A comparison of binary models dealing with an extraneous effect relating to the main risk factor, but not relating to the outcome variable

In a binary model relating a response variable Y to a risk factor X , account may need to take of an extraneous effect Z that is related to X , but not Y . This is known as the association pattern Y − X − Z . The extraneous variable Z is commonly included in models as a covariate. This paper concerns binary models, and investigates the use of deviation from the group mean (D‐GM) and deviation from the fitted fractional polynomial value (D‐FP) for removing the extraneous effect of Z . In a simulation study, D‐FP performed excellently, while the performance of D‐GM was slightly worse than the traditional method of treating Z as a covariate. In addition, estimators with excessive mean square errors or standard errors cannot occur when D‐GM or D‐FP is employed, even in small or sparse data sets. The Y − X − Z association pattern studied here often occurs in fetal studies, where the fetal measurement ( X ) varies with the gestation age ( Z ), but gestation age does not relate to the outcome variable ( Y ; e.g. Down's syndrome). D‐GM and D‐FP perform well with illustrative data from fetal studies, although there is a weak association between X and Z with a lower proportion of case subjects (e.g. 11:1, control to case). It is not necessary to add a new covariate when a model deals with the extraneous effect. The D‐FP or D‐GM methods perform well with the real data studied here, and moreover, D‐FP demonstrated excellent performance in simulations. Copyright © 2009 John Wiley & Sons, Ltd.