Summary. Acute lung injury is a condition that is characterized by acute onset of severe hypoxaemia and bilateral pulmonary infiltrates. Patients typically require mechanical ventilation in an intensive care unit. Low tidal volume ventilation (LTVV), which is a time varying dynamic treatment regime, has been recommended as an effective ventilation strategy. This recommendation was based on the results of a randomized clinical trial designed to compare low versus high tidal volume strategies by the Acute Respiratory Distress Syndrome Network. After publication of the trial, some critics focused on the high non-adherence rates in the LTVV arm suggesting that non-adherence occurred because treating physicians felt that deviating from the prescribed regime would improve patients’ outcomes. We seek to address this controversy by estimating the survival distribution in the counterfactual setting where all patients assigned to LTVV followed the regime. Inference is based on a fully Bayesian implementation of Robins's G-computation formula. In addition to reanalysing data from the original trial, we also apply our methodology to data from a subsequent trial, which implemented the LTVV regime in both of its study arms and also suffered from non-adherence.