On the Log-Logistic Distribution and Its Generalizations: A Survey

Muse, Abdisalam Hassan; Mwalili, Samuel; Ngesa, Oscar

doi:10.5539/ijsp.v10n3p93

Cited by 21 publications

(14 citation statements)

References 93 publications

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“…Mansour [ 22 ] defined one new version of the LL model in his research. Muse et al [ 23 ] reviewed recent research on LL distribution and its generalizations.…”

Section: Introductionmentioning

confidence: 99%

Applications of Bladder Cancer Data Using a Modified Log-Logistic Model

Kayid

2022

Applied Bionics and Biomechanics

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In information science, modern and advanced computational methods and tools are often used to build predictive models for time-to-event data analysis. Such predictive models based on previously collected data from patients can support decision-making and prediction of clinical data. Therefore, a new simple and flexible modified log-logistic model is presented in this paper. Then, some basic statistical and reliability properties are discussed. Also, a graphical method for determining the data from the log-logistic or the proposed modified model is presented. Some methods are applied to estimate the parameters of the presented model. A simulation study is conducted to investigate the consistency and behavior of the discussed estimators. Finally, the model is fitted to two data sets and compared with some other candidates.

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“…Mansour [ 22 ] defined one new version of the LL model in his research. Muse et al [ 23 ] reviewed recent research on LL distribution and its generalizations.…”

Section: Introductionmentioning

confidence: 99%

Applications of Bladder Cancer Data Using a Modified Log-Logistic Model

Kayid

2022

Applied Bionics and Biomechanics

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“…As a baseline hazard rate, many probability distributions for the number of competing causes of the event of interest have been offered. An interesting survey for the classical distributions and their survey can be referred to [30][31][32][33][34][35]. Table 1 shows the chronological review on the competing risk models under progressive censoring scheme with different baseline distributions.…”

Section: Introductionmentioning

confidence: 99%

Estimation for Akshaya Failure Model with Competing Risks under Progressive Censoring Scheme with Analyzing of Thymic Lymphoma of Mice Application

Abushal

Kumar²,

Muse³

et al. 2022

Complexity

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In several experiments of survival analysis, the cause of death or failure of any subject may be characterized by more than one cause. Since the cause of failure may be dependent or independent, in this work, we discuss the competing risk lifetime model under progressive type-II censored where the removal follows a binomial distribution. We consider the Akshaya lifetime failure model under independent causes and the number of subjects removed at every failure time when the removal follows the binomial distribution with known parameters. The classical and Bayesian approaches are used to account for the point and interval estimation procedures for parameters and parametric functions. The Bayes estimate is obtained by using the Markov Chain Monte Carlo (MCMC) method under symmetric and asymmetric loss functions. We apply the Metropolis–Hasting algorithm to generate MCMC samples from the posterior density function. A simulated data set is applied to diagnose the performance of the two techniques applied here. The data represented the survival times of mice kept in a conventional germ-free environment, all of which were exposed to a fixed dose of radiation at the age of 5 to 6 weeks, which was used as a practice for the model discussed. There are 3 causes of death. In group 1, we considered thymic lymphoma to be the first cause and other causes to be the second. On the base of mice data, the survival mean time (cumulative incidence function) of mice of the second cause is higher than the first cause.

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“…Extensive efforts have been made over the last decades to extend classical distributions to use as a baseline distribution for parametric hazard-based regression models. Many modifications to the LL distribution have been introduced to make it more adaptable to a wide range of hazard shapes [ 12 – 16 ]. The generalized log-logistic distribution (GLL) is one such model, which modifies the log-logistic distribution by inducing an additional shape parameter [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

A Flexible Bayesian Parametric Proportional Hazard Model: Simulation and Applications to Right-Censored Healthcare Data

Muse¹,

Ngesa²,

Mwalili

et al. 2022

Journal of Healthcare Engineering

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Survival analysis is a collection of statistical techniques which examine the time it takes for an event to occur, and it is one of the most important fields in biomedical sciences and other variety of scientific disciplines. Furthermore, the computational rapid advancements in recent decades have advocated the application of Bayesian techniques in this field, giving a powerful and flexible alternative to the classical inference. The aim of this study is to consider the Bayesian inference for the generalized log-logistic proportional hazard model with applications to right-censored healthcare data sets. We assume an independent gamma prior for the baseline hazard parameters and a normal prior is placed on the regression coefficients. We then obtain the exact form of the joint posterior distribution of the regression coefficients and distributional parameters. The Bayesian estimates of the parameters of the proposed model are obtained using the Markov chain Monte Carlo (McMC) simulation technique. All computations are performed in Bayesian analysis using Gibbs sampling (BUGS) syntax that can be run with Just Another Gibbs Sampling (JAGS) from the R software. A detailed simulation study was used to assess the performance of the proposed parametric proportional hazard model. Two real-survival data problems in the healthcare are analyzed for illustration of the proposed model and for model comparison. Furthermore, the convergence diagnostic tests are presented and analyzed. Finally, our research found that the proposed parametric proportional hazard model performs well and could be beneficial in analyzing various types of survival data.

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On the Log-Logistic Distribution and Its Generalizations: A Survey

Cited by 21 publications

References 93 publications

Applications of Bladder Cancer Data Using a Modified Log-Logistic Model

Applications of Bladder Cancer Data Using a Modified Log-Logistic Model

Estimation for Akshaya Failure Model with Competing Risks under Progressive Censoring Scheme with Analyzing of Thymic Lymphoma of Mice Application

A Flexible Bayesian Parametric Proportional Hazard Model: Simulation and Applications to Right-Censored Healthcare Data

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