Costs and consequences of alternative designs are commonly considered in practice. The models presented here are practical tools for comparing the time and monetary cost of using alternative allocation designs to improve recruitment rates. Several conclusions follow from this work. First, these equations emphasize the point that trial time and cost may be increased by alternative allocation designs, even when these designs do improve recruitment rates. Nonetheless, the maximum possible increase in time and cost from increasing the allocation ratio is modest, not more than about 4% for a 1.5:1 allocation ratio and not more than about 12% for a 2:1 allocation ratio. Second, the formulas presented here characterize the relative influence of the factors that determine trial cost under alternative allocation designs. Based on the formulas derived here, the trial contexts most likely to benefit from an alternative allocation ratio design are those with a low baseline recruitment rate, large target sample size, or low per sample cost. In these scenarios, even small increases in the recruitment rate may lead to meaningful reductions in trial time and cost.
There are considerations beyond trial time and the tangible cost of performing a trial when comparing study designs. In the case of positive trials of promising new treatments, using an alternative allocation ratio to reduce trial time has the intangible benefit of making an effective medication available sooner. For industry-sponsored trials of patented medications, shorter trial time translates to earlier and longer on-patent marketing of the medication. Higher allocation to experimental treatment also has the advantage of increasing the likelihood of observing rare adverse events. Arguing against alternative allocation ratios, on the other hand, is the increased study subject burden implicit in performing a trial with a larger sample size. Limiting subject burden is a goal of both investigators and the Institutional Review Boards charged with approving study designs. For treatments with known side effects, a higher allocation ratio increases in particular the number of subjects exposed to the additional burden of treatment side-effects. Studies of active treatments known to have significant side effects should consider the trade-offs carefully before implementing an unequal allocation scheme. Similarly, all other things being equal, the choice between study designs that are approximately time and cost neutral should always be the design with the smallest total sample size (that is, the design with allocation ratio closest to 1:1).
A second concern with using alternative allocation to improve recruitment relates to the fact that this approach relies on the perception that the experimental treatment offers more hope of a favorable outcome compared to control or currently available standard care. This perception is most likely for diseases where only palliative treatments are currently available, as for example Alzheimer’s disease, or for diseases where the prognosis is poor given current standard of care, as for example certain cancers. Patients seeking active treatment via enrollment in clinical trials are arguably nonrepresentative and may also be more prone to early dropout if treatment effects are not immediately evident or the treatment arm is unmasked. Alternative allocation designs are attractive to patients seeking active treatment via enrollment in clinical trials, and therefore may be more vulnerable to these potential sources of bias.
Finally, we note that there are only limited data on the effect of alternative allocation ratios on recruitment rates. One exception is within the context of Alzheimer’s disease treatment trials, where a recent survey estimated recruitment yield per 100 contacts under a range of likely scenarios [8
]. This survey found that 2:1 allocation would increase yield from 47 subjects to 60 subjects recruited per 100 contacts within the context of a low risk experimental treatment with only mild side-effects ((13/47) × 100% = 28% faster recruitment), and from 27 to 42 subjects recruited per 100 contacts within the context of a high-risk experimental treatment (56% faster recruitment). To our knowledge, these are the only estimates of the effect of allocation ratio on recruitment rate published to date, although a number of surveys have indicated that concern over randomization to the nonexperimental arm of a trial is a common potential barrier to recruitment (reviewed in [7
]). We expect that the effect of allocation ratio on recruitment is highly context specific in any case, and can only be definitively estimated within the context of an actual trial, that is, by randomizing different allocation ratios to the study sites in a multi-site trial. Absent real data on recruitment rates as a function of allocation ratios, the best course of action is to use plausible but conservative assumptions when considering alternative designs. Given defensible assumptions about recruitment rates, the decision to proceed with an alternative allocation design hinges on whether the improvement in recruitment rate justifies the increased sample size and study subject burden implied. The cost models presented here provide a practical tool for informing this decision process.