Abstract
BackgroundThe effects, in terms of bias and precision, of omitting non-confounding predictive covariates from generalized linear models have been well studied, and it is known that such omission results in attenuation bias but increased precision with logistic regression. However, many epidemiologic risk analyses utilize alternative models that are not based on a linear predictor, and the effect of omitting non-confounding predictive covariates from such models has not been characterized.MethodsWe employed simulation to study the effects on risk estimation of omitting non-confounding predictive covariates from an excess relative risk (ERR) model and a general additive-multiplicative relative-risk mixture model for binary outcome data in a case-control setting. We also compared the results to the effects with ordinary logistic regression.ResultsFor these commonly employed alternative relative-risk models, the bias was similar to that with logistic regression when the risk was small. More generally, the bias and standard error of the risk-parameter estimates demonstrated patterns that are similar to those with logistic regression, but with greater magnitude depending on the true value of the risk. The magnitude of bias and standard error had little relation to study size or underlying disease prevalence.ConclusionsPrior conclusions regarding omitted covariates in logistic regression models can be qualitatively applied to the ERR and the general additive-multiplicative relative-risk mixture model without substantial change. Quantitatively, however, these alternative models may have slightly greater omitted-covariate bias, depending on the magnitude of the true risk being estimated.
Highlights
Binary regression models are often used to estimate the association between an exposure and disease risk with adjustment for other covariates
Estimates of generalized linear models (GLM) parameters of included covariates can change with omission of covariates associated with outcome but not associated with included covariates (“omitted-covariate bias”); the change is towards the null value of no risk with certain classes of link functions, including logistic regression.[1,3]
Depending on sample size and true excess relative risk (ERR) βE, simulated case-control samples occasionally arose in which, by chance, the mean value of exposure among controls was larger than that among cases, resulting in a negative estimate of ^E. This alone is not problematic, but sometimes there arose during the iterations a negative value of the estimate of ^E, such that ^EX À1 for some hypothetical cohort member’s generated dose value; the generalized nonlinear model (GNM) algorithm failed in such situations because log(1 + βEX) is not defined when (1 + βEX) ≤ 0, so we replaced such situations with a new run
Summary
Binary regression models are often used to estimate the association between an exposure and disease risk with adjustment for other covariates. Adjustment covariates can include confounders, as well as risk factors not associated with exposure (non-confounding predictors). It is well known that omitting confounders can result in bias; what concerns us here is omitting non-confounding predictors. The effects, in terms of bias and precision, of omitting non-confounding predictive covariates from generalized linear models have been well studied, and it is known that such omission results in attenuation bias but increased precision with logistic regression. Many epidemiologic risk analyses utilize alternative models that are not based on a linear predictor, and the effect of omitting non-confounding predictive covariates from such models has not been characterized
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