Here is the design of a clinical trial:

Official Title: Transcutaneous Auricular Vagus Nerve Stimulation Following Spontaneous Subarachnoid Hemorrhage

Included conditions:
- Subarachnoid Hemorrhage

Study Armgroups:
- {'label': 'Auricular VNS Stimulation', 'type': 'EXPERIMENTAL', 'description': 'Participants receive twice daily auricular vagal nerve stimulation', 'interventionNames': ['Device: Auricular Vagus Nerve Stimulation']}
- {'label': 'Sham Auricular VNS Stimulation', 'type': 'SHAM_COMPARATOR', 'description': 'Participants will have an auricular vagal nerve stimulator applied twice daily, without the stimulation applied', 'interventionNames': ['Device: Sham Auricular Vagus nerve Stimulation']}

Interventions:
- {'type': 'DEVICE', 'name': 'Auricular Vagus Nerve Stimulation', 'description': 'Transcutaneous auricular vagal nerve stimulation', 'armGroupLabels': ['Auricular VNS Stimulation']}
- {'type': 'DEVICE', 'name': 'Sham Auricular Vagus nerve Stimulation', 'description': 'Transcutaneous auricular vagal nerve ear clip applied without current', 'armGroupLabels': ['Sham Auricular VNS Stimulation']}

Primary Outcomes:
- {'measure': 'Inflammatory markers in the serum on admission', 'description': 'TNF alpha from blood draw', 'timeFrame': 'On hospital day 1'}
- {'measure': 'Change in inflammatory markers in the serum', 'description': 'TNF alpha from blood draws', 'timeFrame': 'Through hospital admission, average of 4 weeks'}
- {'measure': 'Inflammatory markers in the CSF on admission', 'description': 'TNF alpha from cerebrospinal fluid', 'timeFrame': 'On hospital day 1'}
- {'measure': 'Change in inflammatory markers in the CSF', 'description': 'TNF alpha from cerebrospinal fluid', 'timeFrame': 'Through hospital admission, average of 4 weeks'}
- {'measure': 'Cerebral vasospasm', 'description': 'Presence of moderate/severe radiographic vasospasm', 'timeFrame': 'Through hospital admission, average of 4 weeks'}
- {'measure': 'Hydrocephalus', 'description': 'Need for permanent CSF diversion via a ventricular shunt', 'timeFrame': 'Through hospital admission, average of 4 weeks'}

Please estimate the sample size based on the assumption: 
Two-sided, two-sample t-test; equal variance at both time points; weak correlation (0.15) between measurement pairs; compound symmetry covariance structure with Rho of 0.2; significance level (alpha) of 0.05; power of 80%.
Sample size
          Goal enrollment for the pilot NAVSaH trial is 50 patients, based on power calculations to detect significant differences in inflammatory cytokines, radiographic vasospasm, and chronic hydrocephalus.
          Under a 2-by-2 repeated measures design consisting of two groups of patients, each measured at two time points, our goal is to compare the change across time in the taVNS group to the change across time in the Sham group. Based upon previous work from Koopman et al. [67], we assume our study will observe 1.1 standardized inflammatory cytokines mean change difference between the two groups. Using a two-sided, two-sample t-test, assuming both time points have equal variance and there is a weak correlation (i.e., 0.15) between measurement pairs, a sample size of 25 in each group achieves at least 80% power to detect a standardized difference of 1.1 in mean changes, with a significance level (alpha) of 0.05 [68].
          Based upon our preliminary data, we assume this study will observe 25% and 55% severe vasospasm in the taVNS and Sham groups, respectively. Under a design with 2 repeated measurements (i.e., 2 raters), assuming a compound symmetry covariance structure with a Rho of 0.2, at a significance level (alpha) of 0.05, a sample size of 25 in each group achieves at least 80% power when the null proportion is 0.55, and the alternative proportion is 0.25 [69â71].
          As previously described, LV et al. [8] studied the relationship between cytokine levels and clinical endpoints in SAH, including hydrocephalus. From their outcomes, we predict a needed enrollment of approximately 50 to detect these endpoints. From our own preliminary data, with an incidence of chronic hydrocephalus 0% in treated patients and 28.6% in control (despite grade of hemorrhage), alpha = 0.05 and power = 0.80, the projected sample size to capture that change is approximately 44 patients.