A goodness-of-fit test of logistic regression models for case-control data with measurement error

We study goodness-of-fit tests for logistic regression models for case-control data when some covariates are measured with error. We first study the applicability of traditional test methods for this problem, simply ignoring measurement error, and show that in some scenarios they are effective despite the inconsistency of the parameter estimators. We then develop a test procedure based on work of Zhang (2001) that can simultaneously test the validity of logistic regression and correct the bias in parameter estimators for case-control data with nondifferential classical additive normal measurement error. Instead of using the information matrix considered by Zhang (2001), our test statistic uses preselected functions to reduce dimensionality. Simulation studies and an application illustrate its usefulness. Copyright 2011, Oxford University Press.