The proportional hazards model for multiple type recurrent gap times

Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies, and often more than one type of recurrent events is of interest. In this paper, we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covariates on the censored event processes of interest. An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions. We examine asymptotic properties of the proposed estimators. Finite sample properties of these estimators are demonstrated by simulations.     

The Additive-multiplicative Hazards Mo del for Multiple Typ e of Recurrent Gap Times

Recurrent event gap times data frequently arise in biomedical studies and often more than one type of event is of interest. To evaluate the effects of covariates on the marginal recurrent event hazards...     

Additive hazards models for gap time data with multiple causes

Recurrent event data with multiple causes are often observed in biomedical studies. The additive hazards model describes a different aspect of the association between covariates and the failure time than does the proportional hazards model. In this paper, we introduce additive hazards models for the analysis of gap time data of recurrent events with multiple causes. We estimate the regression parameter vector and cumulative baseline cause specific hazard rate function using counting process approach. Asymptotic properties of the estimators are studied. The proposed model is applied to the kidney dialysis data given in Lawless (2003). A simulation study is carried out to assess the performance of the estimates.     

On a General Class of Semiparametric Hazards Regression Models for Recurrent Gap Times

Acta Mathematicae Applicatae Sinica, English Series - In the article, we investigate a general class of semiparametric hazards regression models for recurrent gap times. The general class includes...     

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.     

Asymptotics on Semiparametric Analysis of Multivariate Failure Time Data Under the Additive Hazards Model

Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time data under the additive hazards model. Simple weighted estimating functions for the regression parameters are proposed, and asymptotic distribution theory of the resulting estimators are derived. In addition, a class of generalized Wald and generalized score statistics for hypothesis testing and model selection are presented, and the asymptotic properties of these statistics are examined.     

带相依终止事件的复发事件数据的可加可乘比率模型

本文对带相依终止事件的复发事件数据提出了一个联合建模分析方法,用一个带脆弱变量的可加可乘比率模型来刻画复发事件过程,还用带脆弱变量的Cox风险率模型来刻画终止事件过程,而且这两个过程的相依性由脆弱变量来刻画.我们利用估计方程的方法,对模型参数进行了估计,给出了所得估计的渐近性质.同时,通过数值模拟分析验证了估计的渐近性质.最后,利用该方法分析了弗吉尼亚大学慢性心脏病病人医疗诊费数据.     

Semiparametric additive intensity model with frailty for recurrent events

The seminal Cox’s proportional intensity model with multiplicative frailty is a popular approach to analyzing the frequently encountered recurrent event data in scientific studies. In the case of violating the proportional intensity assumption, the additive intensity model is a useful alternative. Both the additive and proportional intensity models provide two principal frameworks for studying the association between the risk factors and the disease recurrences. However, methodology development on the additive intensity model with frailty is lacking, although would be valuable. In this paper, we propose an additive intensity model with additive frailty to formulate the effects of possibly time-dependent covariates on recurrent events as well as to evaluate the intra-class dependence within recurrent events which is captured by the frailty variable. The asymptotic properties for both the regression parameters and the association parameters in frailty distribution are established. Furthermore, we also investigate the large-sample properties of the estimator for the cumulative baseline intensity function.     

Consistency and Asymptotic Normality of Estimators in a Proportional Hazards Model with Interval Censoring and Left Truncation

Satten et al. (1998, J. Amer. Statist. Assoc., 93, 318–327) proposed an approach to the proportional hazards model for interval censored data in which parameter estimates are obtained by solving estimating equations which are the score equations for the full data proportional hazards model, averaged over all rankings of imputed failure times consistent with the observed censoring intervals. In this paper, we extend this approach to incorporate data that are left-truncated and right censored (dynamic cohort data). Consistency and asymptotic normality of the estimators obtained in this way are established.     

Time to default in credit scoring using survival analysis: a benchmark study

We investigate the performance of various survival analysis techniques applied to ten actual credit data sets from Belgian and UK financial institutions. In the comparison we consider classical survival analysis techniques, namely the accelerated failure time models and Cox proportional hazards regression models, as well as Cox proportional hazards regression models with splines in the hazard function. Mixture cure models for single and multiple events were more recently introduced in the credit risk context. The performance of these models is evaluated using both a statistical evaluation and an economic approach through the use of annuity theory. It is found that spline-based methods and the single event mixture cure model perform well in the credit risk context.     

含有持久生存数据的复发事件的生存函数的一个非参数方法(英文)

在生物学、社会科学、保险理赔、可靠性和人口统计学等的研究中,我们经常会遇到复发事件数据的处理.最近一段时间以来,两个相邻复发事件的时间间隔的一个纵向数据模型已经引起统计工作者的广泛兴趣.本文中,我们提议另一个复发事件时间间隔模型,它可以用来模拟生存数据中带有所谓的持久生存者.非参数方法将用于我们所提议模型的统计推断,模拟和现实数据的例子将用来评价模型和提议估计方法的小样本性质.     

Analyzing right-censored length-biased data with additive hazards model

Length-biased data are often encountered in observational studies, when the survival times are left-truncated and right-censored and the truncation times follow a uniform distribution. In this article, we propose to analyze such data with the additive hazards model, which specifies that the hazard function is the sum of an arbitrary baseline hazard function and a regression function of covariates. We develop estimating equation approaches to estimate the regression parameters. The resultant estimators are shown to be consistent and asymptotically normal. Some simulation studies and a real data example are used to evaluate the finite sample properties of the proposed estimators.     

Markovian modeling for dependent interrecurrence times in bladder cancer

A methodology to model a process in which repeated events occur is presented. The context is the evolution of non-muscle-invasive bladder carcinoma (NMIBC), characterized by recurrent relapses. It is based on the statistical flowgraph approach, a technique specifically suited for semi-Markov processes. A very useful feature of the flowgraph framework is that it naturally incorporates the management of censored data. However, this approach presents two difficulties with the process to be modeled. On one hand, the management of covariates is not straightforward. However, it is of great interest to know how the characteristics of a certain patient influence the evolution of the disease. On the other hand, repeated events on the same subject are generally not independent, in which case the semi-Markov framework is not sufficient because the semi-Markov assumption implies independence among waiting time distributions. We solve this issue by extending the flowgraph methodology using the Markovian arrival process (MAP), which does successfully model the dependence between events. Along the way, we provide a procedure to consider covariates and censored times in MAPs, a pending task needed in this field. In short, we have managed to extend the flowgraph methodology beyond the semi-Markovian framework, simplifying the incorporation of covariates and keeping the management of censored times. All of which has allowed us to build a multistate model of the evolution of NMIBC. The developed model allows us to compute the Survival function for any evolution of a patient with specific clinic-pathological characteristics in this primary tumor.     

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)     

Invariance and homogenization of an adaptive time gap car-following model

In this paper we consider a microscopic model of traffic flow called the adaptive time gap car-following model. This is a system of ODEs which describes the interactions between cars moving on a single line. The time gap is the time that a car needs to reach the position of the car in front of it (if the car in front of it would not move and if the moving car would not change its velocity). In this model, both the velocity of the car and the time gap satisfy an ODE. We study this model and show that under certain assumptions, there is an invariant set for which the dynamics is defined for all times and for which we have a comparison principle. As a consequence, we show rigorously that after rescaling, this microscopic model converges to a macroscopic model that can be identified as the classical LWR model for traffic.     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

Initial classification of joint data in EM estimation of latent class joint model

The latent class mixture-of-experts joint model is one of the important methods for jointly modelling longitudinal and recurrent events data when the underlying population is heterogeneous and there are nonnormally distributed outcomes. The maximum likelihood estimates of parameters in latent class joint model are generally obtained by the EM algorithm. The joint distances between subjects and initial classification of subjects under study are essential to finding good starting values of the EM algorithm through formulas. In this article, separate distances and joint distances of longitudinal markers and recurrent events are proposed for classification purposes, and performance of the initial classifications based on the proposed distances and random classification are compared in a simulation study and demonstrated in an example.     

多类型复发事件下变系数加性乘积比率回归模型

本文基于多类型复发事件数据,讨论了一个新的加性乘积比率回归模型,该模型包括两部分,其中第一部分为可加Aalen模型,其中协变量影响为加性的且与时间有关.第二部分为Cox回归模型,其中协变量有乘性影响.利用估计方程的方法,给出了该模型中未知参数和非参数函数的一种估计方法,并利用现代经验过程理沦证明了所得估计的相合性和渐近正态性.     

An efficient risk estimator with external information under additive hazards model

Rare event data is encountered when the events of interest occur with low frequency, and the estimators based on the cohort data only may be inefficient. However, when external information is available for the estimation, the estimators utilizing external information can be more efficient. In this paper, we propose a method to incorporate external information into the estimation of the baseline hazard function and improve efficiency for estimating the absolute risk under the additive hazards model. The resulting estimators are shown to be uniformly consistent and converge weakly to Gaussian processes. Simulation studies demonstrate that the proposed method is much more efficient. An application to a bone marrow transplant data set is provided.     

Regression Analysis of Doubly Censored Data with a Cured Subgroup under a Class of Promotion Time Cure Models

In some situations, the failure time of interest is defined as the gap time between two related events and the observations on both event times can suffer either right or interval censoring.Such data are usually referred to as doubly censored data and frequently encountered in many clinical and observational studies. Additionally, there may also exist a cured subgroup in the whole population,which means that not every individual under study will experience the failure time of interest eventually. In this paper, we consider regression analysis of doubly censored data with a cured subgroup under a wide class of flexible transformation cure models. Specifically, we consider marginal likelihood estimation and develop a two-step approach by combining the multiple imputation and a new expectation-maximization(EM) algorithm for its implementation. The resulting estimators are shown to be consistent and asymptotically normal. The finite sample performance of the proposed method is investigated through simulation studies. The proposed method is also applied to a real dataset arising from an AIDS cohort study for illustration.