Estimating waiting time for compatible blood: A Negative Binomial approach

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.

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).

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).

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