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Sankha Amarakoon, Jose Martinez-Ciriano, René Wubbels, L van den Born, Suzanne Yzer, Mirjam Van Velthoven, Tom Missotten; Crying wolf or a real problem : poisson distribution statistics for rare events applied to endophthalmitis. Invest. Ophthalmol. Vis. Sci. 2013;54(15):1117.
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The most feared complication of intravitreal (anti-VEGF) injections is endophthalmitis. An incidence of 1/2000 is reported in the literature. Antiseptic protocols for intravitreal injection vary over the world and start from simple iodine drops and gloves as antiseptic measures to injections in full operating theatre circumstances. Whenever a few cases occur in a relative short time span, a search for related causes is started : date, operator, settings or medication preparation are examined. Unfortunately, unrelated endophthalmitis cases do occur randomly and it is often unclear if additional antiseptic procedures or other measures are mandatory. Poisson distribution statistics are used to determine the significance of increased incidence of unrelated rare events.
In the Rotterdam eye hospital, 0 endophthalmitis cases in 8500 injections(2011) and 5 cases in 10300 (2012) were observed. The expected rate would haven been 4 (2011) and 5 (2012) based on an incidence of 1/2000 injections in the literature. Poisson distribution statistics were performed to pre-calculate an incidence that should be regarded as a significant rise in incidence and make an upgrade of standard operating procedures mandatory.
For a given incidence of 1/2000, in a cohort of 10.000 injections, 5 endophthalmitis would have been expected. P-values for significant increased observed cases were : n=0 (p=1,00); n=1(p=0.99); n=2(p=0.96); n=3(p=0.88); n=4 (p=0.74); n=5 (p=0.56); n=6 (p=0.38); n=7(p=0.24); n=8(p=0.13); n=9(p=0.07);n=10(p=0.03); n=11(p=0.01). Significant p values for other sizes of cohort(c) were : c/1000 (n=2, p=0,01); c/2000 (n=3, p=0,02); c/5000 (n=5, p=0,05); c/20000(n=15, p=0,05); c/50000(n=33, p=0,05)
If no related cause can be found in a cluster of endophthalmitis cases, it can be helpful to check the poisson distribution of unrelated rare events, before changing aseptic standard operating procedures, settings (operating theatre) or antibiotic schedules. The ophthalmic community should perhaps set quality standards for the incidence of injection caused endophthalmitis and develop standard operating procedures. Depending on the cohort size, poisson distribution statistics can help set warning points when upgrading of standard operating procedures in mandatory.
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