Study	Reason for exclusion
Coudroy 2019	This was a multicentre RCT of adults with severe acute hypoxaemic respiratory failure in an ICU setting. Participants were randomized to receive either HFNC alone or HFNC and NIV. We excluded this study as HFNC were used in both study arms.
Delorme 2017	This was a cross‐over RCT of adults with moderate respiratory distress in an ICU setting. Participants were given standard oxygen therapy up to baseline and then received HFNC with 3 different flow rates in a random order. We excluded this study as the control intervention (standard oxygen therapy) was delivered to all participants first, so this is not truly randomized.
Di Mussi 2016	This was a non‐randomized cross‐over study where participants were given HFNC, low‐flow oxygen and HFNC sequentially post‐extubation in an ICU setting. We excluded this study as it was not randomized.
Lemiale 2016	This was a multicentre study of critically‐ill immunocompromised adults receiving treatment for haematological malignancies or solid tumours. Participants were randomized to receive either NIV or oxygen therapy. Within the oxygen therapy group, the decision to use low‐flow oxygen or HFNC was at the discretion of the treating clinician. Therefore, randomization was not at the level required for this review (i.e. HFNC vs low‐flow oxygen therapy).
Liu 2019	This was an RCT of weaning and post‐extubation adults receiving invasive mechanical ventilation in an ICU setting. Participants were randomized to receive T‐tube, NIV or high‐flow oxygen via their endotracheal tube during a 2‐hour spontaneous breathing trial. If they passed the SBT, participants receiving T‐tube or NIV were moved onto low‐flow oxygen facemask whilst the high‐flow oxygen group were moved to HFNC. We excluded this study as the participants received different treatment prior to the initiation of oxygen via HFNC or low‐flow oxygen via facemask.
Pennisi 2019	This was an RCT of adults undergoing elective thoracotomic pulmonary lobar resection. Participants received oxygen either using HFNC or Venturi face mask. We excluded this study because very few participants received therapy in the ICU; most participants started therapy in the PACU before transfer to the surgical ward.
Sklar 2018	This was a cross‐over RCT of adults with cystic fibrosis with a clinical indication for NIV in a respiratory ward. Participants received standard oxygen up to baseline then HFNC and NIV in random order. We excluded this study as participants were treated in a respiratory ward, not an ICU.
Thille 2018	This was a multicentre RCT of adults post‐extubation at high risk of post‐extubation failure in an ICU setting. Participants were randomized to receive either HFNC alone or HFNC and NIV. We excluded this study as HFNC were used in both intervention arms.
Thille 2019	This was a multicentre RCT of adults post‐extubation who were at high risk of post‐extubation failure in an ICU setting. Participants were randomized to receive either HFNC alone or HFNC and NIV. We excluded this study as HFNC were used in both intervention arms.

HFNC: high‐flow nasal cannula(e)
ICU: intensive care unit
NIV: non‐invasive ventilation
PACU: post‐anaesthesia care unit
RCT: randomized controlled trial
SBT: spontaneous breathing trial