  The growing availability of observational databases like electronic health
records (EHR) provides unprecedented opportunities for secondary use of such
data in biomedical research. However, these data can be error-prone and need to
be validated before use. It is usually unrealistic to validate the whole
database due to resource constraints. A cost-effective alternative is to
implement a two-phase design that validates a subset of patient records that
are enriched for information about the research question of interest. Herein,
we consider odds ratio estimation under differential outcome and exposure
misclassification. We propose optimal designs that minimize the variance of the
maximum likelihood odds ratio estimator. We develop a novel adaptive grid
search algorithm that can locate the optimal design in a computationally
feasible and numerically accurate manner. Because the optimal design requires
specification of unknown parameters at the outset and thus is unattainable
without prior information, we introduce a multi-wave sampling strategy to
approximate it in practice. We demonstrate the efficiency gains of the proposed
designs over existing ones through extensive simulations and two large
observational studies. We provide an R package and Shiny app to facilitate the
use of the optimal designs.
