Sample Size: When Bigger Is Not Necessarily Better

• Activity Number: 467
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2008 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jeng Mah*+
• Companies: American Medical Systems, Inc.
• Keywords: Bayesian decision ; sample size ; minimal loss

Abstract

Power is a function of sample size. A larger study invariably increases the power of the hypothesis test; only an infinitely large study can result in absolutely correct answers. In any study, some power must be sacrificed to make sample size practical. Nominal power choices (e.g., 80% or 90%) are often used without considering the costs of sampling and the losses incurred from wrong decisions. In a previous study, I proposed a decision model explicitly harnessing loss in clinical trial design and observed that minimal loss can be achieved by choosing decision rules based on posterior probability or the Bayes factor. This paper examines a sample size estimation approach which seeks to minimize the overall expected loss, which is a combination of false positive and negative errors and the cost of sampling. Simple cases with conjugated prior distributions are examined through simulations.