Bring More Data!-A Good Advice? Removing Separation in Logistic Regression by Increasing Sample Size.

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Maximum likelihood (ML) is standard for logistic regression parameter estimation.
• Separation, where ML estimates fail due to data characteristics (small N, unbalanced outcomes), poses a challenge.
• Existing solutions include Firth's correction (FC) and increasing sample size (ISS).

Purpose of the Study:

• To compare the cost-adjusted relative efficiency of ML with ISS versus FC for handling separation in logistic regression.
• To provide guidance on the best approach when encountering separation in statistical analyses.

Main Methods:

• Extensive simulation study comparing ML with ISS against FC.
• Evaluation based on root mean squared errors and efficiency.
• Illustrative examples from colorectal cancer screening and ornithology.

Main Results:

• Firth's correction (FC) yielded reasonably small root mean squared errors.
• FC proved to be the more efficient estimator compared to ML with ISS.
• Increasing sample size (ISS) did not consistently improve estimation over FC.

Conclusions:

• Firth's correction (FC) is a more efficient method for addressing separation in logistic regression than increasing sample size (ISS).
• FC should be considered the default method for analyses with critically low observations or outcome events.
• Avoid increasing sample size solely to resolve separation; opt for FC instead.