Statistical analysis
The primary analysis will follow the intention to treat (ITT) principle with all participants analysed according to their random allocation. All statistical tests will be two-sided with a significance level of α = 0.1, unless otherwise specified. Data will be summarized using descriptive statistics (sample mean, median, standard deviation, minimum, maximum) for continuous variables and frequencies and percentages for discrete variables.
The primary end point, proportion of participants with tree nut allergy at 18 months will be compared between treatment groups using a logistic regression model . The estimate of interest is the odds ratio between the two arms estimated via logistic regression and will be presented with its 95% confidence interval and a two-sided p-value. Secondary outcomes (peanut allergy resolution, adverse event frequency, number of tree nuts ingested and frequency of tree nuts ingested) will also be analysed as difference in proportion between the two treatment arms using logistic regression with 95% confidence intervals and a two sided p value. Differences in Quality of Life (FAQLQ-PF) and parental anxiety (STAI) total scores will be analysed as difference between the two treatment groups using logistic regression with 95% confidence intervals and a two-sided p value. If there is very little missing data (<5% in the primary outcome) then the analysis will be based on the available cases. If, however, there is more than 5% missing data in the primary outcome, and there is evidence that the data are missing at random, then multiple imputation will be used to handle the missing data.