An additive subdistribution hazard model for competing risks data

The cumulative incidence function plays an important role in assessing its treatment and covariate effects with competing risks data. In this article, we consider an additive hazard model allowing the time-varying covariate effects for the subdistribution and propose the weighted estimating equation under the covariate-dependent censoring by fitting the Cox-type hazard model for the censoring distribution. When there exists some association between the censoring time and the covariates, the proposed coefficients’ estimations are unbiased and the large-sample properties are established. The finite-sample properties of the proposed estimators are examined in the simulation study. The proposed Cox-weighted method is applied to a competing risks dataset from a Hodgkin's disease study.     

A competing risks model for correlated data based on the subdistribution hazard

Family-based follow-up study designs are important in epidemiology as they enable investigations of disease aggregation within families. Such studies are subject to methodological complications since data may include multiple endpoints as well as intra-family correlation. The methods herein are developed for the analysis of age of onset with multiple disease types for family-based follow-up studies. The proposed model expresses the marginalized frailty model in terms of the subdistribution hazards (SDH). As with Pipper and Martinussen’s (Scand J Stat 30:509–521, 2003) model, the proposed multivariate SDH model yields marginal interpretations of the regression coefficients while allowing the correlation structure to be specified by a frailty term. Further, the proposed model allows for a direct investigation of the covariate effects on the cumulative incidence function since the SDH is modeled rather than the cause specific hazard. A simulation study suggests that the proposed model generally offers improved performance in terms of bias and efficiency when a sufficient number of events is observed. The proposed model also offers type I error rates close to nominal. The method is applied to a family-based study of breast cancer when death in absence of breast cancer is considered a competing risk.     

Regression analysis of restricted mean survival time based on pseudo-observations for competing risks data

Competing risks data often occur in many medical follow-up studies. When the survival time is the outcome variable, the restricted mean survival time has heuristic and clinically meaningful interpretation. In this article, we propose a class of regression models for the restricted mean survival time in the competing risks setting. We adopt a technique of pseudo-observations to develop estimating equation approaches for the model parameters and establish asymptotic properties of the resulting estimators. The finite-sample behavior of the proposed method is evaluated through simulation studies, and an application to the Women’s Interagency HIV Study is provided.     

Tests for comparison of competing risks under the additive risk model

It is of interest that researchers study competing risks in which subjects may fail from any one of k causes. Comparing any two competing risks with covariate effects is very important in medical studies. In this paper, we develop tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels under the additive risk model by a weighted difference of estimates of cumulative cause-specific hazard rates. Motivated by McKeague et al. (2001), we construct simultaneous confidence bands for the difference of two conditional cumulative incidence functions as a useful graphical tool. In addition, we conduct a simulation study, and the simulation result shows that the proposed procedure has a good finite sample performance. A melanoma data set in clinical trial is used for the purpose of illustration.     

Modelling and analysis of recall-based competing risks data

In this paper we consider the analysis of recall-based competing risks data. The chance of an individual recalling the exact time to event depends on the time of occurrence of the event and time of observation of the individual. In particular, it is assumed that the probability of recall depends on the time elapsed since the occurrence of an event. In this study we consider the likelihood-based inference for the analysis of recall-based competing risks data. The likelihood function is constructed by incorporating the information about the probability of recall. We consider the maximum likelihood estimation of parameters. Simulation studies are carried out to examine the performance of the estimators. The proposed estimation procedure is applied to a real life data set.     

A proportional hazards model for the analysis of doubly censored competing risks data

ABSTRACT

Competing risks data are common in medical research in which lifetime of individuals can be classified in terms of causes of failure. In survival or reliability studies, it is common that the patients (objects) are subjected to both left censoring and right censoring, which is refereed as double censoring. The analysis of doubly censored competing risks data in presence of covariates is the objective of this study. We propose a proportional hazards model for the analysis of doubly censored competing risks data, using the hazard rate functions of Gray (1988 Gray, R.J. (1988). A class of k-sample tests for comparing the cumulative incidence of a competing risk. Ann. Statist. 16:1141–1154.[Crossref], [Web of Science ®] , [Google Scholar]), while focusing upon one major cause of failure. We derive estimators for regression parameter vector and cumulative baseline cause specific hazard rate function. Asymptotic properties of the estimators are discussed. A simulation study is conducted to assess the finite sample behavior of the proposed estimators. We illustrate the method using a real life doubly censored competing risks data.     

A semi-parametric additive model for variance heterogeneity

This paper presents a flexible model for variance heterogeneity in a normal error model. Specifically, both the mean and variance are modelled using semi-parametric additive models. We call this model a Mean And Dispersion Additive Model (MADAM). A successive relaxation algorithm for fitting the model is described and justified as maximizing a penalized likelihood function with penalties for lack of smoothness in the additive non-parametric functions in both mean and variance models. The algorithm is implemented in GLIM4, allowing flexible and interactive modelling of variance heterogeneity. Two data sets are used for demonstration.     

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.     

The alert-delay competing risks model for maintenance analysis

The paper considers the modelling of the dependency between corrective maintenance and condition-based preventive maintenance of complex repairable systems. A new model of dependent competing risks is proposed, called the alert-delay (AD) model. This model has different properties from that of the delay-time, repair-alert and proportional warning constant inspection models and happens to fit some data sets which could not be fitted by the previous models. The main features of the AD model are derived: probabilistic properties and statistical analysis. Simulation results and an application to real data are presented.     

Regression analysis for cumulative incidence probability under competing risks and left-truncated sampling

The cumulative incidence function provides intuitive summary information about competing risks data. Via a mixture decomposition of this function, Chang and Wang (Statist. Sinca 19:391–408, 2009) study how covariates affect the cumulative incidence probability of a particular failure type at a chosen time point. Without specifying the corresponding failure time distribution, they proposed two estimators and derived their large sample properties. The first estimator utilized the technique of weighting to adjust for the censoring bias, and can be considered as an extension of Fine’s method (J R Stat Soc Ser B 61: 817–830, 1999). The second used imputation and extends the idea of Wang (J R Stat Soc Ser B 65: 921–935, 2003) from a nonparametric setting to the current regression framework. In this article, when covariates take only discrete values, we extend both approaches of Chang and Wang (Statist Sinca 19:391–408, 2009) by allowing left truncation. Large sample properties of the proposed estimators are derived, and their finite sample performance is investigated through a simulation study. We also apply our methods to heart transplant survival data.     

Semiparametric analysis of mixture regression models with competing risks data

In the analysis of competing risks data, cumulative incidence function is a useful summary of the overall crude risk for a failure type of interest. Mixture regression modeling has served as a natural approach to performing covariate analysis based on this quantity. However, existing mixture regression methods with competing risks data either impose parametric assumptions on the conditional risks or require stringent censoring assumptions. In this article, we propose a new semiparametric regression approach for competing risks data under the usual conditional independent censoring mechanism. We establish the consistency and asymptotic normality of the resulting estimators. A simple resampling method is proposed to approximate the distribution of the estimated parameters and that of the predicted cumulative incidence functions. Simulation studies and an analysis of a breast cancer dataset demonstrate that our method performs well with realistic sample sizes and is appropriate for practical use.     

A dependent Dirichlet process model for survival data with competing risks

In this paper, we first propose a dependent Dirichlet process (DDP) model using a mixture of Weibull models with each mixture component resembling a Cox model for survival data. We then build a Dirichlet process mixture model for competing risks data without regression covariates. Next we extend this model to a DDP model for competing risks regression data by using a multiplicative covariate effect on subdistribution hazards in the mixture components. Though built on proportional hazards (or subdistribution hazards) models, the proposed nonparametric Bayesian regression models do not require the assumption of constant hazard (or subdistribution hazard) ratio. An external time-dependent covariate is also considered in the survival model. After describing the model, we discuss how both cause-specific and subdistribution hazard ratios can be estimated from the same nonparametric Bayesian model for competing risks regression. For use with the regression models proposed, we introduce an omnibus prior that is suitable when little external information is available about covariate effects. Finally we compare the models’ performance with existing methods through simulations. We also illustrate the proposed competing risks regression model with data from a breast cancer study. An R package “DPWeibull” implementing all of the proposed methods is available at CRAN.

     

Statistical analysis of middle censored competing risks data with exponential distribution

In this paper, we consider some problems of estimation and reconstruction based on middle censored competing risks data. It is assumed that the lifetime distributions of the latent failure times are independent and exponential distributed with different parameters and also that the censoring mechanism is independent. The maximum likelihood estimators (MLEs) of the unknown parameters are obtained. We then use the asymptotic distribution of the MLEs to construct approximate confidence intervals. Based on gamma priors, Lindley's approximation method is applied to obtain the Bayesian estimates of the unknown parameters under squared error loss function. Since it is not possible to construct the credible intervals, we propose and implement the Gibbs sampling technique to construct the credible intervals. Several point reconstructors for failure time of censored units are provided. Finally, a simulation study is given by Monte-Carlo simulations to evaluate the performances of the different methods and a data set is analysed to illustrate the proposed procedures.     

Analysis of hybrid censored competing risks data

In this paper, we consider the analysis of hybrid censored competing risks data, based on Cox's latent failure time model assumptions. It is assumed that lifetime distributions of latent causes of failure follow Weibull distribution with the same shape parameter, but different scale parameters. Maximum likelihood estimators (MLEs) of the unknown parameters can be obtained by solving a one-dimensional optimization problem, and we propose a fixed-point type algorithm to solve this optimization problem. Approximate MLEs have been proposed based on Taylor series expansion, and they have explicit expressions. Bayesian inference of the unknown parameters are obtained based on the assumption that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameters have Beta–Gamma priors. We propose to use Markov Chain Monte Carlo samples to compute Bayes estimates and also to construct highest posterior density credible intervals. Monte Carlo simulations are performed to investigate the performances of the different estimators, and two data sets have been analysed for illustrative purposes.     

Proportional hazards model for competing risks data with missing cause of failure

We consider the semiparametric proportional hazards model for the cause-specific hazard function in analysis of competing risks data with missing cause of failure. The inverse probability weighted equation and augmented inverse probability weighted equation are proposed for estimating the regression parameters in the model, and their theoretical properties are established for inference. Simulation studies demonstrate that the augmented inverse probability weighted estimator is doubly robust and the proposed method is appropriate for practical use. The simulations also compare the proposed estimators with the multiple imputation estimator of Lu and Tsiatis (2001). The application of the proposed method is illustrated using data from a bone marrow transplant study.     

Regression analysis of multivariate current status data under a varying coefficients additive hazards frailty model

This article discusses regression analysis of multivariate current status failure time data for which the observation time may be related to the underlying survival time. A local partial likelihood technique is used to estimate the varying coefficient covariate effect functions under the additive hazards frailty model. The asymptotic properties of the proposed estimators are established. An extensive simulation study is conducted for the evaluation of the proposed procedure, the results of which indicate that the proposed method works well in practice. Also, a real data study is provided to illustrate the performance of the proposed method.     

Nonparametric tests for cause specific hazard rates with censored data for competing risks among several groups

For the competing risk setting where the lifetime data are due to one of several distinct and exclusive causes, comparison of cause-specific hazard rates is of interest to researchers. In this paper we survey existing methods for related tests and provide a new test for a common overall rate for all causes and groups. Tests given in the literature for checking for a common rate for causes and a common rate for the groups are shown to be in the same framework as the proposed test for common overall rate. Asymptotics are shown to follow a common theme for each test. An extensive numerical and graphical investigation and an example are presented to substantiate the proposed methods.     

Nonparametric estimation with recurrent competing risks data

Nonparametric estimators of component and system life distributions are developed and presented for situations where recurrent competing risks data from series systems are available. The use of recurrences of components’ failures leads to improved efficiencies in statistical inference, thereby leading to resource-efficient experimental or study designs or improved inferences about the distributions governing the event times. Finite and asymptotic properties of the estimators are obtained through simulation studies and analytically. The detrimental impact of parametric model misspecification is also vividly demonstrated, lending credence to the virtue of adopting nonparametric or semiparametric models, especially in biomedical settings. The estimators are illustrated by applying them to a data set pertaining to car repairs for vehicles that were under warranty.