Generalized log-logistic proportional hazard model with applications in survival analysis

Abstract

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.

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

“…4.3.1 Khan and Khosa's Generalized Log-Logistic Distribution Khan and Khosa (2015) proposed a generalized log-logistic distribution that belongs to the PH family and they described that it has properties identical to those of log-logistic, and tend to the Weibull in the limit, and they defined that these features enable the model to handle all kinds of hazard functions.…”

Survival model application for analysis of neonatal length of stay

“…The survival analysis plays a vital role in analyzing time-toevent data. 1,2) Among several proposed prediction models, the semiparametric Cox regression model has gained widespread use in the field of medical research because no distribution assumption is required of the probability of survival times and it usually fits the data well. [2][3][4] The "semiparametric" term is used in the Cox model since it does not assume any distribution of survival times (nonparametric), but it estimates the regression coefficient based on the model (parametric).…”

“…However, under certain circumstances, parametric models lead to more efficient and precise estimates than nonparametric models. 1,2) A distributional assumption should be required for a parametric model. If the distributional assumption is valid, a parametric model has smaller standard errors of the estimates, considers the influence of other correlative factors, and achieves a more precise and accurate result.…”

“…The survival analysis plays a vital role in analyzing time-toevent data [ 1 , 2 ]. Among several proposed prediction models, the semiparametric Cox regression model has gained widespread use in the field of medical research because no distribution assumption is required of the probability of survival times and it usually fits the data well [ 2 - 4 ].…”

“…However, under certain circumstances, parametric models lead to more efficient and precise estimates than nonparametric models [ 1 , 2 ]. A distributional assumption should be required for a parametric model.…”