Small sample bias correction or bias reduction?

Abstract

Many problems in biomedical and other sciences are subject to biased estimates (maximum likelihood or of similar types). In two seminal papers Cox and Snell (1968) and Firth (1993) deal with first order bias of maximum likelihood estimates. Cox and Snell obtain a correction term that corrects, approximately, first order bias and Firth uses an adjustment to the score function; the solution of the estimating equation obtained by solving the adjusted score function to zero, removes the first order bias of the maximum likelihood estimates approximately. In many applications authors use one of these two procedures for bias correction without being aware that the other exists or whether these two procedures are equivalent. In this paper we investigate the equivalence issue of the two methods through theoretical analysis, simulation study and data analysis. We show that the two methods yield either exactly the same estimates or that the preventive method has some edge over the other.

Keywords:

• Bias correction
• Bias reduction
• Generalized estimating equations
• Longitudinal data
• Marginal model