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Proportion · PROP-BA

Baseline-Adjusted Binary Outcome

Plan a two-arm comparison of a binary follow-up outcome using logistic regression adjusted for one binary baseline characteristic.

The treatment effect is a conditional odds ratio. Enter percentages, not decimal proportions.

1. Information obtained from previous studies or literature

The expected follow-up probability before stratifying by baseline status.

Odds ratio for baseline characteristic present versus absent.

2. Information decided by the researcher

Experimental versus reference, conditional on baseline status; must differ from 1.

3. Results

Enter the planning assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A two-arm randomized trial compares 12-week smoking abstinence while adjusting the primary logistic-regression analysis for whether each participant was abstinent at an earlier baseline assessment.

Formula and methodological note

The planning model is logit Pr(Y = 1 | T, B) = β₀ + βTT + βBB. The reference intercept is solved so the baseline-prevalence-weighted reference probabilities equal the entered marginal probability. For each candidate allocation, the expected binomial logistic Fisher information is Σp(1 − p)xx′ across treatment-by-baseline strata. The variance of β̂T is the treatment diagonal of the inverse information matrix, and normal-approximation Wald power is evaluated for βT = log(ORT).

The estimand is a conditional odds ratio and is generally not equal to a marginal odds ratio because odds ratios are non-collapsible. The method assumes randomization, the same baseline prevalence in both arms in expectation, one completely observed binary baseline covariate, a common treatment odds ratio with no treatment-by-baseline interaction, and the entered logistic model is adequate.

It does not support risk-difference or risk-ratio estimands, multiple or continuous covariates, repeated outcomes, clustering, matching, missing baseline data, interaction effects, penalized/exact logistic regression, or simulation-based assurance. Sparse expected cells can make the Wald approximation unreliable. This tool supports research planning and does not replace protocol-specific statistical consultation.

Technical results

Method references

  1. Hsieh FY, Bloch DA, Larsen MD. A simple method of sample size calculation for linear and logistic regression. Statistics in Medicine. 1998;17:1623–1634.
  2. Whittemore AS. Sample size for logistic regression with small response probability. JASA. 1981;76:27–32.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for a Baseline-Adjusted Binary Outcome (PROP-BA).” Web calculator. NajibMY, 2026. Accessed August 19, 2026. https://najibmy.netlify.app/tools/sample-size/proportion/baseline-adjusted-binary-outcome/.