Estimating waiting time for compatible blood: A Negative Binomial approach.

Objectives: Screening blood units for compatibility constitutes a Bernoulli series. Estimating the number of units needed to be screened represents a classic waiting time problem that may be resolved using the Negative Binomial Distribution. The currently recommended method for estimating the number of units screened, n, to find a required number of compatible units, r, with a given probability, p, is n = r/p. This coincides with the mean of the Negative Binomial Distribution so that the actual number of units screened will often be underestimated by the current method.

Methods: The cumulative distribution function of the Negative Binomial Distribution provides the probability of success (compatibility), F(n;r,p), as a function of the number of trials performed (attempted crossmatches), n, the probability of success on each trial, p, and the number of successes (compatible units) required, r. Choosing a threshold cumulative probability sufficiently high, such as F ~ 0.9, for example, will provide confidence that the projected number of units screened will be underestimated less often (~10% of the time).

Results: With F ≥ 0.9, the estimated number of attempted crossmatches ranges from 1.3 to 2.3 times as many as the number calculated by the current method. As a rule of thumb approximately 1.6 times the current estimated number provides a similar estimate (n ~ 1.6∙r/p).

Conclusions: Waiting time underestimation will be reduced significantly by using the Negative Binomial Distribution solution and should be accompanied by improved customer satisfaction.