Bayesian sample size determination in non‐sequential clinical trials: Statistical aspects and some regulatory considerations

Abstract

The boundary entropy log(g) of a critical one-dimensional quantum system (or two-dimensional conformal field theory) is known to decrease under renormalization group (RG) flow of the boundary theory. We study instead the behavior of the boundary entropy as the bulk theory flows between two nearby critical points. We use conformal perturbation theory to calculate the change in g due to a slightly relevant bulk perturbation and find that it has no preferred sign. The boundary entropy log(g) can therefore increase during appropriate bulk flows. This is demonstrated explicitly in flows between minimal models. We discuss the applications of this result to D-branes in string theory and to impurity problems in condensed matter.

The Significance Test Controversy Revisited

“…The treatment difference to be detected may be based on a judgment concerning the minimal effect which has clinical relevance in the management of patients or on a judgment concerning the anticipated effect of the new treatment, where this is larger (ICH E9 Expert Working Group 1998, p. 19). Other approaches, which failed to recognize this requirement, such as the methods that control the length of the interval estimates of the difference, are not recommendable (see Grouin et al 2007). …”

The perils with the misuse of predictive power

“…Some of these are briefly mentioned in other literature but are not covered extensively (e.g. 2, 8). These characteristics are illustrated in Figure 1, which illustrates the properties of predictive power assuming that an interim analysis is performed after 50 subjects per group.…”

“…Bayesian methods represent a logical tool to use in this area and predictive power (a semi‐bayesian approach) has been proposed as a tool for specifying stopping rules as well as for sample size re‐estimation following an interim assessment of the data 2–9. The use of predictive power lends itself well to areas where the anticipated or expected treatment effect of interest is not adequately known.…”

“…Consequently, it may be impossible to obtain the required predictive power by simply increasing sample size. Although most of the characteristics we highlight are touched on elsewhere (2, 8), these generally only briefly mention the issues that we detail in this paper. Our purpose is therefore to draw attention to these characteristics and explain their causes.…”

“…These methods can also be applied at the beginning of the trial whereby prior knowledge is incorporated into the power calculation. Such approaches have been extensively covered within the literature (see 8, 9).…”