  We present a comparative study of a set of star-formation rate tracers based
on mid-infrared emission in the 12.81$\mu$m [Ne II] line, the 15.56$\mu$m [Ne
III] line, and emission features from polycyclic aromatic hydrocarbons (PAHs)
between 5.2 and 14.7$\mu$m. We calibrate our tracers with the thermal component
of the radio continuum emission at 33 GHz from 33 extranuclear star-forming
regions observed in nearby galaxies. Correlations between mid-IR emission
features and thermal 33 GHz star-formation rates (SFR) show significant
metallicity-dependent scatter and offsets. We find similar
metallicity-dependent trends in commonly used SFR tracers such as H$\alpha$ and
24$\mu$m. As seen in previous studies, PAH emission alone is a poor SFR tracer
due to a strong metallicity dependence: lower metallicity regions show
decreased PAH emission relative to their SFR compared to higher metallicity
regions. We construct combinations of PAH bands, neon emission lines, and their
respective ratios to minimize metallicity trends. The calibrations that most
accurately trace SFR with minimal metallicity dependence involve the sum of the
integrated intensities of the 12.81$\mu$m [Ne II] line and the 15.56$\mu$m [Ne
III] line combined with any major PAH feature normalized by dust continuum
emission. This mid-IR calibration is a useful tool for measuring SFR as it is
minimally sensitive to variations in metallicity and it is composed of bright,
ubiquitous emission features. The Mid-Infrared Instrument (MIRI) on the James
Webb Space Telescope will detect these features from galaxies as far as
redshift z$\sim$1. We also investigate the behavior of the PAH band ratios and
find that subtracting the local background surrounding a star-forming region
decreases the ratio of PAH 11.3$\mu$m to 7.7$\mu$m emission. This implies PAHs
are more ionized in star-forming regions relative to their surroundings.
