ENBIS Spring Meeting 2018

4 – 6 June 2018; Florence, Italy Abstract submission: 17 November 2017 – 20 April 2018

Optimal target allocation for hypothesis testing in multiarm clinical trials

5 June 2018, 17:20 – 17:45

Abstract

Submitted by
Marco Novelli
Authors
Marco Novelli (University of Bologna)
Abstract
The large majority of randomized clinical trials for treatment comparisons have been designed in order to achieve balanced allocation among the treatment groups, with the aim of maximizing inferential precision in the estimation of the treatment effects. The main justification concerns the so-called ``universal optimality" of the balanced design (see e.g. Silvey, 1980), especially in the context of the linear homoscedastic model, since it optimizes the usual design criteria for the estimation of the treatment contrasts, (like the well-known D-optimality minimizing the volume of the confidence ellipsoid of the contrasts), and it is nearly optimal under several optimality criteria, also under heteroscedasticity (Begg and Kalish, 1984).
Taking into account the problem of testing statistical hypothesis about the equality of the treatment effects, balance is still optimal in the case of two treatments, since it maximizes the power of the test for normal homoscedastic responses and it is asymptotically optimal in the case of binary outcomes (see e.g. Azriel, Mandel and Rinott, 2012; Baldi Antognini 2008). However, in the case of several treatments the balanced allocation may not be efficient, since it is significantly different from the optimal design for hypothesis testing and could be strongly inappropriate for phase III-trials, in which the ethical demand of individual care often induces to skew the allocations to more efficacious (or less toxic) treatments. To derive a suitable compromise between these goals, Baldi Antognini, Novelli and Zagoraiou suggested a constrained optimal target that maximizes the power of the classical Wald test of homogeneity, subject to an ethical constraint on the allocation proportions reflecting the efficacy of the treatments. The aim of the present work is to push forward these results, by providing some important properties of this constrained optimal allocation. The comparisons with some targets proposed in the literature show that the constrained optimal allocation has good performance in terms of statistical power, estimation precision and ethical demands and thus it represents a valid compromise between inference and ethical concerns.

References
Azriel, D., Mandel, M., Rinott, Y. (2012). Optimal allocation to maximize power of two-sample tests for binary response. Biometrika 99, 101-113
Baldi Antognini, A. (2008). A theoretical analysis of the power of biased coin designs. Journal of Statistical Planning and Inference 138, 1792-1798
Baldi Antognini, A., Novelli, M., Zagoraiou, M.: Optimal designs for testing hypothesis in multiarm clinical trials. Submitted.
Begg, C.B., Kalish, L.A. (1984). Treatment Allocation for Nonlinear Models in Clinical Trials: The Logistic Model. Biometrics 40, 409--420
Silvey, S.D. (1980). Optimal Designs. Chapman \& Hall, London

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