We describe a new statistical method for identifying pairs or groups of related events in sequences which resemble, but are not identical to, a Poisson process. For a particular earthquake, we form the ratio r(Nb, Na) of the relative origin times of the Na th subsequent event and the Nb th previous event. We then find the probability that such a ratio could occur if the sequence were a Poisson process. Presumably, sequences where the ratio is too small to be probable contain related events, and the subsequent events are aftershocks. Since the method requires knowledge of the origin times of only a few preceding and subsequent events, it is more powerful than methods which require knowledge of the mean activity rate of the Poisson process. Using this ratios method, we search the ISC catalog for aftershocks of earthquakes with focal depths exceeding 70 km. From the world as a whole, events with at least one aftershocks can be found in all depth ranges, including 250 km to 450 km. However, the incidence of aftershocks is significantly lower or deeper events.