Regression · LOG-1B

Sample Size for Multiple Logistic Regression: One Adjusted Coefficient

Plan a Wald test of one prespecified adjusted odds ratio for a numerical or binary primary predictor.

1. Planning setup

Primary predictor type

Only one prespecified coefficient is tested. A categorical primary predictor is supported only when it has two categories.

2. Information obtained from previous studies or literature

Predictor increment for the odds ratio

Predictor standard deviation (SDx)

Event probability at the predictor mean (%)

R² from regressing the primary predictor on the other predictors

This is not a logistic-model pseudo-R². VIF = 1/(1 − R²).

3. Inputs decided by the researcher for the new study

Smallest clinically important adjusted odds ratio

For a binary predictor, this compares X=1 with X=0. Values below 1 represent a protective association.

Alternative hypothesis

Type I error, alpha (%)

Power (%)

Anticipated dropout/non-response (%)

4. Results

Enter the planning assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A cohort study tests whether elevated troponin status predicts 30-day mortality after adjustment for age, sex, renal function, and illness severity. The target is the adjusted odds ratio for elevated versus non-elevated troponin.

Formula and methodological note

The calculator first applies the Hsieh–Bloch–Larsen simple-logistic approximation used by LOG-1X, then inflates the required sample by 1/(1 − R²), where R² is obtained by regressing the primary predictor on all other model predictors. This R² is not a logistic pseudo-R². The adjusted analysable sample is rounded up before dropout adjustment; the recruitment target is rounded up again.

The method assumes independent observations, a correctly specified logistic model, credible population inputs, and adequate events and non-events. It tests one coefficient only. It is not for joint tests, multi-category primary predictors, interactions, clustering, matched or repeated data, variable selection, rare-event corrections, or prediction-model development. This tool supports research planning and does not replace statistical consultation.

Technical results

Method references

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.
Faul F, Erdfelder E, Buchner A, Lang AG. Statistical power analyses using G*Power 3.1. Behavior Research Methods. 2009;41:1149–1160.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for One Adjusted Logistic-Regression Coefficient (LOG-1B).” Web calculator. NajibMY, 2026. https://najibmy.netlify.app/tools/sample-size/regression/multiple-logistic-regression-one-coefficient/.