The XGTDL family of survival distributions

Non-PH parametric survival modelling is developed within the framework of the mul tiple logistic function. The family considered comprises three basic models: (a) a PH model, (b) an accelerated life model and (c) a model which is non-proportional haz ards and non-accelerated life. The last model, the generalised time-dependent logistic model was described first by the author in 1996 and this model gives its name to the entire family. The family is generalised by means of a Gamma frailty extension which is shown to accommodate crossing hazards data. A further generalisation is the inclusion of a dispersion model. These extensions lead naturally to the concept of a multi-parameter regression model described by Burke and MacKenzie in which the scale and shape parameters are modelled simultaneously as functions of covariates. Where possible, we include the MPR extension in the XGTDL family. Following a simulation study, the new models are used to analyse two sets survival data and the methods are discussed.