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Clinical Trials · RM-ANCOVA

Sample Size for Baseline-Adjusted Repeated-Measures ANCOVA

Plan a two-arm trial with one baseline measurement and multiple post-randomisation follow-ups when the primary hypothesis is a common treatment effect averaged across all follow-ups.

1. Planning setup

Optional. Used only in the protocol-ready wording.

2. Information obtained from previous study / literature

Use the expected common standard deviation of the continuous outcome across follow-up assessments.

Assume the same correlation between every pair of baseline and follow-up measurements.

3. Information decided by the researcher

Enter the smallest treatment-group difference averaged across all follow-ups that the study should detect.

Enter two or more follow-up assessments; do not include the baseline measurement.

Test direction

Use a one-sided calculation only when the directional hypothesis is justified before the study begins.

Inflation is applied separately within each group. The analysable target assumes complete repeated measurements.

4. Results

Enter the trial assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A two-arm diabetes trial compares HbA1c measured at three post-treatment visits while adjusting for baseline HbA1c and accounting for correlation among repeated measurements.

Formula and methodological note

Primary estimand: the treatment-group difference averaged across the post-randomisation follow-up assessments, adjusted for the baseline value of the same continuous outcome.

This is not a group × measurement interaction calculator. Use the repeated-measures ANOVA calculator when the primary question is whether the treatment difference changes across measurement occasions.

This implementation assumes equal 1:1 allocation, a common outcome variance, and compound symmetry: the same within-participant correlation between every pair of baseline and follow-up measurements.

Let k be the number of follow-ups and ρ the common compound-symmetry correlation across the baseline and all follow-ups. The variance ratio for the baseline-adjusted average treatment effect is:

VR = [1 + (k − 1)ρ − kρ²] / k

Raw sample per group = 2 × (Z critical + Z power)² × σ² × VR / Δ²

Analysable sample per group = ceiling(raw sample per group)

Recruitment per group = ceiling[analysable sample per group / (1 − attrition)]

  • One continuous outcome is measured once at baseline and at two or more follow-ups.
  • The primary hypothesis is a constant/common treatment effect averaged across follow-ups.
  • Equal 1:1 allocation, equal variances, compound symmetry, and complete analysable repeated measurements are assumed.
  • The method does not test a treatment-by-time interaction or a specific single follow-up effect.
  • It is not a direct sample-size method for MMRM with unstructured covariance, GEE, binary outcomes, informative missingness, unequal follow-up schedules, or cluster-randomised trials.

This planning tool does not replace study-specific statistical consultation or a sensitivity analysis using plausible covariance assumptions.

Method references

  1. Morgan TM, Case LD. Conservative sample size determination for repeated measures analysis of covariance. Annals of Biometrics & Biostatistics. 2013;1(1):1002.
  2. Frison L, Pocock SJ. Repeated measures in clinical trials: analysis using mean summary statistics and its implications for design. Statistics in Medicine. 1992;11:1685–1704.
  3. Borm GF, Fransen J, Lemmens WAJG. A simple sample size formula for analysis of covariance in randomized clinical trials. Journal of Clinical Epidemiology. 2007;60:1234–1238. doi:10.1016/j.jclinepi.2007.02.006.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Baseline-Adjusted Repeated-Measures ANCOVA (RM-ANCOVA).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/clinical-complex-study-designs/baseline-adjusted-repeated-measures-ancova/.