The Use of Split Exponential and Split Weibull Analyse Survival Data With Long Term Survivors (original) (raw)
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Statistics, Optimization and Information Computing, 2021
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. This article considers frequentist and Bayesian methods to estimate the unknown model parameters of the exponentiated Weibull (EW) distribution considering right-censored survival data with a cure fraction and covariates. The EW distribution is as an extension to the Weibull distribution by considering an additional shape parameter to the model. We consider four types of cure fraction models: the mixture cure fraction (MCF), the nonmixture cure fraction (NMCF), the complementary promotion time cure (CPTC), and the cure rate proportional odds (CRPO) models. Bayesian inferences are obtained by using MCMC (Markov Chain Monte Carlo) methods. A simulation study was conducted to examine the performance of the maximum likelihood estimators for different sample sizes. Two real datasets were considered to illustrate the applicability of the proposed model. The EW distribution and its sub-models have the flexibility to accommodate different shapes for the hazard function and should be an attractive choice for survival data analysis when a cure fraction is present.
A Study of Log-Logistic Model in Survival Analysis
Biometrical Journal, 1999
In survival analysis when the mortality reaches a peak after some finite period and then slowly declines, it is appropriate to use a model which has a nonmonotonic failure rate. In this paper we study the log-logistic model whose failure rate exhibits the above behavior and its mean residual life behaves in the reverse fashion. The maximum likelihood estimation of the parameters is examined and it is proved analytically that unique maximum likelihood estimates exist for the parameters. A lung cancer data set is analyzed. Confidence intervals for the parameters as well as for the critical points of the failure rate and mean residual life functions are obtained for the high performance status (PS) and low PS subgroups, where the term performance status is a measure of general medical status.
On the use and utility of the Weibull model in the analysis of survival data
Controlled Clinical Trials, 2003
In the analysis of survival data arising in clinical trials, Cox's proportional hazards regression model (or equivalently in the case of two treatment groups, the log-rank test) is firmly established as the accepted, statistical norm. The wide popularity of this model stems largely from extensive experience in its application and the fact that it is distribution free-no assumption has to be made about the underlying distribution of survival times to make inferences about relative death rates. However, if the distribution of survival times can be well approximated, parametric failure-time analyses can be useful, allowing a wider set of inferences to be made. The Weibull distribution is unique in that it is the only one that is simultaneously both proportional and accelerated so that both relative event rates and relative extension in survival time can be estimated, the latter being of clear clinical relevance. The aim of this paper is to examine the use and utility of the Weibull model in the analysis of survival data from clinical trials and, in doing so, illustrate the practical benefits of a Weibullbased analysis.
The log-normal, log-logistic and Weibull distributions are commonly utilized to model survival data. Unimodal (or non-monotone) failure rate functions are modeled using the lognormal and the log-logistic families, whereas monotone failure rate functions are modeled using the Weibull family. The growing availability of survival data with a variety of features encourages statisticians to propose more flexible parametric models that can accommodate both monotone (increasing or decreasing), and non-monotone (unimodal or bathtub) failure rate functions. One such model is the generalized log-logistic distribution which not only accommodates unimodal failure rates but also allows for a monotone and non-monotone failure rate functions. This distribution has shown to have a lot of potential in univariate analysis of survival data. However, many studies are primarily concerned with determining the link between survival time and one or more explanatory variables. This leads to the study of hazard-based regression models in survival and reliability analysis, which can be formulated in a variety of ways. One such method concerns formulating
Generalized log-logistic proportional hazard model with applications in survival analysis
Journal of Statistical Distributions and Applications, 2016
Proportional hazard (PH) models can be formulated with or without assuming a probability distribution for survival times. The former assumption leads to parametric models, whereas the latter leads to the semi-parametric Cox model which is by far the most popular in survival analysis. However, a parametric model may lead to more efficient estimates than the Cox model under certain conditions. Only a few parametric models are closed under the PH assumption, the most common of which is the Weibull that accommodates only monotone hazard functions. We propose a generalization of the log-logistic distribution that belongs to the PH family. It has properties similar to those of log-logistic, and approaches the Weibull in the limit. These features enable it to handle both monotone and nonmonotone hazard functions. Application to four data sets and a simulation study revealed that the model could potentially be very useful in adequately describing different types of time-to-event data.
Journal of Economics and Administrative Sciences
The Log-Logistic distribution is one of the important statistical distributions as it can be applied in many fields and biological experiments and other experiments, and its importance comes from the importance of determining the survival function of those experiments. The research will be summarized in making a comparison between the method of maximum likelihood and the method of least squares and the method of weighted least squares to estimate the parameters and survival function of the log-logistic distribution using the comparison criteria MSE, MAPE, IMSE, and this research was applied to real data for breast cancer patients. The results showed that the method of Maximum likelihood best in the case of estimating the parameters of the distribution and survival function
Zenodo (CERN European Organization for Nuclear Research), 2022
This paper develops the Weibull distribution by adding a new parameter to the classical distribution, the generalized power generalized Weibull mixture cure model distribution, and it's extremely useful when modeling survival data with parameter hazard rate function shape. As a result, there is greater flexibility in analyzing and modeling various data types. The essential mathematical and statistical characteristics of the proposed distribution are generated. In this paper. Many well-known life time special sub-models, such as Rayleigh, Power generalized Weibull, Nadarajah-Haghighi, Weibull, and Exponential, are included in the proposed distribution. The maximum likelihood distribution method was used to estimate the unknown parameters of the proposed distribution; and the effectiveness of the estimators was determined using Markov Chain Monte Carlo simulation study. The Markov Chain Monte Carlo used to develop diagnostic methods. This distribution is important because it can model nonmonotone and monotone, upside-down bathtub, and bathtub hazard rate functions. All of which are widely used in survival and efficiency data analysis. Moreover, the flexibility and effectiveness of the proposed distribution are demonstrated in a real-world data set and compared to its sub models. Based on the goodness of fit and information criterion value, the proposed distribution is accurate. Finally, the estimation of the data set is determined using Bayesian inference and Gibb's sampling performance. In addition to Bayes estimates, the highest posterior density reliable intervals and Markov Chain Monte Carlo convergence diagnostic technique were used.
The generalized exponential cure rate model with covariates
Journal of Applied Statistics, 2010
In this article, we consider a parametric survival model that is appropriate when the population of interest contains long-term survivors or immunes. The model referred to as the cure rate model was introduced by Boag [1] in terms of a mixture model that included a component representing the proportion of immunes and a distribution representing the life times of the susceptible population. We propose a cure rate model based on the generalized exponential distribution that incorporates the effects of risk factors or covariates on the probability of an individual being a long-time survivor.
A Logistic Weibull Mixture Models with Long-Term Survivors
2009
1,2,3&4 Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia Email: mrizam@putra.upm.edu.my, isa@putra.upm.edu.my, nakma@putra.upm.edu.my, desirahmatina@yahoo.com Abstract. The mixture model postulates a mixed population with two types of individuals, the susceptible and long-term survivors. The susceptibles are at the risk of developing the event under consideration. However, the long-term survivors or immune individuals will never experience the event. This paper focuses on the covariates associated with individuals such as age, surgery and transplant related to the probability of being immune in a logistic Weibull model and to evaluate the effect of heart transplantation on subsequent survival.