In clinical settings with no commonly accepted standard-of-care, multiple treatment regimens are potentially useful, but some treatments may not be appropriate for some patients. A personalized randomized controlled trial (PRACTical) design has been proposed for this setting. For a network of treatments, each patient is randomized only among treatments which are appropriate for them. The aim is to produce treatment rankings that can inform clinical decisions about treatment choices for individual patients. Here we propose methods for determining sample size in a PRACTical design, since standard power-based methods are not applicable. We derive a sample size by evaluating information gained from trials of varying sizes. For a binary outcome, we quantify how many adverse outcomes would be prevented by choosing the top-ranked treatment for each patient based on trial results rather than choosing a random treatment from the appropriate personalized randomization list. In simulations, we evaluate three performance measures: mean reduction in adverse outcomes using sample information, proportion of simulated patients for whom the top-ranked treatment performed as well or almost as well as the best appropriate treatment, and proportion of simulated trials in which the top-ranked treatment performed better than a randomly chosen treatment. We apply the methods to a trial evaluating eight different combination antibiotic regimens for neonatal sepsis (NeoSep1), in which a PRACTical design addresses varying patterns of antibiotic choice based on disease characteristics and resistance. Our proposed approach produces results that are more relevant to complex decision making by clinicians and policy makers.
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