Optimal Allocation to Treatment Groups Under Variance Heterogeneity

• Activity Number: 279
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Hans Nyquist*+ and Ellinor Fackle-Fornius
• Companies: Stockholm University and Stockholm University
• Keywords: Optimal design ; C-optimality ; DA-optimality ; minimax

Abstract

The problem of allocating experimental units to treatment groups, when interest is in estimating a linear combination of treatment means, is considered. Variance heterogeneity over treatment groups is often present for clinical data, as well as in cases when the response variance is a function of the mean, such as for binary and Poisson responses. C- and DA-optimal allocations are derived for estimation of any linear combination of treatment means under variance heterogeneity. Explicit expressions are provided for the C-optimal design weights. It is also seen that the Neyman allocation, used in stratified sampling, appears as a special case of the C-optimal allocation. As the variances are generally unknown before the experiment is conducted, minimax designs are also considered. This means that allocation is made subject to the worst case as the variances are varied within specified intervals. For the case of independent treatment groups we show that the minimax strategy is very simple to apply. Efficiencies of the allocations according to the minimax strategy are evaluated.