Score tests in the presence of errors in covariates in matched case-control studies

If covariates are measured with errors, failure to account for that errors may result in a biased estimator of the parameters and consequently the test based on the corresponding estimator may turn out to be biased under the non-zero null hypothesis. In this paper we derive score tests for testing the association between a disease and covariates when a covariate is measured with errors in a matched case-control study. In particular, we deal with the scenario where a possibly biased surrogate is measured in the main data set which is accompanied by an external calibration data that contain the biased surrogate and repeated measures of an unbiased surrogate variable. Under the additive, normal, non-differential measurement errors, and flexible parametric model assumptions, we derive a score test for testing the effect of the covariate measured with errors. In addition, we also derive a score test for a more general hypothesis involving the coefficients associated with the covariates measured with and without errors, which is useful for testing a relationship among the effects of the covariates, such as equality of one or more regression coefficients. Finite sample performance of the proposed method is judged via simulation studies. The proposed method is also applied to a real matched case-control data on colon cancer.