Too many covariates and too few cases? - a comparative study.

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Traditional logistic regression requires a minimum number of cases/controls per parameter, which is often unmet in studies with rare outcomes or many confounders.
• Existing methods like propensity scores are available for binary exposures, and shrinkage methods (e.g., lasso) address situations where parameters exceed sample size (p >> n).
• However, guidance is lacking for choosing between regular logistic regression, propensity scores, and shrinkage methods when the number of parameters is similar to the sample size (p≈n).

Purpose of the Study:

• To evaluate and provide guidance on statistical modeling approaches for situations with a large number of parameters relative to the sample size (p≈n).
• To compare regular logistic regression, propensity score methods, and shrinkage approaches in complex epidemiological research.
• To inform the selection of appropriate statistical methods for estimating vaccine effectiveness, particularly for rare outcomes.

Main Methods:

• Conducted extensive simulations to mimic clinical data, specifically estimating vaccine effectiveness against influenza hospitalizations.
• Investigated the performance of various statistical modeling techniques, including regular logistic regression, propensity score methods, and shrinkage approaches (e.g., ridge regression, penalized logistic regression).
• Focused on scenarios where the number of parameters (p) is approximately equal to the sample size (n).

Main Results:

• The simulations provided insights into the performance of different statistical models under various conditions relevant to epidemiological studies.
• Identified that ridge regression and penalized logistic regression models, which penalize coefficients except for the exposure, may be suitable for such studies.
• The findings help bridge the gap in guidance for statistical modeling when p≈n.

Conclusions:

• When the number of parameters is similar to the sample size (p≈n), careful consideration of statistical modeling is crucial.
• Ridge regression and penalized logistic regression offer potential solutions for analyzing complex data, especially when estimating vaccine effectiveness.
• This research provides valuable guidance for biostatisticians and epidemiologists facing challenges with large numbers of variables and rare outcomes in their studies.