Geometric probability distribution for modeling of error risk during prescription dispensing

The relationship between the number of prescriptions dispensed by individual pharmacy staff during a single workday and the probability of committing at least one dispensing error during that same workday period was evaluated using a geometric probability distribution.

A cross-sectional descriptive study involving 50 pharmacies located in six cities across the United States was conducted. A pharmacist trained to detect dispensing errors recorded the number of prescriptions filled by each pharmacy staff member and noted which prescription represented the staff member's first dispensing error (defined as any deviation from the prescriber's order) made during the observation period. The Kolmogorov-Smirnov tests for discrete distributions revealed that the observed cumulative distribution of dispensing errors could have come from a geometric probability distribution that assumed dispensing error rates of 2-3%. In terms of risk analysis, this study's findings suggest that there can be a quantifiable statistical relationship between a measure of workload and the risk of committing at least one dispensing error. The ability to model dispensing errors using a geometric probability distribution enables the safety and health care practitioner to directly assess dispensing error risk as a function of a pharmacy's accuracy rate and the number of prescriptions a pharmacy staff member should dispense during a work shift.

A geometric probability distribution effectively modeled the relationship between the number of prescriptions filled and the occurrence of the first dispensing errors.