Sample Size Calculation in Double Consent Randomized Design

Abstract

In a conventional randomized trial, the assignment of a patient to receive a treatment after obtaining the patient's consent may completely depend on a chance mechanism. Thus, neither the patient nor the physician know exactly which treatment the patient will receive at the time of consent. This can compromise the relationship between the patient and the physician. To alleviate this concern, Zelen proposes use of a double consent randomized design, in which we ask each patient for consent after random assignment of patients to treatments. This paper discusses sample size calculation for the double consent randomized design. Because the variance of the test statistic used to derive the required sample size depends upon the null and alternative hypotheses, this paper derives three approximate sample size formulae. The first two formulae tend to provide a lower and an upper limit of the required sample size, and the third one, a simple average of these two formulae, attempts to provide a better approximation. This paper further employs Monte Carlo simulation to evaluate the performance of these approximate sample size formulae with respect to type I error and power. Finally, to help readers employ the results discussed here, tables that summarize the estimated required sample size in a variety of situations are provided.