Optimising the two-stage randomised trial design when some participants are indifferent in their treatment preferences.

Outcomes in a clinical trial can be affected by any underlying preferences that its participants have for the treatments under comparison and by whether they actually receive their preferred treatment. These effects cannot be evaluated in standard trial designs but are estimable in the alternative two-stage randomised trial design, in which some patients can choose their treatment, while the rest are randomly assigned. We have previously shown that, when all two-stage trial participants have a preferred treatment, the preference effects can be evaluated, in addition to the usual direct effect of treatment. We also determined criteria by which to optimise how many participants should be given a choice of treatment vs being randomised. More recently, we extended our methodology to allow for participants who are unable or unwilling to express a treatment preference if they are assigned to the choice group. In this paper, we show how to optimise the two-stage design when some participants are undecided about their treatment. We demonstrate that the undecided group should be regarded as distinct in the analysis, to obtain valid estimates of the preference effects. We derive the optimal proportion of participants who should be offered a choice of treatment, which in many cases will be close to 50%. More generally, the optima depend on the preference rates for treatments and the proportion of undecided participants, and the parameters of primary interest. We discuss some advantages and disadvantages of the two-stage trial design in this situation and describe a practical example.