Abstract
The present paper discusses drawbacks and limitations of likelihood-based inference in sequential clinical trials for treatment comparisons managed via Response-Adaptive Randomization. Taking into account the most common statistical models for the primary outcome—namely binary, Poisson, exponential and normal data—we derive the conditions under which (i) the classical confidence intervals degenerate and (ii) the Wald test becomes inconsistent and strongly affected by the nuisance parameters, also displaying a non monotonic power. To overcome these drawbacks, we provide a very simple solution that could preserve the fundamental properties of likelihood-based inference. Several illustrative examples and simulation studies are presented in order to confirm the relevance of our results and provide some practical recommendations.
Highlights
Over the past decades a growing stream of statistical papers on the topic of ResponseAdaptive Randomization (RAR) has flourished, especially in the context of phase-III clinical trials for treatment comparisons, due to the encouragement of U.S gov-Since the statistical object of drawing correct inferential conclusions about the identification of the best treatment and its relative superiority often conflicts with the ethical aim of maximizing the subjects care, some authors formalize these goals into suitable combined/constrained optimization problems
We prove that the Wald test could become inconsistent, it may display a strong dependence on the nuisance parameters, and the standard confidence intervals could degenerate
This paper explores in depth the limitations of the likelihood-based approach for RAR experiments, in terms of asymptotic confidence intervals and hypothesis testing
Summary
Over the past decades a growing stream of statistical papers on the topic of ResponseAdaptive Randomization (RAR) has flourished, especially in the context of phase-III clinical trials for treatment comparisons, due to the encouragement of U.S gov-. We stress the crucial role played by the chosen target, the variance function of the statistical model and the presence of nuisance parameters, that could (i) compromise the quality of the Central Limit Theorem (CLT) approximation of the standard MLEs and (ii) lead to a vanishing Fisher information. These degeneracies could happen when the variance function is unbounded or when the target allocations approach either 0 or 1 (that depends on both the chosen ethical component and on the relative superiority of a given treatment wrt the other), showing how the functional form of the target could induce a non monotonic power function.
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