Using the Box-Cox family of distributions to model censored data

Abstract

The study of the expected time until an event of interest is a recurring topic in different fields, suchas medical, economics and engineering. The Kaplan-Meier method and the Cox proportional hazardsmodel are the most used methodologies to deal with such kind of data. Nevertheless, in recent years,the generalised additive models for location, scale and shape (GAMLSS) models – which can be seen asdistributional regression and/or beyond the mean regression models – have been standing out as a resultof its highly flexibility and ability to fit complex data. GAMLSS are a class of semi-parametric regres-sion models, in the sense that they assume a distribution for the response variable, and any and all of itsparameters can be modelled as linear and/or non-linear functions of a set of explanatory variables. In thispaper, we present the Box-Cox family of distributions under the distributional regression framework asa solid alternative to model censored data.