Adaptive Solomon Four-Group Design — Pretest Control with Sequential Allocation

The pretest sensitization estimate depends on contrasting outcomes between groups that received the pretest and groups that did not. As long as the adaptive rules maintain non-trivial allocation to all four groups — both pretest and no-pretest cells — the sensitization estimate remains available. Pre-specify minimum cell proportions (e.g., at least 15% of total allocation per cell) to prevent adaptive rules from depleting any group, and use allocation-weighted analysis to account for unequal group sizes at the end of the study.

Several classes of adaptive rules can be embedded within the Solomon structure: (1) response-adaptive randomization rules such as the randomized play-the-winner or doubly-adaptive biased coin, applied to the treatment dimension; (2) Bayesian adaptive rules that update posterior probabilities of superiority at interim looks; and (3) group-sequential rules that permit early stopping for efficacy or futility without changing allocation ratios but allow sample size re-estimation. All require pre-specification and simulation-based calibration of operating characteristics.

Yes. Standard 2 × 2 factorial ANOVA assumes balanced or fixed-ratio allocation and produces anti-conservative inference when allocation probabilities have shifted adaptively. The recommended approach is a likelihood-based analysis or a weighted least squares regression that incorporates the final allocation probabilities as weights, supplemented by simulation-based confidence intervals. Statistical simulation of the full adaptive trial under the null hypothesis is the gold standard for verifying Type I error control.

Power analysis for adaptive Solomon designs requires simulation rather than closed-form formulas. Simulate the full adaptive trial many times — typically 10,000 or more replicates — under scenarios representing the null hypothesis (to verify Type I error) and plausible alternative hypotheses (to estimate power). Input parameters include the expected treatment effect size, the anticipated sensitization magnitude, the adaptive rule parameters, the interim analysis schedule, and minimum cell size constraints. The resulting simulated power curve guides total sample size selection.

Strong preregistration of the full adaptive plan — including the adaptive algorithm, interim analysis schedule, decision rules, and final inference procedure — is not just recommended but essential for credibility. Without a preregistered plan, reviewers cannot distinguish legitimate pre-specified adaptation from post-hoc manipulation of the design to favor favorable results. Registering the protocol on a recognized platform (e.g., ClinicalTrials.gov, OSF) before enrollment is the professional standard.