Two-part model for ventilator-free days in a cluster randomized cross-over clinical trial

Ventilator-free days, which combine mortality and duration of mechanical ventilation into a single measure, are often considered as a primary endpoint in clinical trials involving critically ill patients. Despite the composite nature, ventilator-free days are commonly analyzed as continuous or count data with no distinction between a zero score from a patient who dies and a zero score from a patient who is alive but still on ventilator. In this study, we propose a two-part statistical model to compare the effects of two airway management strategies on mortality and duration of mechanical ventilation among patients with out-of-hospital cardiopulmonary arrest in a cluster randomized cross-over clinical trial.

In the proposed two-part model, failure to achieve return of spontaneous circulation (ROSC), death after ROSC, and survival are modeled in the first part; the number of ventilator-free days conditional on survival is modeled in the second part. To account for the cluster randomized cross-over design, each part also includes a random cluster effect that is assumed to be either shared or independent across the two parts. We conducted a simulation study to evaluate type I error rates and power of the two-part shared random cluster effect model and the mis-specified two-part model with independent random cluster effects in detecting an overall intervention effect.

We found that parameter estimates were similar whether the random cluster effects were assumed to be shared or independent across the two parts whereas the shared random cluster effect approach showed higher log-likelihood, but lower Akaike information criterion (AIC) and Bayesian information criterion (BIC). Initial laryngeal tube insertion reduced odds of failing to achieve ROSC and marginally decreased odds of death after ROSC compared with initial endotracheal intubation in Part 1, whereas initial laryngeal tube insertion was not associated with duration of mechanical ventilation among patients alive in Part 2. The shared random cluster effect approach showed higher odds of death associated with lower odds of being ventilator-free. This confirms the expectation that a patient who is less likely to achieve ROSC and survive is more likely to require prolonged mechanical ventilation if the patient indeed survives during hospitalization. Our simulation studies found that the two-part model with a shared random cluster effect yielded type I error rates close to the nominal level. The two-part shared random cluster effect model has better power to detect an overall intervention effect when intervention effects are present in both parts rather than in only one of the two part.

The proposed two-part model provides a more comprehensive assessment of intervention effects on ventilator-free days in critical care trials. Researchers and clinicians can obtain greater insights with this approach about the direction and magnitude of the intervention effects on mortality, ROSC, and duration of mechanical ventilation.