Non-parametric Bayesian analysis of clustered survival data

Clustered survival data are often modelled with frailty models which incorporate frailties to model the cluster specific heterogeneity and the dependence between observations in the same cluster. For the analysis of the frailty models, we propose Bayesian modelling with beta process prior on the cumulative hazard function and describe the details of the posterior computation. We demonstrate the method with two data sets using three different frailty distributions: gamma, log-normal and log-logistic distributions. We also empirically demonstrate the difficulty in checking the assumed frailty distribution with the posterior sample of the frailties.     

Discriminant analysis of survey data

We consider the problem of the effect of sample designs on discriminant analysis. The selection of the learning sample is assumed to depend on the population values of auxiliary variables. Under a superpopulation model with a multivariate normal distribution, unbiasedness and consistency are examined for the conventional estimators (derived under the assumptions of simple random sampling), maximum likelihood estimators, probability-weighted estimators and conditionally unbiased estimators of parameters. Four corresponding sampled linear discriminant functions are examined. The rates of misclassification of these four discriminant functions and the effect of sample design on these four rates of misclassification are discussed. The performances of these four discriminant functions are assessed in a simulation study.     

Jointly modeling skew longitudinal survival data with missingness and mismeasured covariates

Jointly modeling longitudinal and survival data has been an active research area. Most researches focus on improving the estimating efficiency but ignore many data features frequently encountered in practice. In the current study, we develop the joint models that concurrently accounting for longitudinal and survival data with multiple features. Specifically, the proposed model handles skewness, missingness and measurement errors in covariates which are typically observed in the collection of longitudinal survival data from many studies. We employ a Bayesian inferential method to make inference on the proposed model. We applied the proposed model to an real data study. A few alternative models under different conditions are compared. We conduct extensive simulations in order to evaluate how the method works.     

Comparing crossing hazard rate functions by joint modelling of survival and longitudinal data

Abstract

It is one of the important issues in survival analysis to compare two hazard rate functions to evaluate treatment effect. It is quite common that the two hazard rate functions cross each other at one or more unknown time points, representing temporal changes of the treatment effect. In certain applications, besides survival data, we also have related longitudinal data available regarding some time-dependent covariates. In such cases, a joint model that accommodates both types of data can allow us to infer the association between the survival and longitudinal data and to assess the treatment effect better. In this paper, we propose a modelling approach for comparing two crossing hazard rate functions by joint modelling survival and longitudinal data. Maximum likelihood estimation is used in estimating the parameters of the proposed joint model using the EM algorithm. Asymptotic properties of the maximum likelihood estimators are studied. To illustrate the virtues of the proposed method, we compare the performance of the proposed method with several existing methods in a simulation study. Our proposed method is also demonstrated using a real dataset obtained from an HIV clinical trial.     

Simple nonparametric tests for a known standard survival based on censored data

It is often of interest in survival analysis to test whether the distribution of lifetimes from which the sample under study was derived is the same as a reference distribution. The latter can be specified on the basis of previous studies or on subject matter considerations. In this paper several tests are developed for the above hypothesis, suitable for right-censored observations. The tests are based on modifications of Moses' one-sample limits of some classical two-sample rank tests. The asymptotic distributions of the test statistics are derived, consistency is established for alternatives which are stochastically ordered with respect to the null, and Pitman asymptotic efficiencies are calculated relative to competing tests. Simulated power comparisons are reported. An example is given with data on the survival times of lung cancer patients.     

Posterior analysis,prediction and reliability in three-parameter weibull distributions

The paper develops Bayesian analysis in the context of samples from three-parameter Weibull distributions and shows how to tackle the problems of prediction and estimation of reliability curves. As Johnson, Kotz and Balakrishnan ( 1994 ) mentioned, the prediction problems for the three-parameter Weibull model seem to be unresolved and is certainly worth looking into (p.671). Posterior analysis organized around Gibbs sampling is shown to perform well. An application to stock returns is used to illustrate the potential of the approach.     

Bayesian analysis of the Box-Cox transformation model based on left-truncated and right-censored data

In this paper, we discuss the inference problem about the Box-Cox transformation model when one faces left-truncated and right-censored data, which often occur in studies, for example, involving the cross-sectional sampling scheme. It is well-known that the Box-Cox transformation model includes many commonly used models as special cases such as the proportional hazards model and the additive hazards model. For inference, a Bayesian estimation approach is proposed and in the method, the piecewise function is used to approximate the baseline hazards function. Also the conditional marginal prior, whose marginal part is free of any constraints, is employed to deal with many computational challenges caused by the constraints on the parameters, and a MCMC sampling procedure is developed. A simulation study is conducted to assess the finite sample performance of the proposed method and indicates that it works well for practical situations. We apply the approach to a set of data arising from a retirement center.     

Model comparison of linear and nonlinear Bayesian structural equation models with dichotomous data

In this article, dichotomous variables are used to compare between linear and nonlinear Bayesian structural equation models. Gibbs sampling method is applied for estimation and model comparison. Statistical inferences that involve estimation of parameters and their standard deviations and residuals analysis for testing the selected model are discussed. Hidden continuous normal distribution (censored normal distribution) is used to solve the problem of dichotomous variables. The proposed procedure is illustrated by a simulation data obtained from R program. Analyses are done by using R2WinBUGS package in R-program.     

Lifetime estimation from doubly censored data and dirichlet process prior knowledge on the observable random vector

The purpose of this paper is to present a nonparametric Bayesian procedure for estimating a survival curve in a double censoring situation. Assuming a proportional hazard rates model, we propose a consistent estimation of lifetime, based on a Dirichlet process prior knowledge on the observable random vector. Some large sample properties of this estimator are also derived, We prove strong consistency and asymptotic weak convergence to a Gaussian pro cess. Finally, a simulation study is presented in order to analyze the behavior of the proposed estimator, and establish some comparisons to other estimators.     

Specification analysis in mixed hazard models and a test of crossing survival functions

The paper investigates diagnostic procedures for the specification of common hazard models in duration analysis. It is shown that under mixed hazard specifications the survival functions of different subgroups cannot cross. A nonparametric test for the crossing of two survival functions is provided and its applications in duration analysis are discussed. In particular, the proportional hazard model with unobserved heterogeneity (PHU) is investigated, and procedures are developed to test whether given data are consistent with the PHU model and whether they contain unobserved heterogeneity within the PHU specification. Examples in which crossing survivals are of substantive concern are discussed, including the dynamics of infectious diseases and the demand for vaccination.     

Bayesian analysis of longitudinal ordered data with flexible random effects using McMC: application to diabetic macular Edema data

In the analysis of correlated ordered data, mixed-effect models are frequently used to control the subject heterogeneity effects. A common assumption in fitting these models is the normality of random effects. In many cases, this is unrealistic, making the estimation results unreliable. This paper considers several flexible models for random effects and investigates their properties in the model fitting. We adopt a proportional odds logistic regression model and incorporate the skewed version of the normal, Student's t and slash distributions for the effects. Stochastic representations for various flexible distributions are proposed afterwards based on the mixing strategy approach. This reduces the computational burden being performed by the McMC technique. Furthermore, this paper addresses the identifiability restrictions and suggests a procedure to handle this issue. We analyze a real data set taken from an ophthalmic clinical trial. Model selection is performed by suitable Bayesian model selection criteria.     

Semi-parametric Bayesian Analysis of the Proportional Hazard Rate Model An Application to the Effect of Training Programs on Graduate Unemployment

In this paper, we introduce a semi-parametric Bayesian methodology based on the proportional hazard model that assumes that the baseline hazard function is constant over segments but, by contrast to what is usually assumed in the literature, with the periods at which the function changes not being specified in advance. The methodology is applied to explore the impact of Vocational Training courses offered by the University of Zaragoza (Spain) on the duration of the initial periods of unemployment experienced by graduate leavers. The framework is very flexible and allows us, in particular, to capture the presence of seasonality in the job insertion of graduates.     

基于贝叶斯方法的比例数据分位数推断及其应用

为了尝试使用贝叶斯方法研究比例数据的分位数回归统计推断问题,首先基于Tobit模型给出了分位数回归建模方法,然后通过选取合适的先验分布得到了贝叶斯层次模型,进而给出了各参数的后验分布并用于Gibbs抽样。数值模拟分析验证了所提出的贝叶斯推断方法对于比例数据分析的有效性。最后,将贝叶斯方法应用于美国加州海洛因吸毒数据,在不同的分位数水平下揭示了吸毒频率的影响因素。     

Bayesian interim analysis of lifetime data

In hypothesis testing involving censored lifetime data that are independently distributed according to an accelerated-failure-time model, it is often of interest to predict whether continuation of the experiment will significantly alter the inferences drawn at an interim point. Approaching the problem from a Bayesian viewpoint, we suggest a possible solution based on Laplace approximations to the posterior distribution of the parameters of interest and on Markov-chain Monte Carlo. We apply our results to Weibull data from a carcinogenesis experiment on mice.     

Estimation Of A Survival Function With Doubly Censored Data And Dirichlet Process Prior Knowledge On The Observable Variable

This article presents a nonparametric Bayesian procedure for estimating a survival curve in a proportional hazard model when some of the data are censored on the left and some are censored on the right. The method works under the assumption that there is a Dirichlet process prior knowledge on the observable variable. Strong consistency of the estimator is proved and an example is given. To finish some simulation is presented to analyze the estimator.     

Including structural measurement errors in the nonlinear regression analysis of clustered data

This paper extends methods for nonlinear regression analysis that have developed for the analysis of clustered data. Its novelty lies in its dual incorporation of random cluster effects and structural error in the measurement of the explanatory variables. Moments up to second order are assumed to have been specified for the latter to enable a generalized estimating equations approach to be used for fitting and testing nonlinear models linking response to these explanatory variables and random effects. Taylor expansion methods are used, and a difficulty with earlier approaches overcome. Finally we describe an application of this methodology to indicate how it can be used. That application concerns the degree of association of hospital admissions for acute respiratory health problems and air pollution.     

Marker processes in survival analysis

In the development of many diseases there are often associated variables which continuously measure the progress of an individual towards the final expression of the disease (failure). Such variables are stochastic processes, here called marker processes, and, at a given point in time, they may provide information about the current hazard and subsequently on the remaining time to failure. Here we consider a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. We develop some basic calculations based on this model. Interest is focused on statistical applications for markers related to estimation of the survival distribution of time to failure, including (i) the use of markers as surrogate responses for failure with censored data, and (ii) the use of markers as predictors of the time elapsed since onset of a survival process in prevalent individuals. Particular attention is directed to potential gains in efficiency incurred by using marker process information.     

Analysis of multivariate categorical data with misclassification errors by triple sampling schemes

Previous work has been carried out on the use of double-sampling schemes for inference from categorical data subject to misclassification. The double-sampling schemes utilize a sample of n units classified by both a fallible and true device and another sample of n₂ units classified only by a fallible device. In actual applications, one often hasavailable a third sample of n₁ units, which is classified only by the true device. In this article we develop techniques of fitting log-linear models under various misclassification structures for a general triple-sampling scheme. The estimation is by maximum likelihood and the fitted models are hierarchical. The methodology is illustrated by applying it to data in traffic safety research from a study on the effectiveness of belts in reducing injuries.     

Semiparametric Bayesian classification with longitudinal markers

Summary.  We analyse data from a study involving 173 pregnant women. The data are observed values of the β human chorionic gonadotropin hormone measured during the first 80 days of gestational age, including from one up to six longitudinal responses for each woman. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from data that are available at the early stages of pregnancy. We achieve the desired classification with a semiparametric hierarchical model. Specifically, we consider a Dirichlet process mixture prior for the distribution of the random effects in each group. The unknown random-effects distributions are allowed to vary across groups but are made dependent by using a design vector to select different features of a single underlying random probability measure. The resulting model is an extension of the dependent Dirichlet process model, with an additional probability model for group classification. The model is shown to perform better than an alternative model which is based on independent Dirichlet processes for the groups. Relevant posterior distributions are summarized by using Markov chain Monte Carlo methods.     

Partial logistic relevance vector machines in survival analysis

The use of relevance vector machines to flexibly model hazard rate functions is explored. This technique is adapted to survival analysis problems through the partial logistic approach. The method exploits the Bayesian automatic relevance determination procedure to obtain sparse solutions and it incorporates the flexibility of kernel-based models. Example results are presented on literature data from a head-and-neck cancer survival study using Gaussian and spline kernels. Sensitivity analysis is conducted to assess the influence of hyperprior distribution parameters. The proposed method is then contrasted with other flexible hazard regression methods, in particular the HARE model proposed by Kooperberg et al. [16]. A simulation study is conducted to carry out the comparison. The model developed in this paper exhibited good performance in the prediction of hazard rate. The application of this sparse Bayesian technique to a real cancer data set demonstrated that the proposed method can potentially reveal characteristics of the hazards, associated with the dynamics of the studied diseases, which may be missed by existing modeling approaches based on different perspectives on the bias vs. variance balance.