Statistical inference methods and applications of outcome-dependent sampling designs under generalized linear models

A cost-effective sampling design is desirable in large cohort studies with a limited budget due to the high cost of measurements of primary exposure variables. The outcome-dependent sampling (ODS) designs enrich the observed sample by oversampling the regions of the underlying population that convey the most information about the exposure-response relationship. The generalized linear models (GLMs) are widely used in many fields, however, much less developments have been done with the GLMs for data from the ODS designs. We study how to fit the GLMs to data obtained by the original ODS design and the two-phase ODS design, respectively. The asymptotic properties of the proposed estimators are derived. A series of simulations are conducted to assess the finite-sample performance of the proposed estimators. Applications to a Wilms tumor study and an air quality study demonstrate the practicability of the proposed methods.