveillance, we search for emerging patterns in spatial subregions.A well-known method for spatial cluster detection is Kulldorff’s [M. Kulldorff, A spatial scan statistic, Communications in Statistics: Theory and Methods 26 (6) (1997)] spatial scan statistic, which directly analyzes the counts of occurrences in the subregions. Neill et al. [D.B. Neill, A.W. Moore, G.F. Cooper, A Bayesian spatial scan statistic, Advances in Neural Information Processing Systems (NIPS) 18 (2005)] developed a Bayesian spatial scan statistic called BSS, which also directly analyzes the counts.We developed a new Bayesian-network-based spatial scan statistic, called BNetScan, which models the relationships among the events of interest and the observable events using a Bayesian network. BNetScan is an entity-based Bayesian network that models the underlying state and observable variables for each individual in a population.We compared the performance of BNetScan to Kulldorff’s spatial scan statistic and BSS using simulated outbreaks of influenza and cryptosporidiosis injected into real Emergency Department data from Allegheny County, Pennsylvania. It is an open question whether we can obtain acceptable results using a Bayesian network if the probability distributions in the network do not closely reflect reality, and thus, we examined the robustness of BNetScan relative to the probability distributions used to generate the data in the experiments. Our results indicate that BNetScan outperforms the other methods and its performance is robust relative to the probability distribution that is used to generate the data.     

Decidability and complexity of event detection problems for ODEs

The ability of ordinary differential equations (ODEs) to simulate discrete machines with a universal computing power indicates a new source of difficulties for event detection problems. Indeed, nearly any kind of event detection is algorithmically undecidable for infinite or finite half-open time intervals, and explicitly given “well-behaved” ODEs (see [18]). Practical event detection, however, usually takes place on finite closed time intervals. In this article, the undecidability of general event detection is extended to such intervals. On the other hand, on finite closed time intervals, event detection in a certain approximate sense is quite generally decidable, which partly saves the case for practicable event detection. The capability of simulating universal Turing machines is still there, and is used to give complexity lower bounds in terms of accuracy of event detection. The ODEs used here are, of course, quite complicated, but not artificial, in that even from the point of view of practical event detection, it would appear difficult to find criteria to exclude them. © 1997 John Wiley & Sons, Inc.     

Efficiency comparison between mean and log-rank tests for recurrent event time data

Recurrent event time data are common in biomedical follow-up studies, in which a study subject may experience repeated occurrences of an event of interest. In this paper, we evaluate two popular nonparametric tests for recurrent event time data in terms of their relative efficiency. One is the log-rank test for classical survival data and the other a more recently developed nonparametric test based on comparing mean recurrent rates. We show analytically that, somewhat surprisingly, the log-rank test that only makes use of time to the first occurrence could be more efficient than the test for mean occurrence rates that makes use of all available recurrence times, provided that subject-to-subject variation of recurrence times is large. Explicit formula are derived for asymptotic relative efficiencies under the frailty model. The findings are demonstrated via extensive simulations. This work was supported by US National Science Foundation (Grant No. DMS-0504269)     

Smoothing estimation of rate function for recurrent event data with informative censoring

This paper proposes kernel estimation of the occurrence rate function for recurrent event data with informative censoring. An informative censoring model is considered with assumptions made on the joint distribution of the recurrent event process and the censoring time without modeling the censoring distribution. Under the validity of the informative censoring model, we also show that an estimator based on the assumption of independent censoring becomes inappropriate and is generally asymptotically biased. To investigate the asymptotic properties of the proposed estimator, the explicit form of its asymptotic mean squared risk and the asymptotic normality are derived. Meanwhile, the empirical consistent smoothing estimator for the variance function of the estimator is suggested. The performance of the estimators are also studied through Monte Carlo simulations. An epidemiological example of intravenous drug user data is used to show the influence of informative censoring in the estimation of the occurrence rate functions for inpatient cares over time.     

Effciency comparison between mean and log-rank tests for recurrent event time data

Recurrent event time data are common in biomedical follow-up studies, in which a study subject may experience repeated occurrences of an event of interest. In this paper, we evaluate two popular nonparametric tests for recurrent event time data in terms of their relative effciency. One is the log-rank test for classical survival data and the other a more recently developed nonparametric test based on comparing mean recurrent rates. We show analytically that, somewhat surprisingly, the log-rank test that onl...