Comparing Variabilities in Clinical Research

In most clinical trials comparing a test drug and a control (e.g., a placebo control or an active control), treatment effect is usually established by comparing mean response change from baseline of some primary study endpoints assuming that their corresponding variabilities are comparable. In practice, however, variabilities associated with the test drug and the control could be very different. When the variability of the test drug is much larger than that of the reference drug, safety of the test drug could be a concern. Thus, in addition to comparing mean responses between treatments, it is also of interest to compare the variabilities associated with the responses between treatments. In practice, the variabilities associated with the response are usually classified into two categories, namely, the intrasubject (or within-subject) variability and the intersubject (or between-subjects) variability. Intrasubject variability refers to the variability observed from repeated measurements from the same subject under the same experimental condition. On the other hand, intersubject variability is the variability due to the heterogeneity among subjects. The total variability is simply the sum of the intraand intersubject variabilities. In practice, it is of interest to test for equality, noninferiority/superiority, and similarity (or equivalence) between treatments in terms of the intrasubject, intersubject, and/or total variabilities. Under a replicated parallel design, the usual F-test can be performed to compare intrasubject variabilities. Under a replicated crossover design, Chinchilli and Esinhart proposed the F-test using an orthogonal transformation to test for difference in intrasubject variability between treatments. Under replicated parallel designs, however, intersubject and total variabilities between two treatments cannot be compared by the usual F-test because the distribution of estimators does not follow a chi-square distribution. In these cases, the modified large sample (MLS) method is suggested (see, e.g., Refs. [2–5]). The MLS method is shown to be superior to the other approximation methods in practice. Under a replicated crossover design, the MLS method is not appropriate to compare intersubject and total variabilities because estimators of variance components are not independent. Lee et al. extend the MLS method when estimators of variance components are dependent. In addition, Lee et al. study a test for comparing intersubject and total variabilities under replicated crossover designs based on the extension of the MLS method. In practice, instead of comparing intrasubject variabilities, it may be of interest to compare intrasubject coefficient of variation (CV). In recent years, the use of intrasubject CV has become popular when assessing the reproducibility, similarity, and stability of a drug product when the drug product is repeatedly administered over a period of time. In this entry, we will discuss two statistical methods by Chow and Tse and Quan and Shih.