Minimum sample size for developing a multivariable prediction model: PART II - binary and time-to-event outcomes.

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Developing prediction models requires careful consideration of sample size.
• Inadequate sample size can lead to overfitting and unreliable results.
• Existing rules of thumb for sample size may not be universally applicable.

Purpose of the Study:

• To propose a method for calculating minimum sample size (n) and outcome events (E) for prediction models.
• To ensure adequate sample size by meeting criteria for optimism, model fit, and risk estimation.
• To provide a data-driven approach to avoid arbitrary sample size rules.

Main Methods:

• Calculate minimum n and E based on three criteria: shrinkage factor (≥0.9), Nagelkerke's R² difference (≤0.05), and precise risk estimation.
• Prespecify anticipated Cox-Snell R² from previous studies.
• Apply the method to diagnostic and prognostic models to determine required events per predictor parameter (EPP).

Main Results:

• The proposed method ensures small optimism in predictor effect estimates.
• It minimizes the absolute difference between apparent and adjusted Nagelkerke's R².
• Examples show a Chagas disease model requires EPP ≥ 4.8 and a venous thromboembolism model requires EPP ≥ 23.

Conclusions:

• The developed method provides a rigorous approach to determine minimum sample size for prediction models.
• It emphasizes the importance of calculating events per predictor parameter (EPP) based on specific criteria.
• This approach is superior to using general rules of thumb, ensuring more reliable model development.