Adequacy radii for stepped-wedge trials with time-varying effects
Abstract
Complete stepped-wedge designs guarantee eventual intervention delivery, but their final periods contain no concurrent controls. Under exposure-time heterogeneity this creates a design-analysis tension: a constant-effect analysis can be precise while targeting a design-dependent contrast, whereas an exposure-time indicator (ETI) analysis targets a prespecified time-averaged effect but may be much less precise. We develop an adequacy radius that quantifies the size of exposure-time heterogeneity compatible with a prespecified tolerance for estimand mismatch, and combine it with precision calculations to compare complete wedges with rollout-constrained hybrid designs that retain a wait-list arm. For a balanced wedge with a wait-list under the Hussey-Hughes model, the wait-list share and the correlation act on the constant-effect GLS estimand through a single scalar; we prove that the radius increases strictly with the wait-list share and decreases strictly with the within-cluster correlation, but remains bounded. Numerical optimisation and a model-based redesign of a weekend allied-health trial show that intermediate hybrids make estimand-aligned ETI analysis materially more affordable, giving a robustness-precision frontier rather than a binary choice between a complete wedge and a parallel trial. A second trial, of digital adherence support for tuberculosis treatment, has the same radius but no detectable heterogeneity; its test of a constant effect would detect heterogeneity large enough to halve the coverage of the nominal interval only 37% of the time. The contribution is a diagnostic and design principle: when exposure-time heterogeneity is plausible, retaining concurrent controls reduces the price of analysing the estimand one intends to report.
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BibTeX
@misc{halkiewicz2026adequacy,
title = {{Adequacy radii for stepped-wedge trials with time-varying effects}},
author = {Stanisław M. S. Halkiewicz and Sergey Alexeev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35853},
eprint = {2610.35853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35853},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Adequacy radii for stepped-wedge trials with time-varying effects
AU - Stanisław M. S. Halkiewicz
AU - Sergey Alexeev
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35853
UR - https://arxiv.org/abs/2610.35853
AB - Complete stepped-wedge designs guarantee eventual intervention delivery, but their final periods contain no concurrent controls. Under exposure-time heterogeneity this creates a design-analysis tension: a constant-effect analysis can be precise while targeting a design-dependent contrast, whereas an exposure-time indicator (ETI) analysis targets a prespecified time-averaged effect but may be much less precise. We develop an adequacy radius that quantifies the size of exposure-time heterogeneity compatible with a prespecified tolerance for estimand mismatch, and combine it with precision calculations to compare complete wedges with rollout-constrained hybrid designs that retain a wait-list arm. For a balanced wedge with a wait-list under the Hussey-Hughes model, the wait-list share and the correlation act on the constant-effect GLS estimand through a single scalar; we prove that the radius increases strictly with the wait-list share and decreases strictly with the within-cluster correlation, but remains bounded. Numerical optimisation and a model-based redesign of a weekend allied-health trial show that intermediate hybrids make estimand-aligned ETI analysis materially more affordable, giving a robustness-precision frontier rather than a binary choice between a complete wedge and a parallel trial. A second trial, of digital adherence support for tuberculosis treatment, has the same radius but no detectable heterogeneity; its test of a constant effect would detect heterogeneity large enough to halve the coverage of the nominal interval only 37% of the time. The contribution is a diagnostic and design principle: when exposure-time heterogeneity is plausible, retaining concurrent controls reduces the price of analysing the estimand one intends to report.
ER -