  Most epidemiologic cohorts are composed of volunteers who do not represent
the general population. To enable population inference from cohorts, we and
others have proposed utilizing probability survey samples as external
references to develop a propensity score (PS) for membership in the cohort
versus survey. Herein we develop a unified framework for PS-based weighting
(such as inverse PS weighting (IPSW)) and matching methods (such as
kernel-weighting (KW) method). We identify a fundamental Strong Exchangeability
Assumption (SEA) underlying existing PS-based matching methods whose failure
invalidates inference even if the PS-model is correctly specified. We relax the
SEA to a Weak Exchangeability Assumption (WEA) for the matching method. Also,
we propose IPSW.S and KW.S methods that reduce the variance of PS-based
estimators by scaling the survey weights used in the PS estimation. We prove
consistency of the IPSW.S and KW.S estimators of population means and
prevalences under WEA, and provide asymptotic variances and consistent variance
estimators. In simulations, the KW.S and IPSW.S estimators had smallest MSE. In
our data example, the original KW estimates had large bias, whereas the KW.S
estimates had the smallest MSE.
