Two advanced methods for adjusting the main coefficient in logistic regression

Abstract

A binary disease outcome is commonly modeled with continuous covariates (e.g., biochemical concentration) in medical research, and the corresponding exploration may employ a normal discrimination approach. The covariate relationship affects the estimated association between binary outcome and the interesting covariate. The method of value deviated from a fitted value (fractional polynomial), which is abbreviated as VDFV, may reduce the estimation bias especially when the relationship between the covariates is nonlinear. However, when the extraneous variable relates to the outcome, the pooled data (cases and controls) are replaced by the control data only for the purpose of fitting values. Based on two association patterns, the extraneous variable unrelated to the outcome (I) and that related to the outcome (II), the simulation study reveals that VDFV-p (using pooled data) is reliable, with less bias and a smaller mean square error (MSE) in pattern (I) and that VDFV-c (using control data) shows less bias in pattern (II). The conventional covariate adjustment performs worse in (I) but fairly well in (II). Note that a huge MSE is never observed in VDFV-p or VDFV-c, while this is a common issue related to small sample size or sparse data in logistic regression. Two fetal studies are illustrated--one for pattern (I) and one for pattern (II).