Units of analysis in accelerated telomere shortening in glycosylphosphatidylinositol (GPI)–negative compared with GPI-positive granulocytes from patients with paroxysmal nocturnal hemoglobinuria (PNH) detected by proaerolysin flow-FISH

The article by Beier et al1 makes an important contribution to the understanding of paroxysmal nocturnal hemoglobinuria (PNH) bone marrow failure syndrome. We are concerned about application of the statistical technique, which was potentially a consequence of a misconception about the study design. We argue that the unit of analysis should have been cell populations rather than patients. In the “Introduction,” the authors state their hypothesis that the glycosylphosphatidylinositol (GPI)–negative hematopoietic stem cells have growth advantage over the GPI-positive ones. Furthermore, the authors clearly state that the objective of the study was to selectively analyze telomere length in GPI-positive and GPI-negative cells from patients diagnosed with the syndrome. The study was executed by comparing telomere lengths from 3 cell populations, GPI-negative and GPI-positive hematopoietic stem cells, and cells from the healthy donors. Finally, in the “Results and discussion,” the authors state that their data support the hypothesis of the growth advantage of the GPI-negative hematopoietic stem cells over GPI-positive ones. The above argument suggests that the hypothesis-driven unit of analysis should have been the cell populations rather than the patients. Therefore, the appropriate statistical application would have been the single-factor analysis of variance with a post hoc test of significance, such as Tukey HSD (honestly significant difference).2 This statistical approach would have tested for differences among all possible combinations of the GPI-negative/GPI-positive cells from patients with the syndrome and cells from the healthy donors while guarding against a type I error. If the study hypothesis had focused on the differences between patients and the healthy individuals, then the unit of statistical analysis should have been the 2 groups and the application of the Student t test of significance would have been correct. Because of the long-standing relationship between statistics and medicine and because of the inherent variability of biologic data, appropriate experimental designs and statistical techniques are required to draw unbiased conclusions.