Design and analysis of individually randomized multiple baseline factorial trials.

Assessing the effectiveness of behavioral interventions in rare diseases is challenging due to extremely limited sample sizes and ethical challenges with withholding intervention when limited treatment options are available. The multiple baseline design (MBD) is commonly used in behavioral science to assess interventions, while allowing all individuals to receive the intervention. MBD is primarily used to evaluate a single intervention so an alternative strategy is needed when evaluating more than one intervention. In this case, a factorial design may be recommended, but a standard factorial design may not be feasible in rare diseases due to extremely limited sample sizes. To address this challenge, we propose the individually randomized multiple baseline factorial design (MBFD), which requires fewer participants but can attain sufficient statistical power for evaluating at least two interventions and their combinations. Furthermore, by incorporating randomization, we enhance the internal validity of the design. This study describes the design characteristics of a standard MBFD, clarifies estimands, and introduces three statistical models under different assumptions. Through simulations, we analyze data from MBFD using linear mixed effect models (LMM) and generalized estimating equations (GEE) to compare biases, sizes, and power of detecting the main effects from the models. We recommend using GEE to mitigate potential random effect misspecifications and suggest small sample corrections, such as Mancl and DeRouen variance estimator, for sample sizes below 120.