Flexible Cure Rate Modelling Under Latent Activation Schemes (original) (raw)
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Flexible Cure Rate Modeling Under Latent Activation Schemes
Journal of the American Statistical Association, 2007
With rapid improvements in medical treatment and health care, many datasets dealing with time to relapse or death now reveal a substantial portion of patients who are cured (i.e., who never experience the event). Extended survival models called cure rate models account for the probability of a subject being cured and can be broadly classified into the classical mixture models of Berkson and Gage (BG type) or the stochastic tumor models pioneered by Yakovlev and extended to a hierarchical framework by Chen, Ibrahim, and Sinha (YCIS type). Recent developments in Bayesian hierarchical cure models have evoked significant interest regarding relationships and preferences between these two classes of models. Our present work proposes a unifying class of cure rate models that facilitates flexible hierarchical model-building while including both existing cure model classes as special cases. This unifying class enables robust modeling by accounting for uncertainty in underlying mechanisms leading to cure. Issues such as regressing on the cure fraction and propriety of the associated posterior distributions under different modeling assumptions are also discussed. Finally, we offer a simulation study and also illustrate with two datasets (on melanoma and breast cancer) that reveal our framework's ability to distinguish among underlying mechanisms that lead to relapse and cure.
Bayesian cure rate model accommodating multiplicative and additive covariates
Statistics and Its Interface, 2009
We propose a class of Bayesian cure rate models by incorporating a baseline density function as well as multiplicative and additive covariate structures. Our model naturally accommodates zero and non-zero cure rates, which provides an objective way to examine the existence of a survival fraction in the failure time data. An inherent parameter constraint needs to be incorporated into the model formulation due to the additive covariates. Within the Bayesian paradigm, we take a Markov gamma process prior to model the baseline hazard rate, and mixture prior distributions for the parameters in the additive component of the model. We implement a Markov chain Monte Carlo computational scheme to sample from the full conditional distributions of the posterior. We conduct simulation studies to assess the estimation and inference properties of the proposed model, and illustrate it with data from a bone marrow transplant study.
A Bayesian Long-term Survival Model Parametrized in the Cured Fraction
Biometrical Journal, 2009
The main goal of this paper is to investigate a cure rate model that comprehends some well-known proposals found in the literature. In our work the number of competing causes of the event of interest follows the negative binomial distribution. The model is conveniently reparametrized through the cured fraction, which is then linked to covariates by means of the logistic link. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis in the proposed model. The procedure is illustrated with a numerical example.
Bayesian Semiparametric Cure Rate Model with an Unknown Threshold
Scandinavian Journal of Statistics, 2008
We propose a Bayesian semiparametric model for survival data with a cure fraction. We explicitly consider a finite cure time in the model, which allows us to separate the cured and the uncured populations. We take a mixture prior of a Markov gamma process and a point mass at zero to model the baseline hazard rate function of the entire population. We focus on estimating the cure threshold after which subjects are considered cured. We can incorporate covariates through a structure similar to the proportional hazards model and allow the cure threshold also to depend on the covariates. For illustration, we undertake simulation studies and a full Bayesian analysis of a bone marrow transplant data set.
2008
Analyses involving longitudinal and time-to-event data are quite common in medical research. The primary goal of such studies to simultaneously study the effect of treatment on both the longitudinal covariate and survival. Often in medical research, there are settings in which it is meaningful to consider the existence of a fraction of individuals who have little to no risk of experiencing the event of interest. In this thesis, we focus on such settings with two different data structures. In early part of the thesis, we focus on the use of a cured fraction survival models performed in a population-based cancer registries. The limitations of statistical models which embodied the concept of a cured fraction of patients lack flexibility for modelling the survival distribution of the uncured group; lead to a not good fit when the survival drops rapidly soon after diagnosis and also when the survival is too high. In this study, a cure mixture model is enhanced by developing a dynamic sem...
Journal of Biopharmaceutical Statistics, 2019
In this study, a Bayesian approach was suggested to estimate a changepoint according to a covariate threshold when some patients never experienced the event of interest. Gibbs sampler algorithm with latent binary cure indicators was used to simplify the implementation of Markov chain Monte Carlo method. Then, the accuracy of new model was demonstrated by simulation studies to compute the point and interval estimates of parameters. Finally, an effective threshold was suggested in age at surgery time to experience the metastasis when the model was applied for a data set of breast cancer patients.
A new latent cure rate marker model for survival data
Annals of Applied Statistics, 2009
To address an important risk classification issue that arises in clinical practice, we propose a new mixture model via latent cure rate markers for survival data with a cure fraction. In the proposed model, the latent cure rate markers are modeled via a multinomial logistic regression and patients who share the same cure rate are classified into the same risk group. Compared to available cure rate models, the proposed model fits better to data from a prostate cancer clinical trial. In addition, the proposed model can be used to determine the number of risk groups and to develop a predictive classification algorithm.
A stochastic joint model for longitudinal and survival data with cure patients
International Journal of Tomography and Simulation, 2009
Many medical investigations generate both repeatedly-measured (longitudinal) biomarker and survival data. One of complex issues arises when investigating the association between longitudinal and time-to-event data when there are cured patients in the population, which leads to a plateau in the survival function S(t) after sufficient follow-up. Thus, usual Cox proportional hazard model Cox (1972) is not applicable since the proportional hazard assumption is violated. An alternative is to consider survival models incorporating a cure fraction. In this paper we present a new class of joint model for univariate longitudinal and survival data in presence of cure fraction. For the longitudinal model, a stochastic Integrated Ornstein-Uhlenbeck process will be presented. For the survival model a semiparametric survival function will be considered which accommodate both zero and non-zero cure fractions of the dynamic disease progression. Moreover, we consider a Bayesian approach which is mot...
Analysis of cure rate survival data under proportional odds model
Lifetime Data Analysis, 2011
Due to significant progress in cancer treatments and management in survival studies involving time to relapse (or death), we often need survival models with cured fraction to account for the subjects enjoying prolonged survival. Our article presents a new proportional odds survival models with a cured fraction using a special hierarchical structure of the latent factors activating cure. This new model has same important differences with classical proportional odds survival models and existing cure-rate survival models. We demonstrate the implementation of Bayesian data analysis using our model with data from the SEER (Surveillance Epidemiology and End Results) database of the National Cancer Institute. Particularly aimed at survival data with cured fraction, we present a novel Bayes method for model comparisons and assessments, and demonstrate our new tool's superior performance and advantages over competing tools.
Approximate Bayesian inference for mixture cure models
TEST
Cure models in survival analysis deal with populations in which a part of the individuals cannot experience the event of interest. Mixture cure models consider the target population as a mixture of susceptible and non-susceptible individuals. The statistical analysis of these models focuses on examining the probability of cure (incidence model) and inferring on the time-to-event in the susceptible subpopulation (latency model). Bayesian inference on mixture cure models has typically relied upon Markov chain Monte Carlo (MCMC) methods. The integrated nested Laplace approximation (INLA) is a recent and attractive approach for doing Bayesian inference. INLA in its natural definition cannot fit mixture models but recent research has new proposals that combine INLA and MCMC methods to extend its applicability to them 2;8;9. This paper focuses on the implementation of INLA in mixture cure models. A general mixture cure survival model with covariate information for the latency and the incidence model within a general scenario with censored and non-censored information is discussed. The fact that non-censored individuals undoubtedly belong to the uncured population is a valuable information that was incorporated in the inferential process.