“Devil’s stairs”, Poisson’s Statistics, and Patient Sorting via Variabilities for Oxygenation: All from Arterial Blood Gas Data

This report deals with arterial oxygen saturation (SaO2) for healthy adults. A comparably small data set (20 persons) holds 3-minute records of SaO2. The sample rate was 200 Hz. The charts have the looks of a “devil’s stairs.” A few (from 1 to 10) detectable oxygenation levels form the stair’s treads, more or less long. “The risers” have two types (up and down), and all have virtually the same height, about 1 %. The inter-level shifts ( 0 to 42 switches per record) turned out a rare event at the actual sample rate. The number of switchings meets the Poisson distribution. There were found three visibly varied intensities for the switch-overs within the data set. Histograms also show the co-existing of no fewer than three subsets into the data set. The subsets differ by the intensity of switch-overs, amounts of possible levels, relative frequencies of most probable levels (modes), etcetera. In short, those all are diverse variability quantifiers. The higher variability subset has about 25 %, the lower one - 45%.