Corrections for exposure measurement error in logistic regression models with an application to nutritional data

Two correction methods are considered for multiple logistic regression models with some covariates measured with error. Both methods are based on approximating the complicated regression model between the response and the observed covariates with simpler models. The first model is the logistic approximation proposed by Rosner et al., and the second is a second-order extension of this model. Only the mean and covariance matrix of the true values of the covariates given the observed values have to be specified, but no distributional assumptions about the measurement error are made. The parameters related to the conditional moments are estimated from a separate validation data set. The correction methods considered here are compared to other methods proposed in the literature. They are also applied to a multiple logistic model describing the effect of nutrient intakes on the ratio of serum HDL cholesterol. The data constitute baseline data from an epidemiological cohort study, in which a separate pilot study has been carried out to obtain validation information. In the example the corrected parameter estimates from the two approximate models are very similar. Both differ considerably from the naive logistic estimates, indicating a large effect of the measurement error. The various assumptions required by the correction methods are also discussed.