Extend design-based estimators to response-guided experimentation

Extend the design-based effect-size estimators for randomized multiple-baseline experiments to response-guided experimentation designs in which intervention onsets are selected after inspecting baseline outcomes and the onset probabilities consequently depend on those outcomes.

Background

The paper’s estimators assume that intervention onsets are randomized according to probabilities that do not depend on the observed baseline outcomes. The authors note that many multiple-baseline studies instead select the onset after examining the baseline, a practice termed response-guided experimentation. In that setting, the randomization mechanism is outcome-dependent, so the inverse-probability weighting and design-based unbiasedness arguments developed in the paper cannot be applied directly without modification.

References

We leave two extensions for future work. In many multiple-baseline studies, the onset is chosen after inspecting the baseline, a practice known as response-guided experimentation \citep{FerronJooLevin2017}. The onset probabilities then depend on the outcomes, and the estimators of this paper would need to be extended to such designs.

— Design-based effect sizes and their synthesis in randomized multiple-baseline experiments  (2610.13001 - Chen et al., 9 Oct 2026) in Discussion, final paragraph (Section 9)