Power Calculations in Clinical Trials With Complex Clinical Objectives

Abstract

Over the past decade, a variety of powerful multiple testing procedures have been developed for the analysis of clinical trials with multiple clinical objectives based, for example, on several endpoints, dose-placebo comparisons and patient subgroups. Sample size and power calculations in these complex settings are not straightforward and, in general, simulation-based methods are used. In this paper, we provide an overview of power evaluation approaches in the context of clinical trials with multiple objectives and illustrate the key principles using case studies commonly seen in the development of new therapies.

To add or not to add a new treatment arm to a multiarm study: A decision‐theoretic framework

“…The former is an example of expectation criteria and the latter is an example of exceedance criteria that are often considered when designing a study that has multiple clinical objectives. 16 We can find the expected values of these utilities by evaluating the probability of rejecting some number of hypotheses. For example, the probability of rejecting K − 2 hypothesis out of K hypotheses is the sum of (1) over all choices of r and u.…”

“…They are examples of design criteria for designing a trial that has multiple clinical objectives. 16 A utility function reflects the point of view of a decision marker. For ease of exposition, we do not include other trial aspects such as monetary values in our illustration.…”

Optimal weighted Bonferroni tests and their graphical extensions

“…20,21 Examples of optimal weights using grid search and simulation are discussed for graphical approaches 22 and chain procedures. 23,24 More recently, optimization using deep learning has been proposed to optimize the weighted power for the graphical approach. 25 Although the weighted (or average) power is easier to optimize numerically, it introduces another set of weights for power that may not be easy to determine or interpret.…”

“…26 For more hypotheses or more flexible approaches such as the graphical approach, simulation over a grid of possible-but-often-limited choices is adopted to search for the optimal solution. [22][23][24] In general, there are three challenges to optimize the disjunctive and conjunctive power. The first challenge is that evaluating these objective functions requires the knowledge of multivariate distributions and hence the correlation structure among test statistics.…”

“…Similarly, analytical formulae are derived for weighted Bonferroni tests to obtain the optimal average power 20,21 . Examples of optimal weights using grid search and simulation are discussed for graphical approaches 22 and chain procedures 23,24 . More recently, optimization using deep learning has been proposed to optimize the weighted power for the graphical approach 25 …”