Cost-efficient designs for three-arm trials with treatment delivered by health professionals: Sample sizes for a combination of nested and crossed designs

Abstract

Background: This article studies the design of trials that compare three treatment conditions that are delivered by two types of health professionals. The one type of health professional delivers one treatment, and the other type delivers two treatments, hence, this design is a combination of a nested and crossed design. As each health professional treats multiple patients, the data have a nested structure. This nested structure has thus far been ignored in the design of such trials, which may result in an underestimate of the required sample size. In the design stage, the sample sizes should be determined such that a desired power is achieved for each of the three pairwise comparisons, while keeping costs or sample size at a minimum. Methods: The statistical model that relates outcome to treatment condition and explicitly takes the nested data structure into account is presented. Mathematical expressions that relate sample size to power are derived for each of the three pairwise comparisons on the basis of this model. The cost-efficient design achieves sufficient power for each pairwise comparison at lowest costs. Alternatively, one may minimize the total number of patients. The sample sizes are found numerically and an Internet application is available for this purpose. The design is also compared to a nested design in which each health professional delivers just one treatment. Results: Mathematical expressions show that this design is more efficient than the nested design. For each pairwise comparison, power increases with the number of health professionals and the number of patients per health professional. The methodology of finding a cost-efficient design is illustrated using a trial that compares treatments for social phobia. The optimal sample sizes reflect the costs for training and supervising psychologists and psychiatrists, and the patient-level costs in the three treatment conditions. Conclusion: This article provides the methodology for designing trials that compare three treatment conditions while taking the nesting of patients within health professionals into account. As such, it helps to avoid underpowered trials. To use the methodology, a priori estimates of the total outcome variances and intraclass correlation coefficients must be obtained from experts’ opinions or findings in the literature.