Table 2 Criteria adopted for risk of bias assessment using Risk of Bias for in Non-randomized Studies of Exposures (ROBINS-E) tool

Bias due to confounding

Studies are considered to be at low risk of bias if they consider the initial magnitude of mandibular incisor crowding, data on incisor protrusion, or information about the maxillary arch, including change in the width or amount of crowding. Studies are considered to be at moderate risk of bias if they consider the sex of individuals in the confounding factors. Studies are considered to be at high risk of bias if adjustment factors are not reported

Bias in measurement of the exposure

Studies are at low risk of bias if a valid way of measuring mandibular incisor crowding is reported. Studies are considered to be at moderate risk of bias if the measurement of incisor crowding is not performed on plaster or digital models. Studies are at high risk of bias if the way of measuring crowding was not reported

Bias in selection of participants

Studies are considered at low risk of bias if mandibular incisor crowding monitoring started concurrently with patient assessment, the exposed cohort has representativeness of the assessed exposure, or in the presence of a control group. Studies are considered at moderate risk of bias if the exposed cohort has some representation of the assessed exposure. Studies are considered at high risk of bias if there is no control group or if the exposed cohort does not faithfully represent the assessed exposure

Bias in post-exposure interventions

Studies are at low risk of bias if no intervention in the mandibular or maxillary arch was performed, while at moderate risk of bias if any intervention in the maxillary arch to attenuate crowding was performed. Studies are considered high risk if any intervention was performed on the mandibular arch, even without the objective of mitigating crowding

Bias due to missing data

Studies are considered at low risk of bias if less than 10% of participants were excluded to missing data, while at moderate risk of bias if less than 20%. Studies with higher proportion (≥ 20%) are considered at high risk of bias

Bias in outcome measurement

Studies are at low risk of bias if raters are not aware of the exposure level of mandibular incisor crowding or method error has been statistically evaluated. Studies are considered at moderate risk of bias if no reliability analysis has been performed in the intra-examiner assessment. Studies are at high risk of bias if the outcome assessment is based solely on self-report, without external validation

Bias in selection of reported results

Studies are at low risk of bias if all data planned by the authors in the entire sample are analyzed. Studies are considered at moderate risk of bias if they present outcome measures for only part of the sample population. Studies are at high risk of bias if all maxillary arch stability values ​​for all recommendations are not presented

Overall risk of bias

If at least one domain was found at high risk of bias, the overall risk was considered high. If at least one domain is at some concerns, but no domains are at high risk, the overall risk was considered moderate. If all domains were at low risk of bias, the overall risk was considered low