  In data collection for predictive modeling, under-representation of certain
groups, based on gender, race/ethnicity, or age, may yield less-accurate
predictions for these groups. Recently, this issue of fairness in predictions
has attracted significant attention, as data-driven models are increasingly
utilized to perform crucial decision-making tasks. Existing methods to achieve
fairness in the machine learning literature typically build a single prediction
model in a manner that encourages fair prediction performance for all groups.
These approaches have two major limitations: i) fairness is often achieved by
compromising accuracy for some groups; ii) the underlying relationship between
dependent and independent variables may not be the same across groups. We
propose a Joint Fairness Model (JFM) approach for logistic regression models
for binary outcomes that estimates group-specific classifiers using a joint
modeling objective function that incorporates fairness criteria for prediction.
We introduce an Accelerated Smoothing Proximal Gradient Algorithm to solve the
convex objective function, and present the key asymptotic properties of the JFM
estimates. Through simulations, we demonstrate the efficacy of the JFM in
achieving good prediction performance and across-group parity, in comparison
with the single fairness model, group-separate model, and group-ignorant model,
especially when the minority group's sample size is small. Finally, we
demonstrate the utility of the JFM method in a real-world example to obtain
fair risk predictions for under-represented older patients diagnosed with
coronavirus disease 2019 (COVID-19).
