Gamma-ray bursts are short but powerful pulses of electromagnetic radiation coming from space. Specially equipped satellites have observed the arrival of several hundred bursts during the past two decades. The origin of these bursts, whether from near the earth, across the galaxy, or out of the deep cosmos, has become a major question for astronomers. At the heart of this question lies a statistical puzzle relating to familiar issues in survival analysis: Kaplan-Meier-type curves, data truncation, hazard rate analysis, Mantel-Haenszel statistics, and so on. Survival analysis is used here to critically examine two different models that have been proposed for the gamma-ray burst data. The analysis contradicts one of these models.