Variations in Posttonsillectomy Hemorrhage Rates Are Scale Invariant

Abstract

Scale invariance is a property of scientific laws or objects that change in a prescribed fashion if measurements are scaled, and is often represented by a power-law relationship. Power laws suggest that events of a large magnitude will be rare, while small events will be much more common, and that a simple mathematical law relates "severity" with frequency. Scale invariance has been demonstrated in scientific fields including physics, social science, and economics. The authors use the complication of a posttonsillectomy hemorrhage to test whether this property is a feature of surgical complications. Non-identifiable data were obtained regarding posttonsillectomy hemorrhage and subcategorized by calendar month, and the percentage rate of posttonsillectomy hemorrhage was calculated. The data were then transformed using a logarithmic function. This transformed data were plotted and a linear regression analysis was performed. The 13-year period studied included 6,381 tonsillectomy procedures. The logarithm of the frequency of a given rate range of posttonsillectomy hemorrhage (y) was linearly related to the logarithm of the geometric mean of the rate range (x). The best-fit straight line was y = -1.3996x + 2.0624 with R2 = 0.851, n = 10, r = 0.922, and P < .001. The authors found that the incidence of posttonsillectomy hemorrhage is scale invariant. The practical implication is that the observation of rare incidences of large hemorrhage rates may not be due to a unique circumstance or a particular operative fault. To reduce the incidence of extreme rates of postoperative hemorrhage, a review of the entire process of tonsillectomy would be required. Scale-invariance analysis may represent a novel tool that should be considered when reviewing surgical complications.