Semiparametric inference for data with a continuous outcome from a two‐phase probability‐dependent sampling scheme

Summary Multiphased designs and biased sampling designs are two of the well‐recognized approaches to enhance study efficiency. We propose a new and cost‐effective sampling design, the two‐phase probability‐dependent sampling design, for studies with a continuous outcome. This design will enable investigators to make efficient use of resources by targeting more informative subjects for sampling. We develop a new semiparametric empirical likelihood inference method to take advantage of data obtained through a probability‐dependent sampling design. Simulation study results indicate that the sampling scheme proposed, coupled with the proposed estimator, is more efficient and more powerful than the existing outcome‐dependent sampling design and the simple random sampling design with the same sample size. We illustrate the method proposed with a real data set from an environmental epidemiologic study.