The analysis of cross‐over trials with baseline measurements
Abstract
The statistical power of cross‐over trials can be increased by taking ‘baseline’ measurements of the outcome variable at the start of each treatment period. Analysis of covariance (ANCOVA), rather than analysis of change scores, takes best advantage of this. However, ANCOVA can give biased treatment effect estimates in observational studies with true baseline imbalance. While in truth balanced, chance baseline imbalance is possible in individual randomized cross‐over studies due to their typically small sample size. Although such chance imbalance does not cause biased estimation on average over repeated trials, this simulation study will aim to confirm the appropriateness of ANCOVA when faced with the analysis of data from an individual trial in which chance baseline imbalance is clearly apparent. Randomized cross‐over trials were simulated, varying in sample size and the pattern and strength of correlation between repeated measures. Estimates from ANCOVA, change scores, and post‐treatment difference were unbiased on average across each set of simulated data sets. ANCOVA and change scores could use baseline information to improve precision, but change scores could also reduce precision if baseline measures were uninformative. Change scores only were correlated with chance within‐subject baseline imbalance. All three estimators could be correlated with chance between‐subjects imbalance in the first period baseline measurements, the strongest associations being with the post‐treatment difference. Consistent results were obtained from a real data example. In conclusion, ANCOVA took best advantage of baseline measures to improve precision, and avoided bias in the widest set of circumstances with chance imbalance in those baseline measures. Copyright © 2010 John Wiley & Sons, Ltd.
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Treatment effects were tested using an ANCOVA approach for AB/BA cross-over designs with baseline measurements before each treatment.
“We tested for treatment effects (oxytocin versus placebo) using the analysis of covariance (ancova) approach described by Senn 49 and Metcalfe 56 for the analysis of AB/BA cross‐over designs with baseline measurements before each treatment.”
From The Analgesic Effect of Oxytocin in Humans: A Double‐Blind, Placebo‐Controlled Cross‐Over Study Using Laser‐Evoked Potentials (2016) · cites this paper as [56]
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- Authors
- Metcalfe, C.
- Affiliations
- University of Bristol (GB)
- Corresponding author
- Metcalfe, Chris
- ORCID
- Metcalfe, Chris
- Venue
- Statistics in Medicine
- Publisher
- Wiley
- Published
- 2010-12-16
- Volume
- 29
- Issue
- 30
- Pages
- 3211-3218
- ISSN
- 0277-6715 (ISSN-L)
- 1097-0258
- OpenAlex
- W2137430824
- Cited by
- 32
- References
- 14
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 6 · 2023: 2 · 2022: 3 · 2021: 1 · 2020: 2 · 2019: 1 · 2018: 3 · 2017: 2 · 2016: 3 · 2015: 1 · 2014: 1 · 2013: 1 · 2012: 1
- FWCI
- 0.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Statistics in Medicine (publishedVersion)
- PubMed (publishedVersion)
- Explore Bristol Research (submittedVersion)
- Funders
- University of Bristol
- Great Ormond Street Hospital for Children
- Health Technology Assessment Programme
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- crossover trial, baseline measurement, covariance analysis, change scores, treatment effect estimation, baseline imbalance, estimation bias, statistical power, repeated measures correlation
- MeSH terms
- Child, Computer Simulation, Cystic Fibrosis, Data Interpretation, Statistical, Deoxyribonucleases, Forced Expiratory Volume, Humans, Randomized Controlled Trials as Topic, Cross-Over Studies
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