Effect of using bias-corrected estimators in logistic regression model in small samples: prostate-specific antigen (PSA) data

Abstract

This study investigates the effect of bias-corrected estimators in analyzing real-world skewed data where categorization and transformation are necessary. It also reports a small-scale simulation study to indicate factors which can influence the bias correction to be small or large. For the complete data-set, it is observed that the maximum likelihood estimates and Schaefer's bias-corrected estimates are not greatly different. However, when the original sample size is reduced by about 50%, the difference between the estimates is found to be much larger, possibly even large enough to influence the conclusions drawn. The impact of transformation and categorization is visibly present. However, the broad impression gained in categorization is the same though difference in types of categorizations can not be overlooked. A factor which seems to influence the size of the bias correction is identified.

Keywords

• Bias correction
• Categorization
• Log transformation
• Small sample
• Skewed data