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In modern observational studies using electronic health records or other routinely collected data, both the outcome and covariates of interest can be error‐prone and their errors often correlated. A cost‐effective solution is the two‐phase design, under which the error‐prone outcome and covariates are observed for all subjects during the first phase and that information is used to select a validation subsample for accurate measurements of these variables in the second phase. Previous research on two‐phase measurement error problems largely focused on scenarios where there are errors in covariates only or the validation sample is a simple random sample of study subjects. Herein, we propose a semiparametric approach to general two‐phase measurement error problems with a quantitative outcome, allowing for correlated errors in the outcome and covariates and arbitrary second‐phase selection. We devise a computationally efficient and numerically stable expectation‐maximization algorithm to maximize the nonparametric likelihood function. The resulting estimators possess desired statistical properties. We demonstrate the superiority of the proposed methods over existing approaches through extensive simulation studies, and we illustrate their use in an observational HIV study. [ABSTRACT FROM AUTHOR]