Abstract: The double consent randomized design, in which the physician and the patient know exactly what treatment the patient receives, has been proposed to alleviate the concern in carrying out a conventional randomized trial. In the latter, the assignment of patients to treatments after obtaining patients' informed consents depends completely on a chance mechanism. We develop four interval estimators, two using the delta method or the principle of Fieller's Theorem calculated over the pooled samples of eligible patients, and two calculated over the samples excluding patients who have treatment preference. Using Monte Carlo simulation, we evaluate and compare the performance of these estimators in a variety of situations. We note that the estimators using the principle of Fieller's Theorem outperform those derived from the delta method with respect to both coverage probability and average length in almost all situations considered here. We further note that when the expected number of patients who have no treatment preference is moderate or large (say) per treatment, the interval estimator using Fieller's Theorem calculated over the restricted samples is generally more efficient than those calculated over the entire pooled samples without much loss of accuracy as measured by coverage probability. On the other hand, when the expected number of patients who have no treatment preference is small, the coverage probability for the estimators calculated over the restricted samples tends to be less than the desired confidence level, while the coverage probability of the estimator using Fieller's Theorem on the pooled samples may still agree with the desired confidence level.
Key words and phrases: Delta method, Fieller's theorem, interval estimation, randomized consent design.