Case-Control Studies With Errors in Covariates

Abstract

We devise methods for estimating the parameters of a prospective logistic model with dichotomous response D and arbitrary covariates X from case-control data when these covariates are measured with error. We suppose that some fraction of the cases and controls provide only the error-prone covariate measurements, W (the “incomplete” or “reduced” data), whereas some of the cases and controls provide measurements on X and W (the “complete” data). We assume a measurement error density with a finite set of parameters α, namely fw|xD(w|x, d, α), and nondifferential error is treated as a special case of this model, fw|x(w|X, α). Our algorithm estimates both the logistic parameters and α from a pseudolikelihood. Because empirical distribution functions are used in place of needed distributions in the pseudolikelihoods, the required asymptotic theory is more elaborate than for pseudolikelihoods based on substitution for a finite number of nuisance parameters. We also examine computationally simpler methods under t...