  Ratios of carefully selected line depths are sensitive to stellar effective
temperature ($T_\mathrm{eff}$). Relations established between line-depth ratio
(LDR) and $T_\mathrm{eff}$ allow one to determine $T_\mathrm{eff}$ precisely.
However, LDRs can also depend on metallicity and abundance ratios, which can
limit the accuracy of the LDR method unless such effects are properly taken
into account. We investigate the metallicity effect using $H$-band spectra and
stellar parameters published by the APOGEE project. We clearly detected the
effects of metallicity and abundance ratios; $T_\mathrm{eff}$ derived from a
given LDR depends on the metallicity, 100-800$\,$K$\,$dex$^{-1}$, and the
dependency on the abundance ratios, 150-1000$\,$K$\,$dex$^{-1}$, also exists
when the LDR involves absorption lines of different elements. For the 11 line
pairs in the $H$-band we investigated, the LDR-$T_\mathrm{eff}$ relations with
abundance-related terms added have scatters as small as 30-90$\,$K within the
range of $3700 < T_\mathrm{eff} < 5000$\,K and $-0.7 < \mathrm{[Fe/H]} <
+0.4$\,dex. By comparing the observed spectra with synthetic ones, we found
that saturation of the absorption lines at least partly explains the
metallicity effect.
