Statistical inference for a two-stage outcome-dependent sampling design with a continuous outcome

The two-stage case-control design has been widely used in epidemiology studies for its cost-effectiveness and improvement of the study efficiency (White, 1982, American Journal of Epidemiology 115, 119-128; Breslow and Cain, 1988, Biometrika 75, 11-20). The evolution of modern biomedical studies has called for cost-effective designs with a continuous outcome and exposure variables. In this article, we propose a new two-stage outcome-dependent sampling (ODS) scheme with a continuous outcome variable, where both the first-stage data and the second-stage data are from ODS schemes. We develop a semiparametric empirical likelihood estimation for inference about the regression parameters in the proposed design. Simulation studies were conducted to investigate the small-sample behavior of the proposed estimator. We demonstrate that, for a given statistical power, the proposed design will require a substantially smaller sample size than the alternative designs. The proposed method is illustrated with an environmental health study conducted at National Institutes of Health.