On Generalized Log-Logistic Model for Censored Survival Data

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

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.

Bayesian and Classical Inference for the Generalized Log-Logistic Distribution with Applications to Survival Data

The generalized log-logistic distribution is especially useful for modelling survival data with variable hazard rate shapes because it extends the log-logistic distribution by adding an extra parameter to the classical distribution, resulting in greater flexibility in analyzing and modelling various data types. We derive the fundamental mathematical and statistical properties of the proposed distribution in this paper. Many well-known lifetime special submodels are included in the proposed distribution, including the Weibull, log-logistic, exponential, and Burr XII distributions. The maximum likelihood method was used to estimate the unknown parameters of the proposed distribution, and a Monte Carlo simulation study was run to assess the estimators' performance. This distribution is significant because it can model both monotone and nonmonotone hazard rate functions, which are quite common in survival and reliability data analysis. Furthermore, the proposed distribution's flexibility and usefulness are demonstrated in a real-world data set and compared to its submodels, the Weibull, log-logistic, and Burr XII distributions, as well as other three-parameter parametric survival distributions, such as the exponentiated Weibull distribution, the three-parameter log-normal distribution, the three-parameter (or the shifted) log-logistic distribution, the three-parameter gamma distribution, and an exponentiated Weibull distribution. The proposed distribution is plausible, according to the goodness-of-fit, log-likelihood, and information criterion values. Finally, for the data set, Bayesian inference and Gibb's sampling performance are used to compute the approximate Bayes estimates as well as the highest posterior density credible intervals, and the convergence diagnostic techniques based on Markov chain Monte Carlo techniques were used.