Accounting for overdispersion and clustering in binomial data from N-of-1 trials

N-of-1 trials are patient centered randomized controlled trials. Although the primary goal of N-of-1 trials is to obtain the results for each patient separately, pooling the results across patients also has relevance. In this paper, we present two analytical strategies to pool the results across N-of-1 trials, when the main outcome for each patient is a binomial variable. Our first method takes into account the extra-binomial variation, while as the second approach takes into account hierarchical clustering in addition to overdispersion. We illustrate the methods using real data analysis and compare the methods using simulations.