Adequate sample size for developing prediction models is not simply related to events per variable.

Area of Science:

• Biostatistics
• Epidemiology
• Health Informatics

Background:

• Sample size determination for Cox regression often relies on the 10 events per variable (EPV) rule of thumb.
• Previous studies suggest the 10 EPV rule may be relaxed in certain scenarios.
• The impact of low-prevalence binary predictors on Cox regression sample size requirements remains underexplored.

Purpose of the Study:

• To investigate the events per variable (EPV) requirements for Cox regression prediction models incorporating low-prevalence binary predictors.
• To evaluate the performance of these models using an external validation dataset.
• To determine data-driven EPV recommendations for clinical practice.

Main Methods:

• An extensive resampling study was performed using a large general-practice dataset (>2 million anonymized patient records).
• Cox regression models were developed with varying numbers of low-prevalence binary predictors.
• Model performance was assessed using an independent external validation dataset, examining both fully specified and variable-selected models.

Main Results:

• A data-driven approach to the EPV rule of thumb is essential.
• An EPV of 20 or greater generally mitigates bias in regression coefficients when numerous low-prevalence predictors are present in Cox models.
• Higher EPV is crucial for reducing bias and enhancing predictive accuracy with low-prevalence predictors.

Conclusions:

• The traditional 10 EPV rule is insufficient for Cox models with low-prevalence predictors.
• An EPV of at least 20 is recommended for models including many low-prevalence predictors to ensure reliable results.
• These findings provide crucial guidance for sample size calculations in epidemiological and clinical research.