Vertical modeling: A pattern mixture approach for competing risks modeling

Nicolaie, van Houwelingen and Putter have a new paper in Statistics in Medicine. This presents a new approach to modeling competing risks data. In essence this involves splitting the model in two parts: firstly model all cause survival, e.g. P(T >=t), secondly model P(D | T=t), the probability of a particular type of failure given a failure at time t, which they term as the relative hazard. The cause specific hazards and cumulative incidence functions can be retrieved under this formulation. A multinomial type model is applied to the relative hazards, with time dependency modelled using either piecewise constant functions or cubic splines. All cause survival can be modelled through any standard survival model e.g. a proportional hazards model. Vertical modeling provides a third approach particularly useful in cases where a proportional hazards assumption is not appropriate on either the cause-specific hazards (the classical approach) or on the sub-distribution hazard (Fine-Gray model).

Whilst it would be relatively straightforward to implement a vertical model using existing R packages, there are plans to include vertical modeling within the mstate package.