Refer to Problem 12.7. Let µk(a, b, c) denote the expected frequency of outcomes (a, b, c) for treatments (A, B, C) under treatment sequence k, where outcome 1 = relief and 0 = nonrelief. With a nonparametric random effects approach, show that one can estimate treatment effects in model (12.19) by fitting the quasi-symmetry model
log µk(a, b, c) = aβA + bβB + cβC + λk(a, b, c),
where λk(a, b, c) = λk(a, c, b) = λk(b, a, c) = λk(b, c, a) = λk(c, a, b) = λk(c, b, a). Fit the model, and show that β̂B – β̂A = 1.64 (SE = 0.34), β̂C – β̂A = 2.23 (SE = 0.39), β̂C – β̂B = 0.59 (SE = 0.39). Interpret. Compare results with Problem 12.7 for model (12.19).
Data from Problem 12.7:
For the crossover study in Table 11.10 (Problem 11.6), fit the model
logit[P(Yi(k)t = 1|ui(k))] = αk + βt + ui(k),
where {ui(k)} are independent N(0, σ2). Interpret {β̂t} and σ̂.
Table 11.10: