Which trial do we need? Combination antimicrobial therapy for hospital-acquired bacterial pneumonia caused by Pseudomonas aeruginosa.

Meropenem therapy will be open-label, while tobramycin or placebo will be administered in a double-blind fashion. The primary trial endpoint will be a composite hierarchical outcome of 1) 28-day all-cause mortality, 2) ventilator-free days, and 3) modified time to clinical stability, evaluated using a win ratio methodology (see below). Secondary trial outcomes will include frequency of safety events (acute kidney injury), resolution of circulatory shock, recurrent HABP, and emergence of meropenem resistance both during treatment and in cases of recurrent infection. Using simulation studies to inform sample size calculations, we estimate that recruitment of 130 patients per treatment arm would provide at least 80% power to detect a win ratio of 1.50 while preserving a two-sided type 1 error rate of 0.05.