## 2 Materials and Methods
### Data Analysis  
2.5.1. Sample Size Calculation  
Since this study was designed as a pilot study, to initially evaluate safety of a new formulation, as well as exploring parameters of efficacy, a convenience sample of 30 patients (15 patients per group) was selected.  
2.5.2. Data Analysis  
For all variables, the patient was the statistical unit for the analysis. PROs were determined as the average values for each of the nine questionnaire items. Additionally, calculations were made for total anaerobic counts, counts of individual pathogens, proportions of microbiota (pathogen counts relative to total counts) and the presence or absence of each pathogen. The primary outcome variable was safety (adverse events and PROs). Secondary outcomes were the mean values and changes in clinical (PII, BOMP, GBI, PD, REC and CAL) and microbiological outcomes, staining (GMSI), dentin hypersensitivity and compliance.  
Categorical outcome data were compared using the Chi-square test or [PERSON]'s exact test. The Shapiro-Wilk goodness-of-fit test was employed to assess the normal distribution of quantitative variables. Differences between groups at baseline, 6 weeks and 12 weeks, as well as changes from baseline to 6 weeks, baseline to 12 weeks and 6 weeks to 12 weeks were analyzed using the Student's \(t\)-test or Mann-Whitney U test for quantitative outcomes. Statistical significance was set at \(p<0.05\) (IBM(r) SPSS(r) Statistics 27.0, IBM Corporation, Armonk, NY, USA).  
2.5.3. Calibration  
Intra-examiner calibration for periodontal variables was carried out on two patients and three evaluations per patient were completed with a difference of, at least, one hour. Calibration for PII (unweighted agreement: 85.5%; kappa = 0.80; 95% confidence interval--95% CI [0.74; 0.85]; \(p<0.001\)), BOMP (unweighted agreement: 89.1%; kappa = 0.58; 95% CI [0.46; 0.71]; \(p<0.001\)), PD (intraclass correlation coefficient--ICC = 0.80; 95% CI [0.74; 0.84]; \(p<0.001\)) and REC (ICC = 0.82; 95% CI [0.77; 0.85]; \(p<0.001\)).  
3. Results  
Recruitment for this study started on September 2021 and the last follow-up visit was carried out in June 2022. During the screening phase, 58 subjects were selected, but 30 participants were finally included in this study, 15 in each group. The reasons for excluding 28 subjects are listed in the study flow chart Figure 1.  
All included participants (n = 30) attended the three visits (baseline, 6 weeks and 12 weeks). No patient was lost to follow-up. The main characteristics of this sample are reported in Table 1, showing no statistically significant differences between groups in terms of age, sex, smoking habit, systemic diseases, chronic medication intake, psychological stress or allergies.  
Figure 1: Flow chart of the study.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{2}{c}{**Test**} & \multicolumn{2}{c}{**Control**} & \multicolumn{1}{c}{\(p\)**-Value**} \\  & **n** & \%** & **n** & **\%** & **\%** & \\ \hline
**Sex** & & & & & & \\ Male & 6 & 40 & 4 & 26.7 & 0.439 \\ Female & 9 & 60 & 11 & 73.3 & \\
**Tobacco** & & & & & \\ Non-smoker & 14 & 93.3 & 14 & 93.3 & 1.000 \\ Smoker & 1 & 6.7 & 1 & 6.7 & \\
**Systemic Diseases** & & & & & \\ No & 10 & 66.7 & 12 & 80 & 0.409 \\ Yes & 5 & 33.3 & 3 & 20 & \\
**Medication** & & & & & \\ No Medication & 7 & 46.7 & 7 & 46.7 & 1.000 \\ Medication & 8 & 53.3 & 8 & 53.3 & \\
**Stress** & & & & & \\ No Stress & 13 & 86.7 & 12 & 80 & 0.624 \\ Stress & 2 & 13.3 & 3 & 20 & \\
**Allergies** & & & & & \\ No Allergies & 13 & 86.7 & 13 & 86.7 & 1.000 \\ Allergies & 2 & 13.3 & 2 & 13.3 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Baseline demographic information.