Appendix 1. Cochrane Oral Health Group's Trials Register search strategy

#1 (("open bite*" or openbite*)) AND (INREGISTER)
#2 ((malocclusion AND anterior):ti,ab) AND (INREGISTER)
#3 (apertognathi* or nonocclusion* or non‐occlusion*) AND (INREGISTER)
#4 (#1 or #2 or #3) AND (INREGISTER)
#5 (orthodontic*) AND (INREGISTER)
#6 ((orthopedic* or orthopaedic*)) AND (INREGISTER)
#7 ((Simoes or edgewise or "straight wire*" or Frankel or "bite block*" or "magnetic active corrector*" or crib* or "tongue thrust*" or "lip seal*" or "repelling magnet splint*")) AND (INREGISTER)
#8 ("myofunctional therap*" or "habit breaker*" or theraspoon or "thera spoon" or thera‐spoon)) AND (INREGISTER)
#9 ("intruder molar*" or intraoral or "intra oral" or intra‐oral or appliance* or device*) AND (INREGISTER)
#10 (#5 or #6 or #7 or #8 or #9) AND (INREGISTER)
#11 (#4 and #10) AND (INREGISTER)

Appendix 2. CENTRAL search strategy

#1 [mh ^"Open bite"]
#2 [mh ^Malocclusion]
#3 anterior
#4 #2 and #3
#5 ("open bite*" or openbite* or apertognathi* or nonocclusion* or non‐occlusion*)
#6 #1 or #4 or #5
#7 [mh Orthodontics]
#8 orthodontic*
#9 (orthopedic* or orthopaedic*)
#10 (Simoes or edgewise or "straight wire*" or Frankel or "bite block*" or "magnetic active corrector*" or crib* or "tongue thrust*" or "lip seal*" or "repelling magnet splint*")
#11 ("myofunctional therap*" or "habit breaker*" or theraspoon or "thera spoon" or thera‐spoon)
#12 "intruder molar*" or intraoral or "intra oral" or intra‐oral or appliance* or device*
#13 #7 or #8 or #9 or #10 or #11 or #12
#14 #6 and #13

Appendix 3. MEDLINE (OVID) search strategy

1. Open bite/
2. Malocclusion/
3. anterior$.tw.
4. 2 and 3
5. ("open bite$" or openbite$ or apertognathi$ or nonocclusion$ or non‐occlusion$).tw.
6. 1 or 4 or 5
7. exp Orthodontics/
8. orthodontic$.tw.
9. (orthopedic$ or orthopaedic$).tw.
10. (Simoes or edgewise$ or "straight wire$" or Frankel or "bite block$" or "magnetic active corrector$" or crib$ or "tongue thrust$" or "lip seal$" or "repelling magnet splint$").tw.
11. ("myofunctional therap$" or "habit breaker$" or theraspoon or "thera spoon" or thera‐spoon).tw.
12. ("intruder molar$" or intraoral or "intra oral" or intra‐oral or appliance$ or device$).tw.
13. or/7‐12
14. 6 and 13

The above subject search was linked to the Cochrane Highly Sensitive Search Strategy (CHSSS) for identifying randomised trials in MEDLINE: sensitivity maximising version (2008 revision) as referenced in Chapter 6.4.11.1 and detailed in box 6.4.c of the Cochrane Handbook for Systematic Reviews of Interventions, Version 5.1.0 [updated March 2011].

1. randomized controlled trial.pt.
2. controlled clinical trial.pt.
3. randomized.ab.
4. placebo.ab.
5. drug therapy.fs.
6. randomly.ab.
7. trial.ab.
8. groups.ab.
9. or/1‐8
10. exp animals/ not humans.sh.
11. 9 not 10

Appendix 4. EMBASE (OVID) search strategy

1. Malocclusion/
2. anterior$.tw.
3. 1 and 2
4. ("open bite$" or openbite$ or apertognathi$ or nonocclusion$ or non‐occlusion$).tw.
5. 3 and 4
6. exp Orthodontics/
7. orthodontic$.tw.
8. (orthopedic$ or orthopaedic$).tw.
9. (Simoes or edgewise$ or "straight wire$" or Frankel or "bite block$" or "magnetic active corrector$" or crib$ or "tongue thrust$" or "lip seal$" or "repelling magnet splint$").tw.
10. ("myofunctional therap$" or "habit breaker$" or theraspoon or "thera spoon" or thera‐spoon).tw.
11. ("intruder molar$" or intraoral or "intra oral" or intra‐oral or appliance$ or device$).tw.
12. or/6‐11
13. 5 and 12

The above subject search was linked to the Cochrane Oral Health Group filter for identifying RCTs in EMBASE via OVID:

1. random$.ti,ab.
2. factorial$.ti,ab.
3. (crossover$ or cross over$ or cross‐over$).ti,ab.
4. placebo$.ti,ab.
5. (doubl$ adj blind$).ti,ab.
6. (singl$ adj blind$).ti,ab.
7. assign$.ti,ab.
8. allocat$.ti,ab.
9. volunteer$.ti,ab.
10. CROSSOVER PROCEDURE.sh.
11. DOUBLE‐BLIND PROCEDURE.sh.
12. RANDOMIZED CONTROLLED TRIAL.sh.
13. SINGLE BLIND PROCEDURE.sh.
14. or/1‐13
15. (exp animal/ or animal.hw. or nonhuman/) not (exp human/ or human cell/ or (human or humans).ti.)
16. 14 NOT 15

Appendix 5. LILACS via BIREME Virtual Health Library search strategy

(Mh Open Bite or "open bite$" or "mordida$ abierta" or "mordida$ aberta") [Words] and (Mh Orthodontics or orthodontic$ or ortodoncia or ortodontia or Mh Orthopedics or orthopedic$ or orthopaedic$ or ortopedia Simoes or edgewise$ or "straight wire$" or Frankel or "bite block$" or "magnetic active corrector$" or crib$ or "tongue thrust$" or "lip seal$" or "repelling magnet splint$" or "myofunctional therap$" or "habit breaker$" or theraspoon or "thera spoon" or thera‐spoon or "intruder molar$" or intraoral or "intra oral" or intra‐oral or appliance$ or device$) [Words] and ((Pt randomized controlled trial OR Pt controlled clinical trial OR Mh randomized controlled trials OR Mh random allocation OR Mh double‐blind method OR Mh single‐blind method) AND NOT (Ct animal AND NOT (Ct human and Ct animal)) OR (Pt clinical trial OR Ex E05.318.760.535$ OR (Tw clin$ AND (Tw trial$ OR Tw ensa$ OR Tw estud$ OR Tw experim$ OR Tw investiga$)) OR ((Tw singl$ OR Tw simple$ OR Tw doubl$ OR Tw doble$ OR Tw duplo$ OR Tw trebl$ OR Tw trip$) AND (Tw blind$ OR Tw cego$ OR Tw ciego$ OR Tw mask$ OR Tw mascar$)) OR Mh placebos OR Tw placebo$ OR (Tw random$ OR Tw randon$ OR Tw casual$ OR Tw acaso$ OR Tw azar OR Tw aleator$) OR Mh research design) AND NOT (Ct animal AND NOT (Ct human and Ct animal)) OR (Ct comparative study OR Ex E05.337$ OR Mh follow‐up studies OR Mh prospective studies OR Tw control$ OR Tw prospectiv$ OR Tw volunt$ OR Tw volunteer$) AND NOT (Ct animal AND NOT (Ct human and Ct animal))) [Words]

Appendix 6. BBO via BIREME Virtual Health Library search strategy

(Mh Open Bite or "open bite$" or "mordida$ abierta" or "mordida$ aberta") [Words] and (Mh Orthodontics or orthodontic$ or ortodoncia or ortodontia or Mh Orthopedics or orthopedic$ or orthopaedic$ or ortopedia Simoes or edgewise$ or "straight wire$" or Frankel or "bite block$" or "magnetic active corrector$" or crib$ or "tongue thrust$" or "lip seal$" or "repelling magnet splint$" or "myofunctional therap$" or "habit breaker$" or theraspoon or "thera spoon" or thera‐spoon or "intruder molar$" or intraoral or "intra oral" or intra‐oral or appliance$ or device$) [Words] and ((Pt randomized controlled trial OR Pt controlled clinical trial OR Mh randomized controlled trials OR Mh random allocation OR Mh double‐blind method OR Mh single‐blind method) AND NOT (Ct animal AND NOT (Ct human and Ct animal)) OR (Pt clinical trial OR Ex E05.318.760.535$ OR (Tw clin$ AND (Tw trial$ OR Tw ensa$ OR Tw estud$ OR Tw experim$ OR Tw investiga$)) OR ((Tw singl$ OR Tw simple$ OR Tw doubl$ OR Tw doble$ OR Tw duplo$ OR Tw trebl$ OR Tw trip$) AND (Tw blind$ OR Tw cego$ OR Tw ciego$ OR Tw mask$ OR Tw mascar$)) OR Mh placebos OR Tw placebo$ OR (Tw random$ OR Tw randon$ OR Tw casual$ OR Tw acaso$ OR Tw azar OR Tw aleator$) OR Mh research design) AND NOT (Ct animal AND NOT (Ct human and Ct animal)) OR (Ct comparative study OR Ex E05.337$ OR Mh follow‐up studies OR Mh prospective studies OR Tw control$ OR Tw prospectiv$ OR Tw volunt$ OR Tw volunteer$) AND NOT (Ct animal AND NOT (Ct human and Ct animal))) [Words]

Appendix 7. SciELO via BIREME Virtual Health Library search strategy

(Mh Open Bite or "open bite$" or "mordida$ abierta" or "mordida$ aberta") and (Mh Orthodontics or orthodontic$ or ortodoncia or ortodontia or Mh Orthopedics or orthopedic$ or orthopaedic$ or ortopedia Simoes or edgewise$ or "straight wire$" or Frankel or "bite block$" or "magnetic active corrector$" or crib$ or "tongue thrust$" or "lip seal$" or "repelling magnet splint$" or "myofunctional therap$" or "habit breaker$" or theraspoon or "thera spoon" or thera‐spoon or "intruder molar$" or intraoral or "intra oral" or intra‐oral or appliance$ or device$)

Appendix 8. ClinicalTrials.gov search strategy

"anterior open bite"