Modeling unemployment duration in a dependent competing risks framework: Identification and estimation

Three Mixed Proportional Hazard models for estimation of unemployment duration when attrition is present are considered. The virtue of these models is that they take account of dependence between failure times in a multivariate failure time distribution context. However, identification in dependent competing risks models is not straightforward. We show that these models, independently derived, are special cases of a general frailty model. It is also demonstrated that the three models are identified by means of identification of the general model. An empirical example illustrates the approach to model dependent failure times.     

A competing risks derivation of a mixture model for the analysis of survival data

Boag (1949) and Berkson and Gage (1952) proposed a mixture model for the analysis of survival time data when aproportion of treated patients are cured. This paper presents a derivation of the Boag/Berkson-Gage mixture model as well as a eneralization of the model based on the theory of competing risks. The assumptions underlying the model are stated and discussed and a general likelihood function is obtained. Use of the model is illustrated ith data from the Stanford Heart Transplant Program.     

Inference for cumulative incidence on discrete failure times with competing risks

In the competing risks analysis, most inferences have been developed based on continuous failure time data. However, failure times are sometimes observed as being discrete. We propose nonparametric inferences for the cumulative incidence function for pure discrete data with competing risks. When covariate information is available, we propose semiparametric inferences for direct regression modelling of the cumulative incidence function for grouped discrete failure time data with competing risks. Simulation studies show that the procedures perform well. The proposed methods are illustrated with a study of contraceptive use in Indonesia.     

Markov chain Monte Carlo estimation of a mixture item response theory model

Markov chain Monte Carlo (MCMC) algorithms have been shown to be useful for estimation of complex item response theory (IRT) models. Although an MCMC algorithm can be very useful, it also requires care in use and interpretation of results. In particular, MCMC algorithms generally make extensive use of priors on model parameters. In this paper, MCMC estimation is illustrated using a simple mixture IRT model, a mixture Rasch model (MRM), to demonstrate how the algorithm operates and how results may be affected by some commonly used priors. Priors on the probabilities of mixtures, label switching, model selection, metric anchoring, and implementation of the MCMC algorithm using WinBUGS are described, and their effects illustrated on parameter recovery in practical testing situations. In addition, an example is presented in which an MRM is fitted to a set of educational test data using the MCMC algorithm and a comparison is illustrated with results from three existing maximum likelihood estimation methods.     

Efficient estimation for the proportional hazards model with competing risks and current status data

The proportional hazards model is the most commonly used model in regression analysis of failure time data and has been discussed by many authors under various situations (Kalbfleisch & Prentice, 2002. The Statistical Analysis of Failure Time Data, Wiley, New York). This paper considers the fitting of the model to current status data when there exist competing risks, which often occurs in, for example, medical studies. The maximum likelihood estimates of the unknown parameters are derived and their consistency and convergence rate are established. Also we show that the estimates of regression coefficients are efficient and have asymptotically normal distributions. Simulation studies are conducted to assess the finite sample properties of the estimates and an illustrative example is provided. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Planning and analyzing clinical trials with competing risks: Recommendations for choosing appropriate statistical methodology

In the analysis of time‐to‐event data, competing risks occur when multiple event types are possible, and the occurrence of a competing event precludes the occurrence of the event of interest. In this situation, statistical methods that ignore competing risks can result in biased inference regarding the event of interest. We review the mechanisms that lead to bias and describe several statistical methods that have been proposed to avoid bias by formally accounting for competing risks in the analyses of the event of interest. Through simulation, we illustrate that Gray's test should be used in lieu of the logrank test for nonparametric hypothesis testing. We also compare the two most popular models for semiparametric modelling: the cause‐specific hazards (CSH) model and Fine‐Gray (F‐G) model. We explain how to interpret estimates obtained from each model and identify conditions under which the estimates of the hazard ratio and subhazard ratio differ numerically. Finally, we evaluate several model diagnostic methods with respect to their sensitivity to detect lack of fit when the CSH model holds, but the F‐G model is misspecified and vice versa. Our results illustrate that adequacy of model fit can strongly impact the validity of statistical inference. We recommend analysts incorporate a model diagnostic procedure and contingency to explore other appropriate models when designing trials in which competing risks are anticipated.     

To move or not to move to find a new job: spatial duration time model with dynamic covariate effects

The aim of this paper is to show the flexibility and capacity of penalized spline smoothing as estimation routine for modelling duration time data. We analyse the unemployment behaviour in Germany between 2000 and 2004 using a massive database from the German Federal Employment Agency. To investigate dynamic covariate effects and differences between competing job markets depending on the distance between former and recent working place, a functional duration time model with competing risks is used. It is build upon a competing hazard function where some of the smooth covariate effects are allowed to vary with unemployment duration. The focus of our analysis is on contrasting the spatial, economic and individual covariate effects of the competing job markets and on analysing their general influence on the unemployed's re-employment probabilities. As a result of our analyses, we reveal differences concerning gender, age and education. We also discover an effect between the newly formed and the old West German states. Moreover, the spatial pattern between the considered job markets differs.     

GMM estimation of a realized stochastic volatility model: A Monte Carlo study

This article investigates alternative generalized method of moments (GMM) estimation procedures of a stochastic volatility model with realized volatility measures. The extended model can accommodate a more general correlation structure. General closed form moment conditions are derived to examine the model properties and to evaluate the performance of various GMM estimation procedures under Monte Carlo environment, including standard GMM, principal component GMM, robust GMM and regularized GMM. An application to five company stocks and one stock index is also provided for an empirical demonstration.     

Inference for a simple step-stress model with progressively censored competing risks data from Weibull distribution

In reliability analysis, it is common to consider several causes, either mechanical or electrical, those are competing to fail a unit. These causes are called “competing risks.” In this paper, we consider the simple step-stress model with competing risks for failure from Weibull distribution under progressive Type-II censoring. Based on the proportional hazard model, we obtain the maximum likelihood estimates (MLEs) of the unknown parameters. The confidence intervals are derived by using the asymptotic distributions of the MLEs and bootstrap method. For comparison, we obtain the Bayesian estimates and the highest posterior density (HPD) credible intervals based on different prior distributions. Finally, their performance is discussed through simulations.     

Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring

In reliability analysis, accelerated life-testing allows for gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the simple step-stress model under Type-II censoring when the lifetime distributions of the different risk factors are independently exponentially distributed. Under this setup, we derive the maximum likelihood estimators (MLEs) of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. The exact distributions of the MLEs of the parameters are then derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions and the parametric bootstrap method, we discuss the construction of confidence intervals for the parameters and assess their performance through Monte Carlo simulations. Finally, we illustrate the methods of inference discussed here with an example.     

Maximum likelihood estimation in a Weibull regression model with type-1 censoring: a Monte Carlo study

Results of the Monte Carlo study of the performance of a maximum likelihood estimation in a Weibull parametric regression model with two explanatory variables are presented. One simulation run contained 1000 samples censored on the average by the amount of 0-30%. Each simulatedsample was generated in a form of two-factor two-level balanced experiment. The confidence intervals were computed using the large-sample normal approximation via the matrix of observed information. For small sample sizes the estimates of the scale parameter b of the loglifetime were significantly negatively biased, which resulted in a poor quality of confidence intervals for b and the low-level quantiles. All estimators improved their quality when the nominal value of b decreased. A moderate amount of censoring improved the quality of point and confidence estimation. The reparametrization b 7 produced rather accurate confidence intervals. Exact confidence intervals for b in case of non-censoring were obtained using the pivotal quantity b/b.     

Joint analysis of occurrence and time to stability after entrance into the Italian labour market: an approach based on a Bayesian cure model with structured stochastic search variable selection

Precarious employment is a serious social problem, especially in those countries, such as Italy, where there are limited benefits from social security. We investigate this phenomenon by analysing the initial part of the career of employees starting with unstable contracts for a panel of Italian workers. Our aim is to estimate the probability of getting a stable job and to detect factors influencing both this probability and the duration of precariousness. To answer these questions, we use an ad hoc mixture cure rate model in a Bayesian framework.     

A joint model for longitudinal data profiles and associated event risks with application to a depression study

Summary.  In many longitudinal studies, a subject's response profile is closely associated with his or her risk of experiencing a related event. Examples of such event risks include recurrence of disease, relapse, drop-out and non-compliance. When evaluating the effect of a treatment, it is sometimes of interest to consider the joint process consisting of both the response and the risk of an associated event. Motivated by a prevention of depression study among patients with malignant melanoma, we examine a joint model that incorporates the risk of discontinuation into the analysis of serial depression measures. We present a maximum likelihood estimator for the mean response and event risk vectors. We test hypotheses about functions of mean depression and withdrawal risk profiles from our joint model, predict depression from updated patient histories, characterize associations between components of the joint process and estimate the probability that a patient's depression and risk of withdrawal exceed specified levels. We illustrate the application of our joint model by using the depression data.     

Pseudo-full likelihood estimation for prospective survival analysis with a general semiparametric shared frailty model: Asymptotic theory

In this work we present a simple estimation procedure for a general frailty model for analysis of prospective correlated failure times. Earlier work showed this method to perform well in a simulation study. Here we provide rigorous large-sample theory for the proposed estimators of both the regression coefficient vector and the dependence parameter, including consistent variance estimators.