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A particular multi-period cross-over design useful in trials where observations naturally are correlated and carryover effect may not die after one period-such as thorough QT, trials on diet, asthma, and others-is shown to be useful for estimation in three practical cases. The cases are: the variance balanced estimation of direct and carryover treatment effects in presence of higher-order carryover and correlated errors using ordinary least squares method; estimation of the said treatment effects under scattered missing observations; and the interim estimation of the same for trials with early stopping rules. We compare treatment effect estimates and their variances with those given in the literature for the higher-order carryover model. We also give a numerical example demonstrating estimation in all three cases.

Crossover designs robust to changes in carryover models are useful in clinical trials where the nature of carryover effects is not known in advance. The designs have been characterized for being optimal and efficient under no carryover-, traditional-, and, self and mixed carryover- models, however, ignoring the number of subjects, which has significant impact on both optimality and administrative convenience. In this article, adding two more practical models, the traditional, and, self and mixed carryover models having carryover effect only for the new or test treatment, a 5M algorithm is presented. The 5M algorithm based computer code searches all possible two treatment crossover designs under the five carryover models and list those which are optimal and /or efficient to all the five carryover models. The resultant exhaustive list consists of optimal and/or efficient crossover designs in two, three, and four periods, having 4 to 20 subjects of which 24 designs are new optimal for one of the established carryover models, and 34 designs are optimal for newly added models.

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