Logistic Sample Size Calculator

Formula Used

The sample size estimation for logistic regression with a continuous predictor relies heavily on the methodology established by Hsieh, Bloch, and Larsen (1998). The fundamental formula connects the standard normal quantiles corresponding to Type I error ($\alpha$) and statistical power ($1 - \beta$) with the variance of the continuous covariate ($\sigma^2$), the baseline event probability ($\pi$), and the square of the log odds ratio ($\beta_1^2$). Adjustments are subsequently applied to account for anticipated study attrition rates.

How to Use This Calculator

• Significance Level: Input your preferred alpha threshold, commonly set at 0.05.
• Statistical Power: Enter the desired power level, typically 0.80 or higher.
• Odds Ratio: Provide the anticipated odds ratio associated with a standard deviation change in your continuous predictor.
• Baseline Event Rate: Specify the expected proportion of positive outcomes in your study population.
• Predictor Metrics: Define the mean and standard deviation of your continuous independent variable.
• Submit: Click the calculate button to instantly review required sample metrics.

Article & Comprehensive Guide

Determining the appropriate sample size for logistic regression is critical for ensuring adequate statistical power and avoiding Type II errors. Unlike linear regression, logistic regression models binary outcomes, making sample size calculations dependent not only on predictor variance and effect size but also on the overall baseline event rate. When utilizing continuous predictors, researchers must carefully specify the expected odds ratio per unit or per standard deviation increase. Failing to account for accurate predictor distribution parameters can lead to severely underpowered studies, rendering significant findings undetectable and wasting valuable research resources. Incorporating attrition rates further safeguards the study against unexpected participant dropouts or missing data issues.

Frequently Asked Questions (FAQs)

Q: Why is a continuous predictor handled differently than a binary predictor?
A: Continuous predictors utilize variance across a spectrum of values, requiring adjustments based on standard deviation and distribution shape rather than simple category proportions.

Q: What is a good baseline event rate to use if unknown?
A: Pilot studies, historical literature, or clinical assumptions should guide this value. If uncertain, running sensitivity analyses across a range of rates is strongly advised.