  In healthcare, clinical risks are crucial for treatment decisions, yet the
analysis of their associations is often overlooked. This gap is particularly
significant when balancing risks that are weighed against each other, as in the
case of atrial fibrillation (AF) patients facing stroke and bleeding risks with
anticoagulant medication. While traditional regression models are ill-suited
for this task due to standard errors in risk estimation, a novel two-stage
Deming regression framework is proposed to address this issue, offering a more
accurate tool for analyzing associations between variables observed with errors
of known or estimated variances. The first stage is to obtain the variable
values with variances of errors either by estimation or observation, followed
by the second stage that fits a Deming regression model potentially subject to
a transformation. The second stage accounts for the uncertainties associated
with both independent and response variables, including known or estimated
variances and additional unknown variances from the model. The complexity
arising from different scenarios of uncertainty is handled by existing and
advanced variations of Deming regression models. An important practical
application is to support personalized treatment recommendations based on
clinical risk associations that were identified by the proposed framework. The
model's effectiveness is demonstrated by applying it to a real-world dataset of
AF-diagnosed patients to explore the relationship between stroke and bleeding
risks, providing crucial guidance for making informed decisions regarding
anticoagulant medication. Furthermore, the model's versatility in addressing
data containing multiple sources of uncertainty such as privacy-protected data
suggests promising avenues for future research in regression analysis.
