Abstract
In this paper, we formulate and develop a log-linear model using a new distribution called the log-gamma-logistic. We show that the new regression model can be applied to censored data since it represents a parametric family of models that includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distributions of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to modified deviance residuals in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models.
Highlights
The log-logistic distribution is widely used in survival analysis and it is an alternative to the Weibull and lognormal distributions since it presents a hazard rate function that increases, reaches a peak after some finite period and declines gradually
The log-gamma logistic (LGL) model presents a better fit to the current data. According to these plots, it can be noted that the LGL regression model can be used to predict the chances of survival of a patient diagnosed as suffering from acute myeloid leukemia (AML)
The new model extends several distributions widely used in the lifetime literature and it is more flexible than the Weibull, log-logistic and log-normal distributions
Summary
The log-logistic distribution is widely used in survival analysis and it is an alternative to the Weibull and lognormal distributions since it presents a hazard rate function (hrf) that increases, reaches a peak after some finite period and declines gradually. One way to study the effects of the explanatory variables on the lifetime or survival time is through a regression location-scale model, known as the accelerated lifetime model. We define a location-scale regression model using the GLL distribuition called the log-gamma-logistic (LGL) regression model. Sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution.
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