  Two-phase outcome dependent sampling (ODS) is widely used in many fields,
especially when certain covariates are expensive and/or difficult to measure.
For two-phase ODS, the conditional maximum likelihood (CML) method is very
attractive because it can handle zero Phase 2 selection probabilities and
avoids modeling the covariate distribution. However, most existing CML-based
methods use only the Phase 2 sample and thus may be less efficient than other
methods. We propose a general empirical likelihood method that uses CML
augmented with additional information in the whole Phase 1 sample to improve
estimation efficiency. The proposed method maintains the ability to handle zero
selection probabilities and avoids modeling the covariate distribution, but can
lead to substantial efficiency gains over CML in the inexpensive covariates, or
in the influential covariate when a surrogate is available, because of an
effective use of the Phase 1 data. Simulations and a real data illustration
using NHANES data are presented.
