Sample Size for Simple Logistic Regression

Example clinical scenario

A cohort study investigates whether higher glycated haemoglobin predicts hospital readmission within 30 days. The binary outcome is readmission; the predictor is either HbA1c as a continuous measurement or diabetes-control status coded 0/1.

Formula and methodological note

The calculator uses the Hsieh–Bloch–Larsen large-sample approximation for a Wald test of one simple logistic-regression coefficient. For a continuous, normally distributed predictor, it uses n = (z critical + z power)² divided by p(1−p) times the squared log-odds coefficient expressed per predictor SD. For a binary predictor it uses the source's unequal-allocation two-proportion approximation, deriving the X=1 event probability from the odds ratio and the X=0 event probability.

It assumes independent observations, correct logistic-model form, an approximately normal continuous predictor where selected, and sufficiently large samples. It is not for adjusted/multiple logistic regression, a multi-category predictor, interactions, clustering, case-control sampling, rare-event corrections, or prediction-model development. This tool supports research planning and does not replace statistical consultation.

Method references

1. Hsieh FY, Bloch DA, Larsen MD. A simple method of sample size calculation for linear and logistic regression. Stat Med. 1998;17:1623–1634.
2. Faul F, Erdfelder E, Buchner A, Lang A-G. Statistical power analyses using G*Power 3.1. Behav Res Methods. 2009;41:1149–1160.