Here is the design of a clinical trial:

Official Title: Symptoms Based Awareness Confirmation Study - CoMiSS Validation

Included conditions:
- Cow Milk Allergy

Study Armgroups:
- {'label': 'CoMiSS', 'type': 'OTHER', 'description': "Measure of CoMiSS followed by two weeks eviction Cow's milk protein diet and second CoMiSS measurement.", 'interventionNames': ['Other: CoMiSS questionnaire']}

Interventions:
- {'type': 'OTHER', 'name': 'CoMiSS questionnaire', 'armGroupLabels': ['CoMiSS']}

Primary Outcomes:
- {'measure': 'The accuracy in terms of the Area Under Curve (AUC) of the Receiver Operating Characteristic (ROC) curve of the change in CoMiSS.', 'timeFrame': 'baseline, Week 2'}

Please estimate the sample size based on the assumption: 
The study aims for 90% power and a 5% significance level (2.5% for one-sided testing). The dropout rate is assumed to be 15-20%.
Sample size calculation
        The hypothesis of interest is that the AUC > A0 (=0.75) and is tested using the test-statistic
        
Z=A^âA0VarÂ 0(AUC)

        where A^Â is the estimated AUC on the holdout set, A0=0.75Â is the benchmark or minimum clinically relevant AUC of the ROC curve and Var0(A) is the variance of the AUC under the null hypothesis H0. The variance of the AUC at a given value AÂ is given by Hajian-Tilaki9

        
VarA(AUC)=0.0099Â eâa22(5a2+8nd+a2+8nh),

        where a=(2)Î¦â1(A)Â Î¦Â is the cumulative distribution function of the standard normal distribution nâ and n+Â and are the number of subjects in the holdout set who test negative and positive in the OFC, respectively.
        The corresponding sample size for the required number of subjects who would test positive on the OFC test when the assumed AUC is A is given by:
        
n+=[zÎ±/2V0(AUC)+zÎ²VA(AUC)]2(AâA0)2

        whereÂ VA(AUC)=n+VarA(AUC).
        The pooled prevalence from three recent CoMiSS trials of children with a positive OFC, that is, confirmed CMPA was 83%.10 Entry criterion for these studies was a CoMiSS â¥12. For the present study, patients will be recruited based on symptoms and the estimated prevalence of CMPA in the study population will therefore lower (estimated prevalence of challenge-proven CMPA 70%). Based on the above asymptotic sample size formula and prevalence estimate for CMPA, around 80 subjects with a positive OFC and 35 subjects with a negative OFC will be required in the holdout set to test the above hypothesis regarding the AUC with 90% power and at 5% level of significance and 2.5% for one-sided testing. Thus, the overall sample size accommodating the training and holdout set splits isÂ N=2Ã115=230. Assuming a 15â20% dropout rate, 300 subjects will need to be enrolled.