Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods

Chapter 42

Sample Size for Comparing Variabilities

Hansheng Wang and Shien-Chung Chow

42.1 Introduction

In practice, the variabilities of responses involved in clinical research can be roughly divided into three categories, namely, intra-subject, inter-subject, and total variabilities [1]. More specifically, the intra-subject variability is the variability observed by repeated measurements on the same subject under exactly the same experiment conditions. This type of variability is very often due to measurement error, biological variability, and so on. In an ideal situation, the intrasubject variability can be eliminated by averaging infinite number of repeated observations from the same subject under the same experiment conditions. However, even if this averaging can be done, one can still expect difference to be observed in terms of the mean responses between different subjects who receive exactly the same treatment. This difference is referred to as intersubject variability, which is caused by the difference between subjects. The total variability is simply the sum of the intrasubject and intersubject variabilities, which is the most often observable variability in a parallel design.

Statistical procedures for comparing intrasubject variabilities are well studied by Chichilli and Esinhart [2]. The problem of comparing intersubject and total variabilities is studied by Lee et al. [3,4], A comprehensive summarization can be found in Lee et al. [5] and Chow et al. [6].

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