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

Abstract

Funding information Natural Sciences and Engineering Research Council of CanadaOutcomes 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.

Two‐stage randomized trial design for testing treatment, preference, and self‐selection effects for count outcomes

“…Using Equations (4), (5), and (6), we can calculate the treatment, selection, and preference effects, Δ = 2, Δ = −2.08 and Δ = 0.42, respectively. We can then plug in the relevant information from Table 4 into the equations derived in Section 2.2 to calculate the sample sizes.…”

“…In these cases, the group of undecided patients forms a particular group which should be considered in the design and analysis of the two‐stage design. While some preliminary work has been done to outline ways to incorporate undecided patients, 4,5 it may be useful to extend much of the current methodology to account for possible existence of this undecided subgroup.…”

“…Here we assume all participants have a preference, although works has begun to weaken this assumption. 4,5 This model was extended to (see Figure 2) include stratification factors closely related to patient's treatment preferences. 6,7 The stratified model tends to be more efficient, since the observed variability in specified outcome is expected to decrease, allowing for more accurate estimate of each effects.…”

“…In the second stage, participants in the random arm are randomized to receive either treatment A or treatment B, while participants in the choice arm are allowed to choose their desired treatment (see Figure 1). Here we assume all participants have a preference, although works has begun to weaken this assumption 4,5 …”

Relative efficiencies of alternative preference-based designs for randomised trials

“…In trials where undecided patients exist, one can define second contrasts for the selection and preference effects, which represent analogous additional functions of the expected differences in outcomes between the patients with or without a definite treatment preference. 3…”