Models For Event Data Research Articles

A class of mixed models for recurrent event data

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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.

A class of Box-Cox transformation models for recurrent event data

In this article, we propose a class of Box-Cox transformation models for recurrent event data, which includes the proportional means models 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 proposed models, we apply a profile pseudo-partial likelihood method to estimate the model parameters via estimating equation approaches and establish large sample properties of the estimators and examine its performance in moderate-sized samples through simulation studies. In addition, some graphical and numerical procedures are presented for model checking. An example of application on a set of multiple-infection data taken from a clinic study on chronic granulomatous disease (CGD) is also illustrated.

Additive–multiplicative rates model for recurrent events

Recurrent events are frequently encountered in biomedical studies. Evaluating the covariates effects on the marginal recurrent event rate is of practical interest. There are mainly two types of rate models for the recurrent event data: the multiplicative rates model and the additive rates model. We consider a more flexible additive-multiplicative rates model for analysis of recurrent event data, wherein some covariate effects are additive while others are multiplicative. We formulate estimating equations for estimating the regression parameters. The estimators for these regression parameters are shown to be consistent and asymptotically normally distributed under appropriate regularity conditions. Moreover, the estimator of the baseline mean function is proposed and its large sample properties are investigated. We also conduct simulation studies to evaluate the finite sample behavior of the proposed estimators. A medical study of patients with cystic fibrosis suffered from recurrent pulmonary exacerbations is provided for illustration of the proposed method.

Cross-classified hierarchical Bayesian models for risk-based analysis of complex systems under sparse data

Decisionmaking problems in risk analysis often involve extreme events, where empirical data are usually either sparse or lacking. With sparse data, important parameters and quantities for risk and safety analyses may not be estimated and tested within an acceptable level of significance. This paper applies Hierarchical Bayesian Models (HBMs) to reduce the estimation variance and thus build relatively robust models for extreme event data through borrowing strength from different but related systems or subsystems. Based on this application, this paper further applied HBMs with cross-classified random effects (CHBMs) to address the multi-dimensional property of complex systems and borrow strength from the multiple dimensions of such systems. Case studies with both simulated and real data demonstrate the effectiveness of HBMs and CHBMs in risk-based systems analysis.

A class of accelerated means regression models for recurrent event data

In this article, we propose a general class of accelerated means regression models for recurrent event data. The class includes the proportional means model, the accelerated failure time model and the accelerated rates 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 developed and both large and final sample properties of the proposed estimators are established. In addition, some graphical and numerical procedures are presented for model checking. An illustration with multiple-infection data from a clinic study on chronic granulomatous disease is also provided.

A General Class of Parametric Models for Recurrent Event Data

The general class of models proposed by Peña and Hollander for recurrent event data is considered under a fully parametric specification of the baseline hazard rate function and under the two cases where the model does and does not incorporate frailty components. Estimators of model parameters are presented, and their finite and asymptotic properties are ascertained. For the asymptotic properties, the results of Borgan concerning maximum likelihood estimators in counting process models are used to obtain weak convergence to Gaussian distributions of estimators. However, the required regularity conditions are reformulated into conditions involving gap times, which make it more feasible to obtain explicit theoretical expressions of asymptotic covariances. The procedures are applied to fit the general class of models with a parametric baseline hazard rate function to a dataset on hydraulic subsystems of “load-haul-dump” machines in mining.

Semiparametric Methods for Clustered Recurrent Event Data

In biomedical studies, the event of interest is often recurrent and within-subject events cannot usually be assumed independent. In addition, individuals within a cluster might not be independent; for example, in multi-center or familial studies, subjects from the same center or family might be correlated. We propose methods of estimating parameters in two semi-parametric proportional rates/means models for clustered recurrent event data. The first model contains a baseline rate function which is common across clusters, while the second model features cluster-specific baseline rates. Dependence structures for patients-within-cluster and events-within-patient are both unspecified. Estimating equations are derived for the regression parameters. For the common baseline model, an estimator of the baseline mean function is proposed. The asymptotic distributions of the model parameters are derived, while finite-sample properties are assessed through a simulation study. Using data from a national organ failure registry, the proposed methods are applied to the analysis of technique failures among Canadian dialysis patients.

Marginal means/rates models for multiple type recurrent event data.

Recurrent events are frequently observed in biomedical studies, and often more than one type of event is of interest. Follow-up time may be censored due to loss to follow-up or administrative censoring. We propose a class of semi-parametric marginal means/rates models, with a general relative risk form, for assessing the effect of covariates on the censored event processes of interest. We formulate estimating equations for the model parameters, and examine asymptotic properties of the parameter estimators. Finite sample properties of the regression coefficients are examined through simulations. The proposed methods are applied to a retrospective cohort study of risk factors for preschool asthma.

Non‐parametric methods for recurrent event data with informative and non‐informative censorings

Recurrent event data are commonly encountered in health-related longitudinal studies. In this paper time-to-events models for recurrent event data are studied with non-informative and informative censorings. In statistical literature, the risk set methods have been confirmed to serve as an appropriate and efficient approach for analysing recurrent event data when censoring is non-informative. This approach produces biased results, however, when censoring is informative for the time-to-events outcome data. We compare the risk set methods with alternative non-parametric approaches which are robust subject to informative censoring. In particular, non-parametric procedures for the estimation of the cumulative occurrence rate function (CORF) and the occurrence rate function (ORF) are discussed in detail. Simulation and an analysis of data from the AIDS Link to Intravenous Experiences Cohort Study is presented.

Survival analysis for recurrent event data: an application to childhood infectious diseases

Many extensions of survival models based on the Cox proportional hazards approach have been proposed to handle clustered or multiple event data. Of particular note are five Cox-based models for recurrent event data: Andersen and Gill (AG); Wei, Lin and Weissfeld (WLW); Prentice, Williams and Peterson, total time (PWP-CP) and gap time (PWP-GT); and Lee, Wei and Amato (LWA). Some authors have compared these models by observing differences that arise from fitting the models to real and simulated data. However, no attempt has been made to systematically identify the components of the models that are appropriate for recurrent event data. We propose a systematic way of characterizing such Cox-based models using four key components: risk intervals; baseline hazard; risk set, and correlation adjustment. From the definitions of risk interval and risk set there are conceptually seven such Cox-based models that are permissible, five of which are those previously identified. The two new variant models are termed the ‘total time – restricted’ (TT-R) and ‘gap time – unrestricted’ (GT-UR) models. The aim of the paper is to determine which models are appropriate for recurrent event data using the key components. The models are fitted to simulated data sets and to a data set of childhood recurrent infectious diseases. The LWA model is not appropriate for recurrent event data because it allows a subject to be at risk several times for the same event. The WLW model overestimates treatment effect and is not recommended. We conclude that PWP-GT and TT-R are useful models for analysing recurrent event data, providing answers to slightly different research questions. Further, applying a robust variance to any of these models does not adequately account for within-subject correlation. Copyright © 2000 John Wiley & Sons, Ltd.

Multivariate spatial models for event data.

This paper describes how estimates made for event rates in small areas may be enhanced through spatial modelling of the data - taking the geographical location of each area into account - and through the addition of further information from each area. In particular we consider the use of spatial models to predict more than one outcome simultaneously. This is done by writing the spatial model as a multi-level model and subsequently enhancing this to encompass a multivariate data structure; estimates are obtained using iterative generalized least squares in the software package MLwiN. The example given considers mortality due to two causes--neoplasms and circulatory disease--in 143 postcode sectors in Greater Glasgow Health Board, Scotland. In addition, a measure of socio-economic deprivation is available for each area. Correlations between causes within areas, between areas within causes and between areas and causes are quantified, as are the relative contributions of the heterogeneous and spatial parts of the model. The results suggest a tendency for there to be pockets with high mortality rates due to neoplasms, whilst mortality due to circulatory disease follows a much smoother pattern. After taking deprivation into account, the spatial component accounts for just 19 per cent of the variation in the mortality due to neoplasms in Greater Glasgow but 66 per cent of the mortality due to circulatory disease.

Generalizations and applications of frailty models for survival and event data.

A variety of survival models with both discrete and continuously distributed frailty is considered within a framework that involves the specification of three sub-models. An intensity sub-model specifies how the intensity is related to values of covariates and frailty; a measurement sub-model specifies how fallible measures of frailty are related to it; and an exposure sub-model specifies how frailty is distributed within the population. The models include those in which frailty is due to omitted covariates and those where it represents a covariate that has been measured subject to error. Multivariate frailty is also considered, with particular emphasis on models suitable for application to genetically related individuals, notably twins. A numerical example illustrates the use of a model with multivariate frailty for data on repeated exercise times.