A parallel alarm processor has a threshold detector, a pattern extractor, a predetermined reference pattern, a first alarm and a second alarm. The threshold detector has a first output responsive to relatively long duration oxygen desaturations. The pattern extractor has a second output responsive to relatively short duration oxygen desaturations. The predetermined reference pattern is indicative of a series of intermittent oxygen desaturations. A first alarm is triggered when the first output crosses a lower limit threshold. A second alarm is triggered when the second output matches the predetermined reference pattern. In an embodiment, an integrator inputs smoothed oxygen saturation measurements to the threshold detector, and a predictor inputs predictive oxygen saturation measurements to the pattern extractor.