A note on the probability structure of a doubly randomized delayed start design - Zhao Yang (Statistical Theory and Related Fields)
The innovative doubly randomized delayed start (DRDS) design has been implemented to tackle the well-known challenge of a high placebo response rate in clinical trials. This design begins with a conventional parallel design phase (period 1), followed by a subsequent phase (period 2) where subjects initially assigned to placebo and who did not respond are re-randomized to either the test drug or placebo. Chi, G. Y., Li, Y., Liu, Y., Lewin, D., & Lim, P. (2016 On clinical trials with a high placebo response rate. Contemporary Clinical Trials Communications, 2, 34–53. https://doi.org/10.1016/j.conctc.2015.10.002) introduced a new statistical methodology with a conditional probability structure to account for the specific characteristics of the DRDS design. However, some critical formulas in Chi et al. (2016, p. 38) for this probability structure are incorrect. Here, we correct these formulas and provide a comprehensive technical background on deriving the probability structure for a DRDS design to support these corrections.