Generalized log-logistic proportional hazard model: a non-penalty shrinkage approach

AbstractThis paper considers the pretest and shrinkage estimation methods for estimating regression parameters of the generalized log-logistic proportional hazard (PH) model. This model is a simple extension of the log-logistic model, which is closed under the PH relationship. The generalized log-logistic PH model also has attributes similar to those of the Weibull model. We consider this model for right-censored data when some parameters shrink to a restricted subspace. This subspace information on the parameters is used to shrink the unrestricted model estimates toward the restricted model estimates. We then optimally combine the unrestricted and restricted estimates in order to define pretest and shrinkage estimators. Although this estimation procedure may increase bias, it also reduces the overall mean squared error. The efficacy of the proposed model and estimation techniques are shown using a simulation study as well as an application to real data. We also compare the performance of generalized log-logistic, Weibull, and Cox PH models for unimodal and increasing hazards. The shrinkage estimator poses less risk than the maximum likelihood estimator when the shrinkage dimension exceeds two; this is shown through simulation and real data applications.Keywords: Generalized log-logistic distributionWeibull distributionCox proportional hazard modelmaximum likelihoodMonte Carlo simulationshrinkage and pretest estimators2020 Mathematics Subject Classification: 62N02 AcknowledgementsThe authors are thankful to the editor, associate editor, and two referees for their valuable and insightful comments, which have significantly enhanced the quality of this article.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research work was partially supported by NSERC through Discovery Grants to S Hossain (#419428) and SA Khan (#368532).