Bayesian Nonparametric Gamma Mixtures For Mean Residual Life Inference (original) (raw)
Use of Bayesian Mixture Models in Analyzing Heterogeneous Survival Data: A Simulation Study
Journal of Biostatistics and Epidemiology, 2020
Background and Aim: One of the statistical methods used to analyze the time-to-event medical data is survival analysis. In survival models, the response variable is time to the occurrence of an event. The main characteristic of survival data is the existence of censored data. When we have the distribution of survival time, we can use parametric methods. Among the important and popular distributions that can be used, we can mention the Weibull distribution. If the data derives from a heterogeneous population, simple parametric models (such as Weibull) would not fit the data appropriately. One of the methods which have been introduced to overcome this problem is the use of mixture models. Methods: To assess the validity of the two-component Weibull mixture model, we use a simulation method on heterogeneous survival data. For this purpose, data with different sample sizes were produced in a batch of 1000. Then, the validity of the model is checked using root mean square error (RMSE...
Monte Carlo methods for nonparametric survival model determination
Journal of the Italian Statistical Society, 1999
In the causal analysis of survival data a time-based response is related to a set of explanatory variables. Definition of the relation between the time and the covariates may become a difficult task, particularly in the preliminary stage, when the information is limited. Through a nonparametric approach, we propose to estimate the survival function allowing to evaluate the relative importance of each potential explanatory variable, in a simple and explanatory fashion. To achieve this aim, each of the explanatory variables is used to partition the observed survival times. The observations are assumed to be partially exchangeable according to such partition. We then consider, conditionally on each partition, a hierarchical nonparametric Bayesian model on the hazard functions. We define and compare different prior distribution for the hazard functions.
Objective Bayesian Survival Analysis Using Shape Mixtures of Log-Normal Distributions
Survival models such as the Weibull or log-normal lead to inference that is not robust to the presence of outliers. They also assume that all heterogeneity between individuals can be modelled through covariates. This article considers the use of infinite mixtures of lifetime distributions as a solution for these two issues. This can be interpreted as the introduction of a random effect in the survival distribution. We introduce the family of Shape Mixtures of Log-Normal distributions, which covers a wide range of density and hazard functions. Bayesian inference under non-subjective priors based on the Jeffreys rule is examined and conditions for posterior propriety are established. The existence of the posterior distribution on the basis of a sample of point observations is not always guaranteed and a solution through set observations is implemented. In addition, a method for outlier detection based on the mixture structure is proposed. A simulation study illustrates the performance of our methods under different scenarios and an application to a real dataset is provided. Supplementary materials, which include R code, are available online. * Catalina Vallejos is Ph.D student (
Monte Carlo methods for Bayesian analysis of survival data using mixtures of Dirichlet priors
1998
Consider the model in which the data consist of possibly censored lifetimes, and one puts a mixture of Dirichlet process priors on the common survival distribution. The exact computation of the posterior distribution of the survival function is in general impossible to obtain. This paper develops and compares the performance of several simulation techniques, based on Markov chain Monte Carlo and sequential importance sampling, for approximating this posterior distribution. One scheme, whose derivation is based on sequential importance sampling, gives an exactly iid sample from the posterior for the case of right censored data. A second contribution of this paper is a battery of programs that implement the various schemes discussed in this paper. The programs and methods are illustrated on a data set of interval-censored times arising from two treatments for breast cancer.
Bayesian mixture cure rate frailty models with an application to gastric cancer data
Statistical Methods in Medical Research, 2020
Mixture cure rate models are commonly used to analyze lifetime data with long-term survivors. On the other hand, frailty models also lead to accurate estimation of coefficients by controlling the heterogeneity in survival data. Gamma frailty models are the most common models of frailty. Usually, the gamma distribution is used in the frailty random variable models. However, for survival data which are suitable for populations with a cure rate, it may be better to use a discrete distribution for the frailty random variable than a continuous distribution. Therefore, we proposed two models in this study. In the first model, continuous gamma as the distribution is used, and in the second model, discrete hyper-Poisson distribution is applied for the frailty random variable. Also, Bayesian inference with Weibull distribution and generalized modified Weibull distribution as the baseline distribution were used in the two proposed models, respectively. In this study, we used data of patients ...
2014
Heterogeneous survival data can have two different distributions before and after a certain time because many factors affect the life of the creatures or machines. For this purpose we use a mixture of two same kind of distribution of Exponential, Gamma, Lognormal and Weibull and a mixture of different binaries of these distributions. In addition to the previous studies, we propose the mixture of Log-normal distribution with the Exponential, Gamma and Weibull distributions. Maximum likelihood estimations of parameters of the mixture distribution models are obtained by using the EM (Expectation Maximization) algorithm. The results obtained with these models are compared with the observed data. It is found that a mixture of two different distributions approximations are even more useful comparing to the mixture of two same kind of distribution for the present datasets.
Mixture Model Approach to the Analysis of Heterogeneous Survival Data
Pakistan Journal of Statistics
In this paper, we examine mixture models to model heterogeneous survival data. Mixture of Gamma distributions, mixture of Lognormal distributions and mixture of Weibull distributions were tested for the best fit to the real survival datasets. Various properties of the proposed mixture models were discussed. Maximum likelihood estimations of the parameters of mixture models were obtained by the EM algorithm. The mixture models were successfully applied for modeling two real heterogeneous survival datasets.
2023
Failure time data are used in survival analysis. The traditional parametric and nonparametric methods of survival analysis must be modified since the existence of censoring renders them inadequate. When one classical model may not be enough, parametric mixture models are used. To handle the heterogeneity of survival data, a more robust parametric mixture is required. For the study of survival data, this paper proposed a mixture of two distributions; the models are the Loglogistic-Loglogistic and Loglogistic-Gamma distributions. The models' performance was investigated using simulated data, and several iterations were run to test consistency. Expectation Maximization (EM) was employed to calculate the models' maximum likelihood parameters. The computed model parameters all fell within a narrow range of the postulated values. The models' consistency and stability were tested repeatedly through simulations using mean square error (MSE) and root mean square error (RMSE), and all were found to be stable and consistent. Real data were used to compare the fit of mixture models and classical distributions using information criteria (AIC). The best fit for the data was found using mixture models, which combine two different distributions. i.e., Loglogistic-Gamma distribution.
Journal of Computational and Graphical Statistics, 2003
Consider the model in which the data consist of possibly censored lifetimes, and one puts a mixture of Dirichlet process priors on the common survival distribution. The exact computation of the posterior distribution of the survival function is in general impossible to obtain. This paper develops and compares the performance of several simulation techniques, based on Markov chain Monte Carlo and sequential importance sampling, for approximating this posterior distribution. One scheme, whose derivation is based on sequential importance sampling, gives an exactly iid sample from the posterior for the case of right censored data. A second contribution of this paper is a battery of programs that implement the various schemes discussed in this paper. The programs and methods are illustrated on a data set of interval-censored times arising from two treatments for breast cancer.