Regression to the Mean-Adjusted Sample-Size Determination for Cutoff-Selected Single-Arm Pre-Post Studies
Abstract
Studies enrolling participants on the basis of an extreme baseline value are susceptible to regression to the mean (RTM), such that some observed pre-post change is expected even without treatment. Existing methods estimate and decompose RTM retrospectively. We extend this framework to prospective study design by deriving a closed-form sample-size method for continuous, cutoff-selected, single-arm pre-post studies. The method partitions anticipated total change into that expected from RTM and the residual treatment effect, and powers the study to detect the latter. It uses the general bivariate-normal RTM expression, allowing baseline and follow-up variances to differ, and incorporates the corresponding conditional variance of the pre-post change. To our knowledge, no published method or software implements this cutoff-based RTM framework for prospective closed-form sample-size determination in this setting. The Stata command power onemean_rtm provides solutions for sample size and minimum detectable effect, normal-theory power evaluation, attrition adjustment, and sensitivity analysis. Monte Carlo simulation across 58 scenarios demonstrated accurate Type I error control and showed that achieved power rapidly approached nominal power as sample size increased, with the closed-form calculation generally conservative at very small sample sizes.
Related
- Anytime-Valid Inference in Linear Models with Applications to Regression-Adjusted Causal Inference
- Sample size determination for randomized decentralized clinical trials with longitudinal outcomes
- Multilevel network meta-regression for multistate models: Population-adjusted joint synthesis of progression and survival from individual and aggregate data
- On E-Backtesting: Generalizations and Sample Size Determination
- Bayesian Sample Size Determination: Sampling Distribution Estimation or Exploration?
BibTeX
@misc{linden2026regression,
title = {{Regression to the Mean-Adjusted Sample-Size Determination for Cutoff-Selected Single-Arm Pre-Post Studies}},
author = {Ariel Linden},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27919},
eprint = {2609.27919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27919},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Regression to the Mean-Adjusted Sample-Size Determination for Cutoff-Selected Single-Arm Pre-Post Studies
AU - Ariel Linden
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27919
UR - https://arxiv.org/abs/2609.27919
AB - Studies enrolling participants on the basis of an extreme baseline value are susceptible to regression to the mean (RTM), such that some observed pre-post change is expected even without treatment. Existing methods estimate and decompose RTM retrospectively. We extend this framework to prospective study design by deriving a closed-form sample-size method for continuous, cutoff-selected, single-arm pre-post studies. The method partitions anticipated total change into that expected from RTM and the residual treatment effect, and powers the study to detect the latter. It uses the general bivariate-normal RTM expression, allowing baseline and follow-up variances to differ, and incorporates the corresponding conditional variance of the pre-post change. To our knowledge, no published method or software implements this cutoff-based RTM framework for prospective closed-form sample-size determination in this setting. The Stata command power onemean_rtm provides solutions for sample size and minimum detectable effect, normal-theory power evaluation, attrition adjustment, and sensitivity analysis. Monte Carlo simulation across 58 scenarios demonstrated accurate Type I error control and showed that achieved power rapidly approached nominal power as sample size increased, with the closed-form calculation generally conservative at very small sample sizes.
ER -