Online Supplement for: DIAGNOSIS OF SLEEP APNEA BY AUTOMATIC ANALYSIS OF NASAL PRESSURE AND FORCED OSCILLATION IMPEDANCE APPENDIX A Weighted Kappa Statistic

The weighted kappa statistic provides a measure of agreement κ w (scorer1, scorer2) between two scorers (scorer1 and scorer2) who classify observations into one of several groups or categories. The following description is adapted from reference (E1). Two scorers (scorer1 and scorer2) analyze a set of N observations by classifying each observation into one of g groups. This leads to a g × g-matrix n, the table of occurrences. A cell n ij represents the number of observations that have been classified as belonging to category i by scorer1 and to category j by scorer2. Depending on the particular situation to be investigated, a weight w ij between zero and 1 is given to each cell n ij. The weight w ij quantifies the degree of discrepancy between the two categories i and j. Cells on the diagonal of the table of occurrences n, corresponding to equal classification by both scorers, are given weights of 1; whereas cells n ij with highly different categories i and j receive weights w ij close to or equal to zero. The weights w ij given to the different cells n ij of this second-by-second table of occurrences are displayed in Table E1. Whereas weights w ij close to 1 indicate that the respective classes i and j are close, weights close to zero correspond to classes that are very different. On the one hand, the choice of this particular set of weights is motivated by the intention to penalize a missed apnea (weight zero) more severely than a missed hypopnea (weight 0.5) or than a respiratory event detected by both