Corrections for Exposure Measurement Error in Logistic Regression Models With an Application to Nutritional Data

this paper is to show how the method of Rosner et al. may be extended by including a second term in the Taylor series approximation. The resulting estimates can then be compared with one another. The two approximations are derived under less restrictive assumptions than those used by Rosner et al. In particular, the distribution of the measurement error need not be specified and the disease under study does not have to be rare. The formulae for the corrected estimates and their standard errors are essentially similar for the two approximations. When the measurement error model is linear, the standard errors include a component which reflects the variability of the measurement error parameters estimated from the validation data. We apply the two approximate correction methods to baseline data from an epidemiological cohort study. A logistic model of the effect of nutrient intake on the ratio of serum HDL cholesterol to total cholesterol is used as an example. The two correction methods lead to very similar estimates, both of which are markedly different from the naive logistic estimates. The approach of Rosner et al. together with the extension is described in the next section. There we also compare the corrections to others proposed in the literature, and describe the software used in the computations. The example is presented in section 3, where we also examine the assumptions of the correction methods. Section 4 gives some conclusions. 2. APPROXIMATE MODELS Suppose a dichotomous response variable Y (disease status, for example) depends on predictor vectors X (p 1 \Theta 1) and U (p 2 \Theta 1) through a logistic model P(Y = 1jx; u) = F (ff + f