Too Many Covariates and Too Few Cases? A Comparative Study

• Activity Number: 659
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Qingxia Chen*+ and Yuwei Zhu and Keipp H Talbot and Marie R Griffin and Frank E Harrell and Patrick Arbogast
• Companies: Vanderbilt University and Vanderbilt University and Vanderbilt University and Vanderbilt University and Vanderbilt University and Kaiser Permanente
• Keywords: penalized regression ; ridge regression ; propensity score ; logistic regression ; LASSO ; vaccine study

Abstract

For the multivariable logistic regression model, it is recommended to include at most 10-15 parameters per valid sample size m in order to reliably estimate the regression coefficients, where m is the number of cases or controls, whichever is less. This condition is, however, hard to be met even in a well designed study when the number of confounders is overwhelmed, rare disease is studied, and/or subgroup analysis is of interest. Extensive simulations were conducted to evaluate various existing methods including various propensity score methods, and penalized regression models including ridge regression, LASSO, and SCAD. The methods were evaluated in the setups mimicing our motivating clinical data and the results showed that the penalized logistic regression model with ridge penalty and the logistic regression model with propensity score adjustment outperform the other methods in our setting. There are some factors that will affect the choice between the aforementioned two methods: (a) exposure rate; (b) number of valid sample size per parameter; (c) ratio between cases and controls.We applied the methods to estimate the vaccine effectiveness in the motivating vaccine study.