<p>Asteroid impact monitoring systems search for potential collisions of near-Earth objects (NEOs) with the Earth over 100 years. A necessary condition for an impact is the intersection between the orbit of the asteroid and the orbit of the Earth. This condition is measured by the Minimum Orbit Intersection Distance (MOID), which can be computed reliably for longer periods of time to identify when an Earth impact is possible. As the orbit is propagated into the future, the uncertainty in position grows faster than the uncertainty in the MOID. If the MOID is low but the position along the orbit is unknown, we compute an analytical approximation of the frequency of close encounters for a given distance. The NEO population spreads widely in orbital uncertainty, which we consider by propagating multiple samples from the initial orbital uncertainty distribution. We demonstrate and validate the methodology for 99942 Apophis, whose MOID is secularly increasing at a slow rate that still allows for future deep encounters. We apply this methodology to the NEO population, and for a large fraction we rule out the crossing of Earth’s orbit in the next 1000 years. Otherwise, we rank NEOs in terms of how long their MOID will be low, long-term frequency of close encounters, and frequency relative to the background close encounter frequency for objects of similar size. These rankings identify NEOs that should be prioritized for future tracking and orbit refinement.</p>