Bottom line:  In ICU units many intubated patients who remove their own tubes do so while some type of physical restraint is in use.

A search of PubMed, CINAHL and EMBASE retrieved only studies of patients in intensive care.  No direct published evidence addresses efficacy of restraints at reducing self-extubations in patients outside of ICU units.  The following systematic review addresses association between use of restraints and self-extubation in patients on ICU units.

da Silva PS, Fonseca MC. Unplanned endotracheal extubations in the intensive care unit: systematic review, critical appraisal, and evidence-based recommendations. Anesth Analg. 2012;114(5):1003-1014.
Seventeen of the fifty studies that were included in this systematic review examined the incidence of unplanned extubation in physically restrained patients. The percentage of restrained patients under physical restraint at the time of unplanned extubations ranged from 25%” to 87%. Only one study identified the use of physical restraints as a risk factor for unplanned extubations on multivariate analysis (OR 3.1, 95% CI 1.71–5.7). The article concluded that use of physical restraints remains controversial.

Reviewed and updated 4/10/2014 ldt