  The rate of noise-induced escape from a metastable state of a periodically
modulated overdamped system is found for an arbitrary modulation amplitude $A$.
The instantaneous escape rate displays peaks that vary with the modulation from
Gaussian to strongly asymmetric. The prefactor $\nu$ in the period-averaged
escape rate depends on $A$ nonmonotonically. Near the bifurcation amplitude
$A_c$ it scales as $\nu\propto (A_c-A)^{\zeta}$. We identify three scaling
regimes, with $\zeta = 1/4, -1$, and 1/2.
