## Tuesday, 2 October 2012

### Applying competing risks regression models: an overview

Bernhard Haller, Georg Schmidt and Kurt Ulm have a new paper in Lifetime Data Analysis. This reviews approaches to building regression models for competing risks data. In particular, they consider cause specific hazard regression, subdistribution hazard regression (via both the Fine-Gray model and pseudo-observations), mixture models and vertical modelling. The distinction between mixture models and vertical modelling is the order of the conditioning. In mixture models, $P(D,T) = P(D)P(T|D)$ imply a separate time to event model is developed for each cause of death. Whereas in vertical modelling, $P(D,T) = P(T)P(D|T)$ meaning there is an overall "all cause" model for survival with a time dependent model for the conditional risk of different causes. Vertical modelling fits in much nearer to the standard hazard based formulation used in classical competing risks. Haller et al also prefer it to mixture modelling for computational reasons. The authors conclude however that vertical modelling's main purpose is as an exploratory tool to check modelling assumptions which may be made in a more standard competing risks model. They suggest that in a study, particularly a clinical trial, it would be more appropriate to use a Cox model either on the cause-specific hazards or on the sub-distribution hazard. The choice between these two models would depend on the particular research question of interest.