The analysis of case-control studies under validation subsampling.

In case-control studies, one often finds that covariates are missing or measured with error in the entire sample, whereas complete or exact covariate information is available only in a subsample. This paper discusses the analysis of case-control studies under a double-sampling scheme, where at the first stage covariates are measured with error or missing, and at the second stage are validated in a subsample. The method proposed combines the risk information from both samples by assuming that (1) the disease incidence model is logistic, (2) the partial or proxy information takes on finitely many values, and (3) the error is non-differential. The estimator is obtained by jointly fitting logistic models to the first and second stage data, a variance formula is presented. Parameters can be estimated by use of standard packages for dose-response data. Data from an ongoing case-control study on lung cancer serve as an example.