Sample size formulae for trials comparing group and individual treatments in a multilevel model

In disease screening and prevention trials, subjects in the experimental condition are frequently nested within therapy groups, whereas subjects in the control group receive individual or no therapy and are therefore not nested within groups. Outcomes of subjects within the same therapy group are expected to be more alike than outcomes of subjects within different therapy groups. Ignoring this dependency in the design stage may result in less powerful designs. This paper presents a multilevel model for analyzing such trials and sample size formulae for continuous and binary outcomes with unequal variances and costs across groups. The proposed optimal design ensures that there is adequate power to detect a treatment effect with either minimal cost or a minimal number of subjects. We apply our strategy and design an improved trial where all subjects with musculoskeletal pain received conventional therapy and subjects in the intervention arm participated in a group-learning program.