  Machine learning models $-$ now commonly developed to screen, diagnose, or
predict health conditions $-$ are evaluated with a variety of performance
metrics. An important first step in assessing the practical utility of a model
is to evaluate its average performance over an entire population of interest.
In many settings, it is also critical that the model makes good predictions
within predefined subpopulations. For instance, showing that a model is fair or
equitable requires evaluating the model's performance in different demographic
subgroups. However, subpopulation performance metrics are typically computed
using only data from that subgroup, resulting in higher variance estimates for
smaller groups. We devise a procedure to measure subpopulation performance that
can be more sample-efficient than the typical subsample estimates. We propose
using an evaluation model $-$ a model that describes the conditional
distribution of the predictive model score $-$ to form model-based metric (MBM)
estimates. Our procedure incorporates model checking and validation, and we
propose a computationally efficient approximation of the traditional
nonparametric bootstrap to form confidence intervals. We evaluate MBMs on two
main tasks: a semi-synthetic setting where ground truth metrics are available
and a real-world hospital readmission prediction task. We find that MBMs
consistently produce more accurate and lower variance estimates of model
performance for small subpopulations.
