Chi-Squared Goodness-of-Fit Tests for Parametric Accelerated Failure Time Models

We give chi-squared goodness-of fit tests for parametric regression models such as accelerated failure time, proportional hazards, generalized proportional hazards, frailty models, transformation models, and models with cross-effects of survival functions. Random right censored data are used. Choice of random grouping intervals as data functions is considered.     

Analysis of Failure Time Data with Mixed-Effects Accelerated Failure Time Model

In randomized clinical trials or observational studies, subjects are recruited at multiple treating sites. Factors that vary across sites may have some influence on outcomes; therefore, they need to be taken into account to get better results. We apply the accelerated failure time (AFT) model with linear mixed effects to analyze failure time data, accounting for correlations between outcomes. Specifically, we use Bayesian approach to fit the data, computing the regression parameters by Gibbs sampler combined with Buckley-James method. This approach is compared with the marginal independence approach and other methods through simulations and an application to a real example.     

Using Frailties in the Accelerated Failure Time Model

The accelerated failuretime (AFT) model is an important alternative to the Cox proportionalhazards model (PHM) in survival analysis. For multivariate failuretime data we propose to use frailties to explicitly account forpossible correlations (and heterogeneity) among failure times.An EM-like algorithm analogous to that in the frailty model forthe Cox model is adapted. Through simulation it is shown thatits performance compares favorably with that of the marginalindependence approach. For illustration we reanalyze a real dataset.     

Test-Based Interval Estimation Under the Accelerated Failure Time Model

Some new results of a distance—based (DB) model for prediction with mixed variables are presented and discussed. This model can be thought of as a linear model where predictor variables for a response Y are obtained from the observed ones via classic multidimensional scaling. A coefficient is introduced in order to choose the most predictive dimensions, providing a solution to the problem of small variances and a very large number n of observations (the dimensionality increases as n). The problem of missing data is explored and a DB solution is proposed. It is shown that this approach can be regarded as a kind of ridge regression when the usual Euclidean distance is used.     

A Discrete Time Parametric Model for the Analysis of Failure Time Data

This paper introduces a parametric discrete failure time model which allows a variety of smooth hazard function shapes, including shapes which are not readily available with continuous failure time models. The model is easy to fit, and statistical inference is simple. Further, it is readily extended to allow for differences between subjects while retaining the ease of fit and simplicity of statistical inference. The performance of the discrete time analysis is demonstrated by application to several data sets.     

Semiparametric Estimation Methods for the Accelerated Failure Time Mixture Cure Model

This paper provides an overview of two semiparametric estimation methods recently proposed in the literature for the accelerated failure time mixture cure model. We prove that the two estimation methods are asymptotically equivalent. A simulation is conducted to investigate the rate of convergence of the two methods. We apply these methods to fit the accelerated failure time mixture cure model to the survival times of leukemia patients receiving bone marrow transplantation.     

Robust Smoothed Rank Estimation Methods for Accelerated Failure Time Model Allowing Clusters

Smoothed Gehan rank estimation methods are widely used in accelerated failure time (AFT) models with/without clusters. However, most methods are sensitive to outliers in the covariates. In order to solve this problem, we propose robust approaches based on the smoothed Gehan rank estimation methods for the AFT model, allowing for clusters by employing two different weight functions. Simulation studies show that the proposed methods outperform existing smoothed rank estimation methods regarding their biases and standard deviations when there are outliers in the covariates. The proposed methods are also applied to a real dataset from the “Major cardiovascular interventions” study.     

Jackknife Empirical Likelihood for the Accelerated Failure Time Model with Censored Data

Kendall and Gehan estimating functions are commonly used to estimate the regression parameter in accelerated failure time model with censored observations in survival analysis. In this paper, we apply the jackknife empirical likelihood method to overcome the computation difficulty about interval estimation. A Wilks’ theorem of jackknife empirical likelihood for U-statistic type estimating equations is established, which is used to construct the confidence intervals for the regression parameter. We carry out an extensive simulation study to compare the Wald-type procedure, the empirical likelihood method, and the jackknife empirical likelihood method. The proposed jackknife empirical likelihood method has a better performance than the existing methods. We also use a real data set to compare the proposed methods.     

An Alternative Estimation Method for the Semiparametric Accelerated Failure Time Mixture Cure Model

We propose an alternative estimation method for the semiparametric accelerated failure time mixture cure model by incorporating the profile likelihood into the M-step of the EM algorithm. The proposed method performs as well as the existing methods when the censoring is light and better than the existing methods when the censoring is moderate from the simulation studies. Regarding to the computational time, the proposed method runs faster than the existing methods.     

Linear Bayesian Inference for Accelerated Weibull Model

In this paper, we present a Bayesian approach for inference from accelerated life tests when the underlying life model is Weibull. Our approach is based on the General Linear Models framework of West, Harrison and Migon (1985). We discuss inference for the model and show that computable results can be obtained using linear Bayesian methods. We illustrate the usefulness of our approach by applying it to some actual data from accelerated life tests. This revised version was published online in July 2006 with corrections to the Cover Date.     

Calibration of Proportional Hazards and Accelerated Failure Time Models

Given a prognostic model based on one population, one may ask: Can this model be used to accurately predict disease in a different population? When the underlying rate of disease differs in the new population, the model must be calibrated. van Houwelingen (2000 van Houwelingen , H. ( 2000 ). Validation, calibration, revision and combination of prognostic survival models . Statistics in Medicine 19 : 3401 – 3415 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) considered this calibration problem focusing on proportional hazards models. We extend the validation by calibration to the log-logistic accelerated failure time model. We use calibration of proportional hazards models and log-logistic accelerated failure time models to examine whether a survival model based on the Framingham Heart Study can be applied to diverse studies around the world.     

Methods for Bivariate Survival Data with Mismeasured Covariates Under an Accelerated Failure Time Model

Accelerated failure time models are useful in survival data analysis, but such models have received little attention in the context of measurement error. In this paper we discuss an accelerated failure time model for bivariate survival data with covariates subject to measurement error. In particular, methods based on the marginal and joint models are considered. Consistency and efficiency of the resultant estimators are investigated. Simulation studies are carried out to evaluate the performance of the estimators as well as the impact of ignoring the measurement error of covariates. As an illustration we apply the proposed methods to analyze a data set arising from the Busselton Health Study (Knuiman et al., 1994 Knuiman , M. W. , Cullent , K. J. , Bulsara , M. K. , Welborn , T. A. , Hobbs , M. S. T. ( 1994 ). Mortality trends, 1965 to 1989, in Busselton, the site of repeated health surveys and interventions . Austral. J. Public Health 18 : 129 – 135 . [CSA] [Crossref], [PubMed] , [Google Scholar]).     

Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure

Consider a J-component series system which is put on Accelerated Life Test (ALT) involving K stress variables. First, a general formulation of ALT is provided for log-location-scale family of distributions. A general stress translation function of location parameter of the component log-lifetime distribution is proposed which can accommodate standard ones like Arrhenius, power-rule, log-linear model, etc., as special cases. Later, the component lives are assumed to be independent Weibull random variables with a common shape parameter. A full Bayesian methodology is then developed by letting only the scale parameters of the Weibull component lives depend on the stress variables through the general stress translation function. Priors on all the parameters, namely the stress coefficients and the Weibull shape parameter, are assumed to be log-concave and independent of each other. This assumption is to facilitate Gibbs sampling from the joint posterior. The samples thus generated from the joint posterior is then used to obtain the Bayesian point and interval estimates of the system reliability at usage condition.     

贝叶斯隐马尔科夫异质面板模型及应用研究

针对不可观测异质性非时变假设导致的删失变量偏差及推断无效问题,构建贝叶斯隐马尔科夫异质面板模型,刻画截面个体间的动态时变不可观测异质性,诊断经济系统环境中可能存在的隐性变点,设计相应的马尔科夫链蒙特卡洛抽样算法估计模型参数,并对中国各地区的金融发展与城乡收入差距关系进行实证分析,捕捉到金融发展与城乡收入差距间长期稳定关系的隐性变化,发现了区域个体不可观测异质性存在的动态时变特征。研究结果表明各参数的迭代轨迹收敛且估计误差非常小,验证了贝叶斯隐马尔科夫异质面板模型的有效性。     

Accelerated Rates Regression Models for Recurrent Failure Time Data

In this article, we formulate a semiparametric model for counting processes in which the effect of covariates is to transform the time scale for a baseline rate function. We assume an arbitrary dependence structure for the counting process and propose a class of estimating equations for the regression parameters. Asymptotic results for these estimators are derived. In addition, goodness of fit methods for assessing the adequacy of the accelerated rates model are proposed. The finite-sample behavior of the proposed methods is examined in simulation studies, and data from a chronic granulomatous disease study are used to illustrate the methodology.     

Analyzing Length-biased Data with Semiparametric Transformation and Accelerated Failure Time Models

Right-censored time-to-event data are often observed from a cohort of prevalent cases that are subject to length-biased sampling. Informative right censoring of data from the prevalent cohort within the population often makes it difficult to model risk factors on the unbiased failure times for the general population, because the observed failure times are length biased. In this paper, we consider two classes of flexible semiparametric models: the transformation models and the accelerated failure time models, to assess covariate effects on the population failure times by modeling the length-biased times. We develop unbiased estimating equation approaches to obtain the consistent estimators of the regression coefficients. Large sample properties for the estimators are derived. The methods are confirmed through simulations and illustrated by application to data from a study of a prevalent cohort of dementia patients.     

A Semiparametric Approach for Accelerated Failure Time Models with Covariates Subject to Measurement Error

There are relatively few discussions about measurement error in the accelerated failure time (AFT) model, particularly for the semiparametric AFT model. In this article, we propose an adjusted estimation procedure for the semiparametric AFT model with covariates subject to measurement error, based on the profile likelihood approach and simulation and exploration (SIMEX) method. The simulation studies show that the proposed semiparametric SIMEX approach performs well. The proposed approach is applied to a coronary heart disease dataset from the Busselton Health study for illustration.     

Composite Estimating Equation Method for the Accelerated Failure Time Model with Length‐biased Sampling Data

Length‐biased sampling data are often encountered in the studies of economics, industrial reliability, epidemiology, genetics and cancer screening. The complication of this type of data is due to the fact that the observed lifetimes suffer from left truncation and right censoring, where the left truncation variable has a uniform distribution. In the Cox proportional hazards model, Huang & Qin (Journal of the American Statistical Association, 107, 2012, p. 107) proposed a composite partial likelihood method which not only has the simplicity of the popular partial likelihood estimator, but also can be easily performed by the standard statistical software. The accelerated failure time model has become a useful alternative to the Cox proportional hazards model. In this paper, by using the composite partial likelihood technique, we study this model with length‐biased sampling data. The proposed method has a very simple form and is robust when the assumption that the censoring time is independent of the covariate is violated. To ease the difficulty of calculations when solving the non‐smooth estimating equation, we use a kernel smoothed estimation method (Heller; Journal of the American Statistical Association, 102, 2007, p. 552). Large sample results and a re‐sampling method for the variance estimation are discussed. Some simulation studies are conducted to compare the performance of the proposed method with other existing methods. A real data set is used for illustration.     

空间滞后模型的贝叶斯估计

本文采用Bayes方法对空间滞后模型进行全面分析。在构建模型的贝叶斯框架时,对模型系数与误差方差分别选取正态先验分布和逆伽玛先验分布,这样以便获得参数的联合后验分布和条件后验分布。在抽样估计时,文章主要使用MCMC方法,同时还设计了一个简单随机游动Metropolis抽样器,以方便从空间权重因子系数的条件后验分布中进行抽样。最后应用所建议的方法进行数值模拟。     

Two-Sample Statistics for Testing the Equality of Survival Functions Against Improper Semi-parametric Accelerated Failure Time Alternatives: An Application to the Analysis of a Breast Cancer Clinical Trial

This paper presents two-sample statistics suited for testing equality of survival functions against improper semi-parametric accelerated failure time alternatives. These tests are designed for comparing either the short- or the long-term effect of a prognostic factor, or both. These statistics are obtained as partial likelihood score statistics from a time-dependent Cox model. As a consequence, the proposed tests can be very easily implemented using widely available software. A breast cancer clinical trial is presented as an example to demonstrate the utility of the proposed tests.