A flexible model for survival data with a cure rate: a Bayesian approach

A new flexible regression model with application to recovery probability Covid-19 patients

The aim of this study is to propose a generalized odd log-logistic Maxwell mixture model to analyze the effect of gender and age groups on lifetimes and on the recovery probabilities of Chinese individuals with COVID-19. We add new properties of the generalized Maxwell model. The coefficients of the regression and the recovered fraction are estimated by maximum likelihood and Bayesian methods. Further, some simulation studies are done to compare the regressions for different scenarios. Model-checking techniques based on the quantile residuals are addressed. The estimated survival functions for the patients are reported by age range and sex. The simulation study showed that mean squared errors decay toward zero and the average estimates converge to the true parameters when sample size increases. According to the fitted model, there is a significant difference only in the age group on the lifetime of individuals with COVID-19. Women have higher probability of recovering than men and individuals aged ≥ 60 years have lower recovered probabilities than those who aged < 60 years. The findings suggest that the proposed model could be a good alternative to analyze censored lifetime of individuals with COVID-19.

Bayesian mixture cure rate frailty models with an application to gastric cancer data

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 with gastric cancer to show the application of these models in real data analysis. The parameters and regression coefficients were estimated using the Metropolis with Gibbs sampling algorithm, so that this algorithm is one of the crucial techniques in Markov chain Monte Carlo simulation. A simulation study was also used to evaluate the performance of the Bayesian estimates to confirm the proposed models. Based on the results of the Bayesian inference, it was found that the model with generalized modified Weibull and hyper-Poisson distributions is a suitable model in practical study and also this model fits better than the model with Weibull and Gamma distributions.

Defective regression models for cure rate modeling with interval-censored data

Regression models in survival analysis are most commonly applied for right-censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval-censored mechanism is ignored. We present a cure rate defective model for interval-censored event-time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.

Bayesian cure rate models induced by frailty in survival analysis

Frailty models provide a convenient way of modeling unobserved dependence and heterogeneity in survival data which, if not accounted for duly, would result incorrect inference. Gamma frailty models are commonly used for this purpose, but alternative continuous distributions are possible as well. However, with cure rate being present in survival data, these continuous distributions may not be appropriate since individuals with long-term survival times encompass zero frailty. So, we propose here a flexible probability distribution induced by a discrete frailty, and then present some special discrete probability distributions. We specifically focus on a special hyper-Poisson distribution and then develop the corresponding Bayesian simulation, influence diagnostics and an application to real dataset by means of intensive Markov chain Monte Carlo algorithm. These illustrate the usefulness of the proposed model as well as the inferential results developed here.

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors

Our present work proposes a new survival model in a Bayesian context to analyze right-censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region-specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa.

Relaxed Poisson cure rate models

The purpose of this article is to make the standard promotion cure rate model (Yakovlev and Tsodikov, ) more flexible by assuming that the number of lesions or altered cells after a treatment follows a fractional Poisson distribution (Laskin, ). It is proved that the well-known Mittag-Leffler relaxation function (Berberan-Santos, ) is a simple way to obtain a new cure rate model that is a compromise between the promotion and geometric cure rate models allowing for superdispersion. So, the relaxed cure rate model developed here can be considered as a natural and less restrictive extension of the popular Poisson cure rate model at the cost of an additional parameter, but a competitor to negative-binomial cure rate models (Rodrigues et al., ). Some mathematical properties of a proper relaxed Poisson density are explored. A simulation study and an illustration of the proposed cure rate model from the Bayesian point of view are finally presented.

Bayesian bivariate generalized Lindley model for survival data with a cure fraction

The cure fraction models have been widely used to analyze survival data in which a proportion of the individuals is not susceptible to the event of interest. In this article, we introduce a bivariate model for survival data with a cure fraction based on the three-parameter generalized Lindley distribution. The joint distribution of the survival times is obtained by using copula functions. We consider three types of copula function models, the Farlie-Gumbel-Morgenstern (FGM), Clayton and Gumbel-Barnett copulas. The model is implemented under a Bayesian framework, where the parameter estimation is based on Markov Chain Monte Carlo (MCMC) techniques. To illustrate the utility of the model, we consider an application to a real data set related to an invasive cervical cancer study.

Mixture and non-mixture cure fraction models based on the generalized modified Weibull distribution with an application to gastric cancer data

The cure fraction models are usually used to model lifetime time data with long-term survivors. In the present article, we introduce a Bayesian analysis of the four-parameter generalized modified Weibull (GMW) distribution in presence of cure fraction, censored data and covariates. In order to include the proportion of "cured" patients, mixture and non-mixture formulation models are considered. To demonstrate the ability of using this model in the analysis of real data, we consider an application to data from patients with gastric adenocarcinoma. Inferences are obtained by using MCMC (Markov Chain Monte Carlo) methods.

The destructive negative binomial cure rate model with a latent activation scheme

A new flexible cure rate survival model is developed where the initial number of competing causes of the event of interest (say lesions or altered cells) follow a compound negative binomial (NB) distribution. This model provides a realistic interpretation of the biological mechanism of the event of interest as it models a destructive process of the initial competing risk factors and records only the damaged portion of the original number of risk factors. Besides, it also accounts for the underlying mechanisms that leads to cure through various latent activation schemes. Our method of estimation exploits maximum likelihood (ML) tools. The methodology is illustrated on a real data set on malignant melanoma, and the finite sample behavior of parameter estimates are explored through simulation studies.