Here is the design of a clinical trial:

Official Title: Influence of Probiotics on Clinical Parameters, the Oral Microbiome and the Immune System During an Orthodontic Treatment: a Prospective, Double-blind, Randomized, Clinical Study

Included conditions:
- Gingivitis
- Orthodontic Appliance Complication

Study Armgroups:
- {'label': 'Lactobacillus reuteri Prodentis®-lozenges', 'type': 'ACTIVE_COMPARATOR', 'interventionNames': ['Dietary Supplement: Lactobacillus reuteri Prodentis®-lozenges (DSM 17938, ATCC PTA 5289)']}
- {'label': 'Placebo-lozenges (BioGaia)', 'type': 'PLACEBO_COMPARATOR', 'interventionNames': ['Dietary Supplement: Placebo-lozenges (BioGaia)']}

Interventions:
- {'type': 'DIETARY_SUPPLEMENT', 'name': 'Lactobacillus reuteri Prodentis®-lozenges (DSM 17938, ATCC PTA 5289)', 'description': 'Supplementary intake of Lactobacillus reuteri Prodentis®-lozenges (DSM 17938, ATCC PTA 5289) 2 times per day for 12 weeks', 'armGroupLabels': ['Lactobacillus reuteri Prodentis®-lozenges']}
- {'type': 'DIETARY_SUPPLEMENT', 'name': 'Placebo-lozenges (BioGaia)', 'description': 'Placebo-lozenges (BioGaia) 2 times per day for 12 weeks', 'armGroupLabels': ['Placebo-lozenges (BioGaia)']}

Primary Outcomes:
- {'measure': 'Gingival Index (GI)', 'description': 'Primary endpoint is the change of the Gingival Index (GI) from baseline to week 4. The measurement of GI is described by Löe et al, which scores the gingival condition according to the defined criteria. The scores will be measured at four sites per tooth, added and divided by four to obtain the "GI for the tooth"-Index. We will use the \'GI for the tooth\' described there, but only for those teeth with fixed ortodontic brackets. The \'GI for the patient\' is then the mean of the GIs for the teeth.\n\nCRITERIA FOR THE GINGIVAL INDEX SYSTEM\n\n0 = Absence of inflammation.\n\n1. = Mild inflammation - slight cliange in color and little change in texture.\n2. = Moderate inflammation - modcrate glazing, redness,oedema, hypertrophy, bleeding on pressure.\n3. = Severe inflammation - marked redness and hypertrophy, tendency to spontaneous bleeding, ulceration.', 'timeFrame': 'Baseline to week 4 of intake'}

Please estimate the sample size based on the assumption: 
Two sample t-test, alpha = 0.05, Power = 0.85, one-sided test (superiority), H0: no difference between treatment and control, H1: difference in means between treatment and control is at least one SD (effect size > 1). The Wilcoxon rank-sum test (WRT) is used for significance, with an estimated power of at least 80%. A low dropout rate of 5% is assumed.
Sample size
        The primary endpoint is the change of the Gingival Index from baseline to week four. The selected studies [45, 46, 86â88] were designed as randomized controlled trials (RCTs) and compared L. reuteri lozenges with control in various populations (Table 5). Effect size was calculated as follows: the change of the GI at a follow up visit and baseline was calculated. Then, the difference of this change in treatment and the control group was calculated and divided by the pooled standard deviation. Effect size varies across the studies. Notably, Iniesta et al. [88] reported no effect of lozenges compared to control. The other studies reported a significant effect [45, 46, 86, 87]. The smallest effect size of 1.00 was reported by Schlagenhauf et al. 2016 [45]. We use this worst case for the sample size estimation.Table 5Effect size of L. reuteri lozenges versus control lozenges on Gingival Index (GI)PaperEffect sizeNumber of study participantsSchlagenhauf et al. [45]1,0055Schlagenhauf et al. [46]1,3372Vivekananda et al. [86]2,7930Tekce et al. [87]1,5240Iniesta et al. [88]0,0040
        It cannot be assumed that the change in GI is normally distributed. Hence a Wilcoxon rank-sum test (WRT) is used to decide for significance. As the WRT is non-parametric, a sample size estimation for this test is not possible. Blair et al. 1980 [89] compared WRT with the t-test. The comparison showed that the power of the WRT is comparable to the power of t-test for various distributions. In the worst case, the WRT showed a power that was 5 percentage points lower than the power of the t-test. Thus, we will perform a power calculation for the t-test with 85% power and get the power of WRT of at least 80%.
        Sample size estimation is performed with the following parameters: Two sample t-test, alphaâ=â0.05, Powerâ=â0.85, one-sided test (superiority), H0: no difference between treatment and control and H1: difference in means between treatment and control is at least one SD (effect sizeâ>â1). The sample size calculation yielded as a result 16 study participants per arm, i.e. 32 participants in total. A greater effect size will yield smaller sample sizes. Sample size was calculated with Software R [90] using the functionâpower.t.testâ by the CCS (A.S.). The formula for this sample size estimation is nâ=â(Ï/Î´)2 * (z1âÎ±â+âz1âÎ²)2 where Î´/Ï is the effect size and z1âÎ± is the 1-Î±-quantile of the t-distribution. We estimate that two study participants will drop out till week four. This corresponds to a low drop-out rate of 5%, in line with the selected studies [45, 46, 86â88]. Therefore, 34 patients have to be recruited. The analysis of the primary endpoint is applied to the per-protocol population. Therefore, the number of cases will be 17 study participants for each study and each control group: 34 adolescents (17 study participants for the study group, 17 study participants for the control group) and 34 adults (17 study participants for the study group, 17 study participants for the control group).