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Title: Penalized power-generalized Weibull distributional regression Authors:  Shirin Moghaddam - University of Limerick (Ireland)
Kevin Burke - University of Limerick (Ireland)
Laura McQuaid - University of Limerick (Ireland) [presenting]
Abstract: Multi-parameter regression (MPR) modelling refers to the approach whereby covariates enter a parametric model through multiple distributional parameters simultaneously (e.g., scale and shape parameters), allowing more complex covariate effects to be captured. Standard techniques allow for one parameter, usually the scale, to be a function of covariates but this may result in the potential impact of the shape parameter on the hazard to be lost. Having multiple parameters depending on covariates may lead to a computationally expensive variable selection procedure. On the other hand, penalized estimation procedures such as the least absolute shrinkage and selection operator (LASSO) and adaptive LASSO are commonly used to perform variable selection and estimation simultaneously but they have primarily been developed for classical regression problems where covariates enter only through a single distributional parameter. We introduce a flexible penalized multi-parameter modelling framework and investigate its performance through simulation studies and real data analysis. We particularly focus on the three-parameter (one scale, two shapes) Power Generalized Weibull (PGW) distribution. The PGW distribution encompasses key shapes of hazard function (constant, increasing, decreasing, up then down, down then up) and a variety of common survival distributions (Weibull, log-logistic, Gompertz). This allows for a highly flexible approach for modelling survival data.