Abstract

Experimental outcomes may be affected by the choice of treatment that participants might make (if they were indeed allowed to choose), a so-called selection effect, and by whether they actually receive their preferred treatment, a so-called preference effect. Selection and preference effects can be important (possibly even larger than the usual treatment effect), but they cannot be estimated in conventional randomised experimental designs.

An alternative approach is the two-stage randomised design, in which participants are first randomly divided into two subgroups. In one subgroup, participants are randomly assigned to treatments, while in the other, participants are allowed to choose their own treatment. This approach can yield estimates of the direct treatment effect, and of the preference and selection effects. The latter two provide insight that goes considerably beyond what is possible in standard randomised experiments, notably the usual parallel group design.

In this presentation, we will consider the optimal proportion of participants who should be allocated to the choice subgroup and allowed to determine their own treatment. The precision of the estimated selection, preference and treatment effects are functions of: the total sample size; the proportion of participants allocated to choose their treatment; the variances of the response (or outcome); the proportions of participants who select each treatment in the choice group; and the selection, preference and treatment effects themselves. We develop general expressions for the optimum proportion of participants in the choice group, depending on the inverses of these variances, and on which effects are of primary interest. We illustrate the results with trial data comparing alternative clinical management strategies for women with abnormal results on cervical screening.