Recurrent Gap Time Research Articles

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

In the article, we investigate a general class of semiparametric hazards regression models for recurrent gap times. The general class includes the proportional hazards model, the accelerated failure time model and the accelerated hazards models as special cases. The model is flexible in modelling recurrent gap times since a covariate effect is identified as having two separate components, namely a time-scale change on hazard progression and a relative hazards ratio. In order to infer the model parameters, the procedure is proposed based on estimating equations. The asymptotic properties of the proposed estimators are established and the finite sample properties are investigated via simulation studies. In addition, a lack of fit test is presented to assess the adequacy of the model and an application of data from a bladder cancer study is reported for illustration.

A class of additive transformation models for recurrent gap times

The gap time between recurrent events is often of primary interest in many fields such as medical studies, and in this article, we discuss regression analysis of the gap times arising from a general class of additive transformation models. For the problem, we propose two estimation procedures, the modified within-cluster resampling (MWCR) method and the weighted risk-set (WRS) method, and the proposed estimators are shown to be consistent and asymptotically follow the normal distribution. In particular, the estimators have closed forms and can be easily determined, and the methods have the advantage of leaving the correlation among gap times arbitrary. A simulation study is conducted for assessing the finite sample performance of the presented methods and suggests that they work well in practical situations. Also the methods are applied to a set of real data from a chronic granulomatous disease (CGD) clinical trial.

Marginal regression of recurrent gap times based on semiparametric transformation cure model

Recurrent event data frequently arise in longitudinal studies. In this article, we consider a marginal semiparametric transformation cure model for gap times between recurrent events. We assume that each individual has the possibility of being cured after each event. We proposed generalized estimating equations for parameter estimation of the regression parameters in this model. The asymptotic properties of the proposed estimators are established under independent censoring. A simulation study is conducted to investigate finite sample properties of the proposed estimators. The proposed method is illustrated using an example of the tumor recurrent data for bladder cancer patients.

SEMIPARAMETRIC REGRESSION MODEL FOR RECURRENT BACTERIAL INFECTIONS AFTER HEMATOPOIETIC STEM CELL TRANSPLANTATION.

Patients who undergo hematopoietic stem cell transplantation (HSCT) often experience multiple bacterial infections during the early post-transplant period. In this article, we consider a semiparametric regression model that correlates patient- and transplant-related risk factors with inter-infection gap times. Existing regression methods for recurrent gap times are not directly applicable to study post-transplant infection because the initiating event (transplant) is different than the recurrent events of interest (post-transplant infections); as a result, the time from transplant to the first infection and the time elapsed between consecutive infections have distinct biological meanings and hence follow different distributions. Moreover, risk factors may have different effects on these two types of gap times. We propose a semiparametric estimation procedure to evaluate the covariate effects on time from transplant to thefirst infection and on gap times between consecutive infections simultaneously. The proposed estimator accounts for dependent censoring induced by within-subject correlation among recurrent gap times and length bias in the last censored gap time due to intercept sampling. We study the finite sample properties through simulations and present an application of the proposed method to the post-HSCT bacterial infection data collected at the University of Minnesota.

An Additive Hazards Model for Clustered Recurrent Gap Times

In this article, clustered recurrent gap time is investigated. A marginal additive hazards model is proposed without specifying the association of the individuals within the same cluster. The relationship among the gap times for the same individual is also left unspecified. An estimating equation-based inference procedure is developed for the model parameters, and the asymptotic properties of the resulting estimators are established. In addition, a lack-of-fit test is presented to assess the adequacy of the model. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a clinic study on chronic granulomatous disease (CGD) is illustrated.

Induced smoothing for rank-based regression with recurrent gap time data.

Various semiparametric regression models have recently been proposed for the analysis of gap times between consecutive recurrent events. Among them, the semiparametric accelerated failure time (AFT) model is especially appealing owing to its direct interpretation of covariate effects on the gap times. In general, estimation of the semiparametric AFT model is challenging because the rank-based estimating function is a nonsmooth step function. As a result, solutions to the estimating equations do not necessarily exist. Moreover, the popular resampling-based variance estimation for the AFT model requires solving rank-based estimating equations repeatedly and hence can be computationally cumbersome and unstable. In this paper, we extend the induced smoothing approach to the AFT model for recurrent gap time data. Our proposed smooth estimating function permits the application of standard numerical methods for both the regression coefficients estimation and the standard error estimation. Large-sample properties and an asymptotic variance estimator are provided for the proposed method. Simulation studies show that the proposed method outperforms the existing nonsmooth rank-based estimating function methods in both point estimation and variance estimation. The proposed method is applied to the data analysis of repeated hospitalizations for patients in the Danish Psychiatric Center Register.

A class of partially linear transformation models for recurrent gap times

ABSTRACTIn this article, we propose a general class of partially linear transformation models for recurrent gap time data, which extends the linear transformation models by incorporating non linear covariate effects and includes the partially linear proportional hazards and the partially linear proportional odds models as special cases. Both global and local estimating equations are developed to estimate the parametric and non parametric covariate effects, and the 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 clinic study on chronic granulomatous disease is provided.

Semiparametric regression analysis of recurrent gap times in the presence of competing risks

Semiparametric regression analysis of recurrent gap times in the presence of competing risks

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.

Nonparametric Methods for Analyzing Recurrent Gap Time Data with Application to Infections After Hematopoietic Cell Transplant

Infection is one of the most common complications after hematopoietic cell transplantation. Many patients experience infectious complications repeatedly after transplant. Existing statistical methods for recurrent gap time data typically assume that patients are enrolled due to the occurrence of an event of interest, and subsequently experience recurrent events of the same type; moreover, for one-sample estimation, the gap times between consecutive events are usually assumed to be identically distributed. Applying these methods to analyze the post-transplant infection data will inevitably lead to incorrect inferential results because the time from transplant to the first infection has a different biological meaning than the gap times between consecutive recurrent infections. Some unbiased yet inefficient methods include univariate survival analysis methods based on data from the first infection or bivariate serial event data methods based on the first and second infections. In this article, we propose a nonparametric estimator of the joint distribution of time from transplant to the first infection and the gap times between consecutive infections. The proposed estimator takes into account the potentially different distributions of the two types of gap times and better uses the recurrent infection data. Asymptotic properties of the proposed estimators are established.

Serial association analyses of recurrent gap time data via Kendall's tau.

Recurrent event data are frequently encountered in long-term follow-up studies. In many applications, the gap times between two successive recurrent events are natural outcomes of interest. Investigation on patterns of associations among recurrent gap times within subjects is an important inferential issue. In this paper, we introduce flexible functions of previous gap times to create a class of summary measures of serial associations for a sequence of recurrent gap times through Kendall's tau. Such a general class of serial association measures provides a useful tool to quantify the predictive abilities of event history with different aspects. Non-parametric estimators of the proposed measures of serial associations are developed by generalizing the existing estimator of Kendall's tau for two serial gap times, in which inverse probability of censoring weights is used to overcome the induced dependent censoring. Various tests are further constructed for testing the constancy of serial associations over different events. Our method is applied to Denmark schizophrenia data and the results show that association structures are different for distinct ages of onset of schizophrenia.

Additive mixed effect model for recurrent gap time data.

Gap times between recurrent events are often of primary interest in medical and observational studies. The additive hazards model, focusing on risk differences rather than risk ratios, has been widely used in practice. However, the marginal additive hazards model does not take the dependence among gap times into account. In this paper, we propose an additive mixed effect model to analyze gap time data, and the proposed model includes a subject-specific random effect to account for the dependence among the gap times. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the resulting estimators are established. In addition, some graphical and numerical procedures are presented for model checking. The finite sample behavior of the proposed methods is evaluated through simulation studies, and an application to a data set from a clinic study on chronic granulomatous disease is provided.

Buckley–James-type estimation of quantile regression with recurrent gap time data

In longitudinal studies, an individual may potentially undergo a series of repeated recurrence events. The gap times, which are referred to as the times between successive recurrent events, are typically the outcome variables of interest. Various regression models have been developed in order to evaluate covariate effects on gap times based on recurrence event data. The proportional hazards model, additive hazards model, and the accelerated failure time model are all notable examples. Quantile regression is a useful alternative to the aforementioned models for survival analysis since it can provide great flexibility to assess covariate effects on the entire distribution of the gap time. In order to analyze recurrence gap time data, we must overcome the problem of the last gap time subjected to induced dependent censoring, when numbers of recurrent events exceed one time. In this paper, we adopt the Buckley–James-type estimation method in order to construct a weighted estimation equation for regression coefficients under the quantile model, and develop an iterative procedure to obtain the estimates. We use extensive simulation studies to evaluate the finite-sample performance of the proposed estimator. Finally, analysis of bladder cancer data is presented as an illustration of our proposed methodology.

A class of transformed hazards models for recurrent gap times

In this article, a class of transformed hazards models is proposed for recurrent gap time data, including both the proportional and additive hazards models as special cases. An estimating equation-based inference procedure is developed for the model parameters, and the asymptotic properties of the resulting estimators are established. In addition, a lack-of-fit test is presented to assess the adequacy of the model. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a clinic study on chronic granulomatous disease (CGD) is illustrated.

Estimation of a recurrent event gap time distribution: an application to morbidity outcomes following lower extremity fracture in Veterans with spinal cord injury

Recurrent event data is frequently encountered in biomedical research. Estimators describing the time to the next event occurrence could be useful information in healthcare settings to deliver targeted, preemptive, patient-specific care. Distribution estimation of recurrence times is varied based on both the underlying assumptions of the estimator (e.g., dependence vs. independence of recurrence times within individual) and estimator construct. In an example among Veterans with spinal cord injury, distributional changes in recurrence times of health complications subsequent lower extremity (LE) fracture are explored. Veterans with LE fracture (cases) were matched to Veterans without LE fracture (controls) on demographic (age, race), level of injury (paraplegia vs. tetraplegia), extent of injury, Veterans Affairs connected service status, and comorbidities using Mahalanobis metric matching. Stratified distributional estimates of recurrence times between successive morbidity outcomes are compared between Veterans with/without LE fracture using three estimators: independent identically distributed product limit estimator, Wang–Chang product limit estimator, and a gamma frailty maximum likelihood estimator. It can be seen that the estimator selection can provide a very different showcasing of a recurrence time distribution. There is a change in the time-to-recurrence of recurrent urinary tract infections and pressure ulcers for fracture cases directly following LE fracture, however testing if this difference is statistically significant remains unclear. Causal inference of gap time analyses in observational data with recurrent events is considered and a call for methods in this area is much warranted.

불완전한 관측틈을 가진 재발 사건 소요시간에 대한 자료 분석

불완전한 관측틈을 가진 재발 사건 소요시간에 대한 자료 분석

Quantile Regression for Recurrent Gap Time Data

Evaluating covariate effects on gap times between successive recurrent events is of interest in many medical and public health studies. While most existing methods for recurrent gap time analysis focus on modeling the hazard function of gap times, a direct interpretation of the covariate effects on the gap times is not available through these methods. In this article, we consider quantile regression that can provide direct assessment of covariate effects on the quantiles of the gap time distribution. Following the spirit of the weighted risk-set method by Luo and Huang (2011, Statistics in Medicine 30, 301-311), we extend the martingale-based estimating equation method considered by Peng and Huang (2008, Journal of the American Statistical Association 103, 637-649) for univariate survival data to analyze recurrent gap time data. The proposed estimation procedure can be easily implemented in existing software for univariate censored quantile regression. Uniform consistency and weak convergence of the proposed estimators are established. Monte Carlo studies demonstrate the effectiveness of the proposed method. An application to data from the Danish Psychiatric Central Register is presented to illustrate the methods developed in this article.

Properties of the Estimators for Additive-Accelerated Hazard Ratio Model

Recurrent events gap time is the time difference between two adjacent failures of recurrent events. In this paper, an additive-accelerated hazard ratio model is presented for multiple type recurrent events gap time data, and the estimation methods of unknown parameter and non-parameter function is given. Moreover, the asymptotic properties of estimators are proved.

Additive-Accelerated Hazard Ratio Model for Multiple Type Recurrent Events Gap Time

Multiple type recurrent event data is often observed in clinical medicine, epidemiology, biostatistics, and other related applied research fields. This paper presents an additive-accelerated hazard ratio model for multiple type recurrent events data, and gives the estimation methods of unknown parameter and non-parameter function based on the idea of estimating equation. In addition, it provides the expression of unknown regression coefficient as well as the benchmark hazard ratio function.

Event‐weighted proportional hazards modelling for recurrent gap time data

The analysis of gap times in recurrent events requires an adjustment to standard marginal models. One can perform this adjustment with a modified within-cluster resampling technique; however, this method is computationally intensive. In this paper, we describe a simple adjustment to the standard Cox proportional hazards model analysis that mimics the intent of within-cluster resampling and results in similar parameter estimates. This method essentially weights the partial likelihood contributions by the inverse of the number of gap times observed within the individual while assuming a working independence correlation matrix. We provide an example involving recurrent mammary tumours in female rats to illustrate the methods considered in this paper.