*Practical and Optimal Crossover Designs for Clinical Trials DOI: http://dx.doi.org/10.5772/intechopen.104694*

optimal designs for binary responses requires special attention. Due in part to these difficulty, there are limited studies on response-adaptive designs and optimal designs in the literature for binary outcome data. In this chapter, we compared approaches of constructing response-adaptive designs. Also, we conducted a simulation study based on an actual data example to investigate the performance of the multiple objective response-adaptive designs using the GEE over the other two methods.

We demonstrated by constructing response-adaptive designs using an objective function, namely the multiple objective function. The designs constructed using the multiple objective function were highly efficient, successful with respect to desirable or beneficial treatment outcomes. In **Tables 5** and **6**, we observed that the choice of *λ* for an efficient and successful design would depend on the sample size and the true values of *μ*, *π*<sup>0</sup> *i s*, *τ*, and *γ*. The efficiencies drop significantly when *n* increases or *λ* decreases. These designs may have significantly higher success ratios but may also have significantly low efficiency (<0.6), which is undesirable.

We then compared the approach by Kim [23] to other multiple objective adaptive designs using the GEE to the response-adaptive design by Mukhopadhyay [20] and multiple objective adaptive designs using binary probability modeling approach by Li [13] for two-period two-treatment crossover designs. The proposed designs responded to the differences in the treatment effects in a rather robust manner. When the treatment difference is very small, the proposed designs were very close to the optimal design with an equal allocation on four treatment sequences, *AA=AB=BA=BB*, as expected. On the other hand, the other two methods assign too large a proportion of subjects to treatment sequences *BB* and lose efficiencies for very small gain in successful outcome ratios. When the treatment difference is large, the design with *λ* ¼ 1 assigns more subjects to a better treatment sequences compared with the other two designs considered by Bandyopadhyay et al. [5] and Li [13].

We observed that the choice of *λ* was very important in finding a balance between the relative efficiency and a success ratio. One may suggest some appropriate range of *λ*, but it is valid for only a certain set of parameters and sample size, and the true parameters are usually unknown. To overcome this challenge, Kim [23] devised a multiple objective response-adaptive scheme, which utilizes all of the two components of Eq. (10), not simultaneously but in a sequential manner. The simulation results show that this adaptive scheme can construct designs with desired relative ratios without having to select the weight parameter *λ*. The scheme by Kim [23] allows researchers to run an adaptive trial knowing that their design would find the balance between two important components of the trial—statistically efficiency and higher allocation to a beneficial treatment.

*Recent Advances in Medical Statistics*
