Regression · LOG-BI

Sample Size for Multiple Logistic Regression: Block Increase

Plan a likelihood-ratio test of whether a prespecified predictor block improves a binary-outcome model beyond an existing reduced model.

1. Information obtained from previous studies or literature

Anticipated Cox–Snell R² for the reduced model

Anticipated Cox–Snell R² for the full model

The full model contains every reduced-model predictor plus the added block and must have a larger Cox–Snell R².

Anticipated outcome event probability (%)

Used to check the attainable Cox–Snell range and event balance.

Use Cox–Snell R² values from comparable nested models, not Nagelkerke, McFadden, Tjur, or ordinary R².

Help convert reported Nagelkerke R² values

Reduced-model Nagelkerke R²

Full-model Nagelkerke R²

Anticipated event probability (%)

2. Inputs decided by the researcher for the new study

Predictor columns in the reduced model

Exclude the intercept. Enter 0 when the reduced model is intercept-only.

Predictor columns added as the block

Count dummy variables, interactions, polynomial terms, and spline basis columns separately.

Type I error, alpha (%)

Power (%)

Anticipated dropout/non-response (%)

3. Results

Enter the nested-model assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A mortality model contains age, sex, blood pressure, and renal function. Researchers plan to test whether adding a prespecified biomarker block containing troponin status and C-reactive protein improves model fit.

Formula and methodological note

The likelihood-ratio block test evaluates whether all q added-block coefficients equal zero. For reduced and full Cox–Snell values R²R and R²F, the effect per participant is D=ln[(1−R²R)/(1−R²F)]. At N analysable participants, λ=ND and power is the upper tail of a noncentral chi-square distribution beyond the central chi-square critical value with q degrees of freedom.

The calculator separately rounds the analysable sample and dropout-adjusted recruitment target upward. Event-balance checks are diagnostics only. It assumes independent observations, genuinely nested prespecified models, correct logistic form, credible population effects, and adequate likelihood-ratio asymptotics. It is not for one coefficient, an omnibus intercept-only comparison unless the reduced model has zero columns, data-driven variable selection, prediction-model development, clustering, matching/repeated data, or penalized rare-event models. This tool supports research planning and does not replace statistical consultation.

Technical results

Method references

Cox DR, Snell EJ. The Analysis of Binary Data. 2nd ed. Chapman and Hall; 1989.
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 Logistic-Regression Block Increase (LOG-BI).” Web calculator. NajibMY, 2026. https://najibmy.netlify.app/tools/sample-size/regression/logistic-regression-block-increase/.