9.2 Synopsis

For the two-way crossover design, each patient receives two treatments, A and B, in one of two sequences, that is, A followed by B (A-B) or B followed by A (B-A). Samples of n₁ and n₂ patients are randomly assigned to each of the two sequence groups, A-B and B-A, respectively (usually, n₁ = n₂). Response measurements (y_ijk) are taken for each patient following each treatment for a total of N = 2n₁ + 2n₂ measurements, where y_ijk is the measurement for the k^th patient in the sequence group for which Treatment i (i = 1 for Treatment A, i = 2 for Treatment B) is given in Period j (j =1, 2). A sample layout is shown in Table 9.1.

Table 9.1. Crossover Layout

Sequence	Patient Number	Period 1	Period 2
		(Treatment A)	(Treatment B)
A-B	1	y111	y221
	3	y112	y222
	6	y113	y223
	7	y114	y224
	.	.	.
	.	.	.
	.	.	.
		(Treatment B)	(Treatment A)
B-A	2	y211	y121
	4	y212	y122
	5	y213	y123
	8	y214	y124
	.	.	.
	.	.	.
	.	.	.