AMBER 2020.

Study characteristics
Methods	Parallel RCT, individuals randomised
Data	UK, secondary care settings. Not all participants in the host trial that took part in this embedded trial. Only those who had yet to complete the study at the time of the SWAT set up. Total n = 64, age NR; sex NR.
Comparisons	Intervention group received a tested a theoretically informed letter sent with the questionnaire Control group received a standard letter
Outcomes	Questionnaires returned
Notes	6 months
Risk of bias
Item	Authors' judgement	Support for judgement
Allocation concealment?	Unclear	No information of the nested RCT was provided.
Adequate sequence generation?	No	According to the authors, the randomisation list was generated and was not concealed.
Blinding of participants and personnel?	Unclear	Participants were unaware if they were receiving a standard or theory‐based cover letter but may have noticed from earlier letters that it had a different “tone”
Blinding of outcome assessment?	Unclear	No information of the nested RCT was provided.
Incomplete outcome data addressed? All outcomes	Unclear	No concerns raised.
Free of selective outcome reporting?	Unclear	No concerns raised.
Other sources of bias	No	No further concerns raised.
Overall Risk of Bias	Unclear	Unclear