Minimum sample size for developing a multivariable prediction model: Part I - Continuous outcomes.

Area of Science:

• Medical Statistics
• Epidemiology
• Biostatistics

Background:

• Hundreds of prediction models are developed for health outcomes.
• Linear regression models are commonly used for continuous outcomes.
• Overfitting is a risk in model development, necessitating adequate sample size.

Purpose of the Study:

• To propose four key criteria for determining the minimum sample size (n) for developing prediction models.
• To ensure reliability and reduce overfitting in linear regression models.
• To provide a method for sample size calculation based on predictor parameters (p) and anticipated R-squared.

Main Methods:

• Proposed four criteria: shrinkage factor ≥0.9, R-squared difference ≤0.05, precise residual standard deviation estimation, and precise mean predicted outcome estimation.
• Required prespecification of predictor parameters (p) and anticipated R-squared.
• Applied criteria to an example of predicting lung function in African-American women.

Main Results:

• The minimum sample size (n) must meet all four proposed criteria.
• An example model with 25 predictor parameters requires at least 918 subjects (36.7 subjects per parameter).
• Larger sample sizes may be needed for precise estimation of specific predictor effects, especially with low-prevalence categories.

Conclusions:

• The proposed four criteria provide a robust method for determining the minimum sample size for developing prediction models.
• Meeting these criteria ensures model reliability, precise estimation, and reduced overfitting.
• The findings have implications for the design and validation of health prediction models in various populations.