Estimating waiting time for compatible blood: A Negative Binomial approach
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.013 | 0.040 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".