Caveats on Using Firth's Penalization in the Model-Based Regression Standardization for Rare Diseases

Area of Science:

• Epidemiology
• Biostatistics
• Medical Informatics

Background:

• Model-based regression standardization (parametric g-formula) estimates marginal effects but struggles with rare diseases due to data separation.
• Firth's penalized likelihood method addresses separation but can introduce bias in standardization by shrinking probabilities.
• Surgical site infections (SSI) are a relevant rare disease for evaluating these statistical methods.

Purpose of the Study:

• To examine the bias introduced by Firth's method in model-based regression standardization for rare diseases.
• To propose and evaluate novel ad hoc corrections to mitigate Firth's method bias.
• To assess the association between SSI and smoking status using the corrected methods.

Main Methods:

• Empirical study on surgical site infections (SSI) in orthopedic surgery patients.
• Application of Firth's penalized likelihood regression.
• Development and simulation-based evaluation of two ad hoc corrections: intercept correction and added covariate.
• Comparison with propensity score-based methods.

Main Results:

• Firth's method, while resolving convergence issues, demonstrated bias in regression standardization, leading to discrepancies in event rates.
• The proposed ad hoc corrections effectively mitigated the bias associated with Firth's method.
• The corrected methods showed improved performance compared to standard propensity score approaches in simulations.
• The final analysis identified an association between SSI and smoking status in orthopedic surgery patients.

Conclusions:

• Firth's penalized likelihood method requires careful consideration when used for regression standardization in rare disease settings.
• The proposed ad hoc corrections offer a viable approach to reduce bias and improve the accuracy of rare disease effect estimation.
• These corrected methods can be reliably applied to investigate associations between rare diseases and risk factors, such as smoking and SSI.