Background Traditional methods in survival analysis inadequately summarise the timing of outcomes in critical care trials because they accommodate only one clinical endpoint. We sought to develop an analytical approach to detect differences when there are two clinical endpoints where one may preclude the other.

Methods We used a mixture of parametric survival distributions that belong to the three-parameter generalised γ family (generalised γ, γ, Weibull, log-normal, and exponential) to model the timing and frequency of two clinical endpoints jointly. Study outcomes were hospital mortality at 60 days and time to unassisted breathing (UAB) at 28 days. We used data from a trial of methylprednisolone vs placebo in 180 critically ill patients with persistent ARDS to show our approach.

Results The best model to fit these data was a mixture of log-normal distributions. Patients who received methylprednisolone achieved UAB earlier than did those who received placebo (p=0.05); however, this effect decreased over time: by day 5, 55% more patients (95% CI 16% to 79%) achieved UAB in the methylprednisone group while by day 20, 25% more patients (95% CI 6% to 42%) achieved UAB. The overall probability of achieving UAB was similar between both study groups (p=0.82), as were the times to death (p=0.15).

Conclusions Times of UAB between the study groups were not proportional over time and are unlikely to be proportional in any trial where duration of mechanical ventilation is affected. Furthermore, our approach can easily accommodate mixtures of several well-known parametric distributions under a single comprehensive family, which simplifies hypothesis testing.