Expressing Rates of Low Frequency Events Using the 10-Span Method

Background: Progress in decreasing nosocomial infections make it increasingly difficult to precisely estimate rates for internal or external comparison. Since infections per device- or patient-days follow the Poisson distribution (Pdist), the rates are often reported as "zero" when the expected number of infection events per interval is low. Graphs of these rates are hectic (or monotonous), confusing the message.

Objective: (1) To confirm that infection counts follow the Pdist and (2) to express rates with consistent variability using a 10-span (10S) methodology.

Methods: Surveillance data is collected at intervals with number of events (infections) and number of denominator days per interval. For a date, the number of denominator days and infections is totaled backwards in time until 10 infections (the span) have been found. If more than one event occurred in an interval, the day count is incremented by the fraction of days per infection. The 10S rate is the number of events per denominator days. Four monthly surveillance graphs for Clostridium difficile infection (CDI) and central line associated blood stream infections (CLABSI by month were evaluated.

Results: By the Poisson distribution, the 95% confidence interval around 10 is 4.8 to 18.3, which translates to approximately half to twice the observed rate (0.5 to 1.8 times). In comparing hospital units, the 10S rates differ by 6 fold, which is statistically significant. The months with counts of 0 vary with the expected rates, consistent with the Pdist (C² P = 0.51). The differences from month to month on the same unit averaged 14 to 20% of the rate. The graph shows the CDI rate by month as points, with the 10S rate per 1000 patient days shown as a line. This method showed less advantage as the expected rate per interval exceeds 5.

Conclusions: For low incidence events, the 10S method provides a prospective method for tracking and reporting rates. Rates at a given point vary by multiplying or dividing by 2, and month to month changes over 40% are likely significant.