摘要 : This paper addresses optimal design and efficiency of two-phase (2P) case–control studies in which the first phase uses an error-prone exposure measure, Z, while the second phase measures true, dichotomous exposure, X, in a subset... 展开 This paper addresses optimal design and efficiency of two-phase (2P) case–control studies in which the first phase uses an error-prone exposure measure, Z, while the second phase measures true, dichotomous exposure, X, in a subset of subjects. Optimal design of a separate second phase, to be added to a preexisting study, is also investigated. Differential misclassification is assumed throughout. Results are also applicable to 2P cohort studies with error-prone and error-free measures of disease status but error-free exposure measures. While software based on the mean score method of Reilly and Pepe (1995, Biometrika 82, 299–314) can find optimal designs given pilot data, the lack of simple formulae makes it difficult to generalize about efficiency compared to one-phase (1P) studies based on X alone. Here, formulae for the optimal ratios of cases to controls and first- to second-phase sizes, and the optimal second-phase stratified sampling fractions, given a fixed budget, are given. The maximum efficiency of 2P designs compared to a 1P design is deduced and is shown to be bounded from above by a function of the sensitivities and specificities of Z. The efficiency of ‘balanced’ separate second-phase designs (Breslow and Cain, 1988, Biometrika 75, 11–20)—in which equal numbers of subjects are chosen from each first-phase strata—compared to optimal design is deduced, enabling situations where balanced designs are nearly optimal to be identified. 收起