Optimum treatment allocation rules under a variance heterogeneity model

We provide optimal treatment allocation schemes when the outcome variance varies across the treatment groups and our objectives are to estimate treatment effects with equal or unequal interest. Unlike other optimal designs, such as A-optimal designs, the proposed designs can be found without an iterative scheme. We evaluate robustness properties of the optimal designs to mis-specification in the expected variance from each group and identify situations when popular allocation schemes have poor efficiencies. An application to design a randomized rheumatoid arthritis trial is discussed, along with a potential application to design a cancer screening trial when the main outcome is a continuous variable.