**6. Concluding remarks**

In this Chapter, we discussed and reviewed construction of universally optimal Nof-1 designs and how they may be aggregated to estimate treatment effects for the average patients. Originally, Kiefer [13] proposed the concept of universal optimality with zero row and column sums in the information matrices. We examined conditions when such universally optimal designs exist with special application to N-of-1 trial designs that will make them optimal no matter what criteria are applied. In particular, we first presented a sufficient condition that ensures N-of-1 designs are universally optimal for the traditional model that accommodates the carryover effects. Additionally, we discussed extensions of our work to finding optimal aggregated N-of-1 designs. Using numerical results from our simulation for comparing the estimated precision of several six- and eight-period designs, we were able to obtain realistic guidelines for the practitioners.

Overall, there are three key conclusions from this chapter. The first is that alternating between *AB* and *BA* pairs in sequence will result in an optimal or nearly optimal N-of-1 trial for a single patient for models considered in this chapter. In particular, our work suggests that alternating between *AB* and *BA* pairs in a single trial is quite robust to mis-specification in the error structures considered in the chapter. Consequently, there is less need to guess or conduct a pilot study to verify model assumptions and the error structures.

Another take home message is that when an experiment has been carried out with the optimal N-of-1 trial and additional patients are accrued in the trial, we can aggregate these N-of-1 trials optimally by allocating the same number of patients to its dual sequence, thereby optimizing the trial for both the individual and average patients.

Lastly, we also provided a strategy for finding N-of-1 trials with more than 2 treatments. By restricting the class of designs and utilizing each subsequence, we constructed universally optimal N-of-1 trial designs when there are *t* ¼ 3, 4, or 5 treatments.
