Northern Ireland group meeting: The XGDTL family of survival distributions

The Northern Ireland group held a meeting on Wednesday, February 20, 2019 at 1pm in the  Peter Froggatt Centre in Queen's University of Belfast. The speaker was Professor Gilbert MacKenzie, formerly of the University of Limerick, Ireland and ENSAI, Rennes, France. 

Much survival data do not follow the Proportional Hazards (PH) paradigm, but PH models are ubiquitous and are often employed uncritically. There are several remedies to this problem and Professor MacKenzie described one based on the extended GTDL family of survival distributions (XGTDL) which is based on the logistic function. The basic GTDL family contains three models: (a) a logistic PH model, the LPH, (b) a logistic accelerated life model, the LAL, and (c) the TDL model which is not PH nor accelerated life. The model is wholly parametric and become cure rate models for negative values of the shape parameter., Although this family can handle a wide range of survival data there are some types, such as Crossing Hazards data, with which it could not cope.

Professor MacKenzie then showed a motivating example based on a gastric cancer randomized control trial with crossing hazards data. His analysis showed that an excellent fit was obtained when an extended GTDL was used. The extensions required were: 1. Gamma Frailty (GF) and 2 Modelling the shape parameter as well as the scale parameter (called MPR Modelling by Burke and MacKenzie, 2017 in their Biometrics paper.) Prof. MacKenzie considered a third extension - that of adding a Dispersion Model to the frailty variance (DM). Orthodox frailty models assumed that the frailty variance was constant across subjects but this could be generalised to a third regression giving additional flexibility.  Accordingly, the next step was to implement these three extensions in the basic GTDL family.

With the extended family derived, Professor MacKenzie included an extended Weibull model as a comparator and fitted the various variants (eg, LPH, LPH+GF, LPH+MPR, LPH+MPR+GF and LPH+MPR+GF+DM of all four models, fitting 20 models in all to non-PH treatment survival data from the Northern Ireland Lung Cancer Study. The pattern to emerge was that GF models were better than basic models and MPR models were generally better than GF frailty models. In the TDL, LAL and Weibull classes the best model was the (TDL or LAL or Weibull)+MPR+GF, and in the LPH  class the best model was the LPH+MPR. Overall, the Weibull+MPR+GF was best with an AIC of 3875.89 and 11 parameters fitted. However, the fits of the competing models, as judged by the AIC, were close and several dealt satisfactorily with the non-PH data. Professor MacKenzie finished by warning against becoming too devoted to a particular model or model class.

The talk was well received and led to a discussion which covered, inter alia, the selection of covariates with multiple linear predictors, the selection of information criteria and issues surrounding selecting the best model among different classes of model.

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