Explicit Optimization of Clinical Trials for Statistical Power
Sebastian Ueckert, Joakim Nyberg, Andrew C. Hooker
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives: Optimal design (OD) theory as a tool to increase the efficiency of clinical studies, though theoretically well-established, still suffers from a low frequency of practical implementation. Among the reasons for this discrepancy is the poor communication of benefits and potential gains, which are mainly based on measures of parameter precision. Statistical power, where applicable, constitutes a more accessible quantity to measure the quality of a design, but its connection with OD has been investigated only in isolated cases [1,2]. In this work we propose an improved statistic more generally applicable and demonstrate the direct optimization of a clinical trial design for statistical power.
Methods: A new statistic derived from the general formulation of the Wald approximation was used to predict the statistical power for given trial designs using different pharmacometric models. The predicted value was compared, together with the classical Wald statistic [1,2], to a type I error-corrected model-based power determined via clinical trial simulations. In a second step, a study design for maximal power was determined by directly maximizing the new statistic. The resulting power-optimal designs and their corresponding performance based on empirical power calculations were compared to designs determined with the D and Ds optimality criteria. All OD related calculations were performed using PopED V2.11 , simulation and estimations used PsN V3.3 in connection with NONMEM 7.1.2.
Results: Comparisons of empirically determined power and the newly developed statistic, showed excellent agreement across all models and scenarios investigated. This was in contrast to the classical Wald statistic, which consistently over-predicted the reference power with deviations of up to 90%. Designs maximized using the proposed metric differed from D and Ds optimal designs and showed equal or up to 20% higher power in the subsequent clinical trial simulations. Furthermore, the proposed method was used to minimize the number of individuals required to achieve 80% power through a simultaneous optimization of study size and study design. The targeted power of 80% was confirmed in subsequent simulation studies.
Conclusions: A new statistic was developed, allowing for the explicit optimization of a clinical trial design with respect to statistical power. The method can also facilitate in the communication of the value of optimal design calculations to non-modelers.
 Ogungbenro K, Aarons L. Sample size/power calculations for repeated ordinal measurements in population pharmacodynamic experiments. J Pharmacokinet Pharmacodyn. 2010 Feb;37(1):67-83.
 Retout S, Comets E, Samson A, Mentré F. Design in nonlinear mixed effects models: optimization using the Fedorov-Wynn algorithm and power of the Wald test for binary covariates. Stat Med. 2007 Dec 10;26(28):5162-5179.
 Foracchia M, Hooker A, Vicini P, Ruggeri A. POPED, a software for optimal experiment design in population kinetics. Computer Methods and Programs in Biomedicine. 2004 Apr;74(1):29-46.