Modelling two cause-specific hazards of competing risks in one cumulative proportional odds model?

Competing risks extend standard survival analysis to considering time-to-first-event and type-of-first-event, where the event types are called competing risks. The competing risks process is completely described by all cause-specific hazards, ie, the hazard marked by the event type. Separate Cox models for each cause-specific hazard are the standard approach to regression modelling, but they come with the interpretational challenge that there are as many regression coefficients as there are competing risks. An alternative approach is to directly model the cumulative event probabilities, but again, there will be as many models as there are competing risks. The aim of this paper is to investigate the usefulness of a third alternative. Proportional odds modelling of all cause-specific hazards summarizes the effect of one covariate on "opposing" competing outcomes in one regression coefficient. For instance, if the competing outcomes are hospital death and alive discharge from hospital, the modelling assumption is that a covariate affects both outcomes in opposing directions, but the effect size is of the same absolute magnitude. We will investigate the interpretational aspects of the approach analysing a data set on intensive care unit patients using parametric methods.