Background: Clinical trials are typically designed using the classical frequentist framework to constrain type I and II error rates. Sample sizes required in such designs typically range from hundreds to thousands of patients which can be challenging for rare diseases. It has been shown that rare disease trials have smaller sample sizes than non-rare disease trials. Indeed some orphan drugs were approved by the European Medicines Agency based on studies with as few as 12 patients. However, some studies supporting marketing authorisation included several hundred patients. In this work, we explore the relationship between disease prevalence and other factors and the size of interventional phase 2 and 3 rare disease trials conducted in the US and/or EU. We downloaded all clinical trials from Aggregate Analysis of ClinialTrials.gov (AACT) and identified rare disease trials by cross-referencing MeSH terms in AACT with the list from Orphadata. We examined the effects of prevalence and phase of study in a multiple linear regression model adjusting for other statistically significant trial characteristics. Results: Of 186941 ClinicalTrials.gov trials only 1567 (0.8%) studied a single rare condition with prevalence information from Orphadata. There were 19 (1.2%) trials studying disease with prevalence <1/1,000,000, 126 (8.0%) trials with 1-9/1,000,000, 791 (50.5%) trials with 1-9/100,000 and 631 (40.3%) trials with 1-5/10,000. Of the 1567 trials, 1160 (74%) were phase 2 trials. The fitted mean sample size for the rarest disease ( prevalence <1/1,000,000) in phase 2 trials was the lowest ( mean, 15.7; 95% CI, 8.7-28.1) but were similar across all the other prevalence classes; mean, 26.2 ( 16.1-42.6), 33. 8 (22.1-51.7) and 35.6 (23.3-54.3) for prevalence 1-9/1,000,000, 1-9/100,000 and 1-5/10,000, respectively. Fitted mean size of phase 3 trials of rarer diseases, <1/1,000,000 (19.2, 6.9-53.2) and 1-9/1,000,000 (33.1, 18.6-58.9), were similar to those in phase 2 but were statistically significant lower than the slightly less rare diseases, 1-9/100,000 (75.3, 48.2-117.6) and 1-5/10,000 (77.7, 49.6-121.8), trials. Conclusions: We found that prevalence was associated with the size of phase 3 trials with trials of rarer diseases noticeably smaller than the less rare diseases trials where phase 3 rarer disease ( prevalence <1/100,000) trials were more similar in size to those for phase 2 but were larger than those for phase 2 in the less rare disease ( prevalence >= 1/100,000) trials.