In higher order five period cross-over designs with two treatments, thirty two possible treatment sequences can result; AAAAA, BAAAA, ABAAA, AABAA, AAABA, AAAAB, BBAAA, BABAA,BAABA, BAAAB, ABBAA, ABABA, ABAAB, AABBA, AABAB, AAABB and their duals. Higher-order cross-over designs allow; estimation of treatment effects even in the presence of carry-over effects, provide estimates of intra-subject variability, and draw inference on the carry-over effects. This paper considers four designs; Design 1: BABAA and its dual, design 2: BAABA and its dual, design 3: BABAA, ABABB, BAABA, ABBAB, and design 4: BAAAB, ABBBA, ABBAA, BAABB. The methods for estimating direct treatment effects and treatment carry-over effects are outlined using best linear unbiased estimation method (BLUE), where atraditional modelthat specifies a first order carry-over effect is assumed.
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