Optimum Response-Adaptive Designs with Covariates

To find adaptive designs in the presence of covariates, we adapt the skewed designs of §6.6 to make the skewing proportions pj functions of the estimated treatment effects αˆj . The desired adaptive allocation is found by again seeking to minimise the variance of the linear combination (6.41)

lT1 α = ±p1α1 ∓ . . .± ptαt, (7.1)

with the proportions pj , j = 1, . . . , t such that 0 < pj < 1, ∑

pj = 1.