Non-iterative Estimation Update for Parametric and Semiparametric Models with Population-based Auxiliary Information

With the advancement in disease registries and surveillance data, population-based
information on disease incidence, survival probability or other important biological
characteristics become increasingly available. Such information can be leveraged in
studies that collect detailed measurements but with smaller sample sizes. In contrast
to recent proposals that formulate the additional information as constraints in opti-
mization problems, we develop a general framework to construct simple estimators that
update usual regression estimators with some functionals of data and the initial esti-
mator based on the additional information. We consider general settings which include
nuisance parameters in the auxiliary information, non-i.i.d. data such as case-control
sampling, and semiparametric models with infinite dimensional parameters. Detailed
examples of several important data and sampling settings are provided.