Cost -efficient design of main cohort and calibration studies where one or more exposure variables are measured with error

Calibration studies are often performed on a subgroup contained within or external to large studies, for the purpose of correcting risk estimates for the effect of measurement errors. In this paper, we present a method to optimally allocate the number of subjects in the main cohort and calibration studies by minimizing the total cost while maintaining a fixed statistical power to detect a specified log relative risk.;Measurement errors in the observed exposure are allowed to be subject to both random and systematic errors. It is shown that when errors in observed exposure variable contain both random and systematic errors, the optimal sizes of main and calibration studies are unaffected by the magnitude of systematic errors as long as the correlation between true exposure and observed exposure is fixed. We also deal with the case when a gold standard is not available and repeated reference measures are obtained in calibration studies. We find that non-optimal choice of the number of replicates of reference measures per calibration study subject could result in a considerable waste of resources.;Furthermore, the cost-efficient design is extended to a multivariate setting where covariates in the risk model are correlated in their true values as well as in errors. As the correlation between two covariates becomes stronger, the optimal sizes for both main cohort and calibration studies increase. When the risk of the confounding variable is stronger, the optimal design requires even larger number of subjects in calibration studies to detect a non-zero relative risk for the variable of interest. However, main cohort study sizes are relatively unaffected by the strength of the association between the confounding variable and the outcome. When the true covariates are correlated, required main cohort study size is also influenced by the correlation between errors in two observed exposures. The stronger error correlations are, the smaller main cohort size is needed when true covariates and errors in observed exposures are correlated in the same direction.