Sample Size Calculation in Double Consent Randomized Design
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Sample Size Calculation in Double Consent Randomized Design
Kung-long Lui, PbD Chii-Dean Lia, PhD Department of Mathematics and Statistics, San Diego State University, San Dieeo. Califoiia
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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 thepatient nor thephysician know exactly which treatment the patient will receive at the time of consent. This can compromise the relationship between thepatient and thephysician. 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 detive the re-
Key Words Sample size determination; Power; Double consent randomized design: Efficiency
Correspondence Address Kung-long Lui, PhD, Department of Mathematics and Statistics, San Diego State Universib, San Diego,
CA 92182-7720 (e-mail: kjl @rohan.sdsu.edu).
INTRODUCTION In a conventional randomized trial, because the assignment of a patient to receive a treatment after obtaining the patient’s consent may completely depend upon a chance mechanism, neither the patient nor the physician know exactly which treatment the patient will receive at the tsime of consent. As noted by Zelen ( l , Z ) , this can seriously compromise the relationship between the physician and the patient. Furthermore, some patients may originally agree to participate in a conventional randomized trial, but decline to continue the trial after the treatment is known to them. To alleviate these concerns, Zelen proposes use of a double consent randomized design, in which we ask each patient for consent after random assignment of patients to treatments. If the patient has no treatment preference, then the patient will receive the treatment randomly assigned to him/her. Otherwise, the patient will receive the particular treatment which the patient choos-
quired sample size depends upon the null and alternative hypotheses, this paper derives three approximatesample size formulae. Thefirst 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 ewor and powa Finally, to help readers employ the results discussed here, tables that summarize the estimated required sample size in a variety of situationsare provided.
es. Thus, both the physician and the patient know exactly which treatment the patient will receive. However, one of the major criticisms of using this type of design is the possibility that the treatment effect under investigation is confounded with the bias due to self selection. To account for
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