Cost-efficient study designs for binary response data with Gaussian covariate measurement error

When mismeasurement of the exposure variable is anticipated, epidemiologic cohort studies may be augmented to include a validation study, where a small sample of data relating the imperfect exposure measurement method to the better method is collected. Optimal study designs (i.e., least expensive subject to specified power constraints) are developed that give the overall sample size and proportion of the overall sample size allocated to the validation study. If better exposure measurements can be collected on a sample of subjects, an optimal design can be suggested that conforms to realistic budgetary constraints. The properties of three designs--those that include an internal validation study, those where the validated subsample is derived from subjects external to the primary investigation, and those that use the better method of exposure assessment on all subjects--are compared. The proportion of overall study resources allocated to the validation substudy increases with increasing sample disease frequency, decreasing unit cost of the superior exposure measurement relative to the imperfect one, increasing unit cost of outcome ascertainment, increasing distance between two alternative values of the relative risk between which the study is designed to discriminate, and increasing magnitude of hypothesized values. This proportion also depends in a nonlinear fashion on the severity of measurement error, and when the validation study is internal, measurement error reaches a point after which the optimal design is the smaller, fully validated one.