Here is the design of a clinical trial:

Official Title: Structural and Functional Correlates of Clinical Response to Repetitive Transcranial Magnetic Stimulation (rTMS) Treatment in Schizophrenia Patients With Resistant Auditory Hallucinations

Included conditions:
- Schizophrenia

Study Armgroups:
- {'label': 'Active Repetitive Transcranial Magnetic Stimulation (rTMS)', 'type': 'ACTIVE_COMPARATOR', 'description': 'low-frequency (1 Hertz) rTMS', 'interventionNames': ['Device: Repetitive Transcranial Magnetic Stimulation (rTMS)']}
- {'label': 'Sham Repetitive Transcranial Magnetic Stimulation (rTMS)', 'type': 'SHAM_COMPARATOR', 'description': 'sham TMS', 'interventionNames': ['Device: Sham Repetitive Transcranial Magnetic Stimulation (rTMS)']}

Interventions:
- {'type': 'DEVICE', 'name': 'Repetitive Transcranial Magnetic Stimulation (rTMS)', 'description': 'Participants are sequentially randomly assigned to either 20 active rTMS sessions or 20 sham rTMS sessions that were applied over the left temporoparietal junction. Treatments are administered daily, over a period of two weeks.', 'armGroupLabels': ['Active Repetitive Transcranial Magnetic Stimulation (rTMS)']}
- {'type': 'DEVICE', 'name': 'Sham Repetitive Transcranial Magnetic Stimulation (rTMS)', 'armGroupLabels': ['Sham Repetitive Transcranial Magnetic Stimulation (rTMS)']}

Primary Outcomes:
- {'measure': 'Changes in the integrity of white matter tracts between responder and non-responder patients', 'timeFrame': 'Baseline'}
- {'measure': 'Changes in the variations of the blood-oxygen-dependent level (BOLD) signal between responder and non-responder patients', 'timeFrame': 'Baseline'}

Please estimate the sample size based on the assumption: 
An α risk of 0.05, a 1-β power of 0.80, and an estimated 10% dropout rate were assumed.
Sample size
          The aim of this trial is to investigate the difference in brain functional and structural connectivity in schizophrenia patients receiving an active rTMS treatment and clinically responding to it or not as assessed by an amelioration of their AVH symptoms. Therefore, the sample size was calculated to determine the number of patients to be included in the active rTMS group on the basis of the primary outcome, namely the difference in FA values at baseline between ârespondersâ and ânon-respondersâ. Unfortunately, no study provides a significant difference of rs-fMRI measures or FA values for a given tract (such as the left arcuate fasciculus) before and following a clinically effective versus a non-clinically effective rTMS treatment in schizophrenia patients, which would allow us to accurately estimate the adequate sample size for our trial. Nonetheless, FA values are highly reproducible and have a reliable estimation of variance. Therefore, we focused on FA values to determine sample size. Therefore, on the basis of a significant difference in the FA values between schizophrenia patients and healthy subjects for the left arcuate fasciculus [51] and assuming an Î± risk of 0.05 and a 1-Î² power of 0.80, we estimated the need to include 32 patients for the active rTMS group. To overcome an estimated 10% drop-out, we increased our recruitment needs for active rTMS group to 35 patients. Given a proportion of ârespondersâ and ânon-respondersâ to rTMS treatment as the one we propose for AVH in schizophrenia estimated at 40% and 60%, respectively [52], we will divide our cohort into 14 ârespondersâ and 21 ânon-responderâ patients. According to a prior study [22], a minimum of 14 participants per group (ârespondersâ or ânon-respondersâ) has been deemed sufficient to conduct statistical analysis in neuroimaging and detect a significant effect of rTMS on brain structural connectivity. Moreover, a sham rTMS group of 10 patients will be followed in parallel to control for the placebo rTMS effect on AVH. As a result, the total number of participants required for the study is of 45 patients.