The Genomic Birthday Paradox: How Much Is Enough?
Bibliographic record
Abstract
Genomic matchmaking databases (GMDs) allow participants to submit genomic and phenotypic data with the goal of identifying previously uncharacterized disease-associated genes by "matching" to other comparable cases. Current estimates suggest that there are at least 3,000 Mendelian disease-associated genes that have not yet been characterized as such, but the true number may be substantially higher. Therefore, GMDs are addressing a pressing medical need, and it is important to ask how they should be designed and how much data they should strive to contain in order to identify a certain number of these genes. In this work, we argue that genomic matchmaking has similarities to the so-called "birthday paradox," which refers to the observation that within a group of just 23 persons, two people will have the same birthday with probability greater than 50%. We develop a series of simulations to provide a rough estimate of the number of cases required and to explore the influence of parameters such as genetic heterogeneity, mode of inheritance, background variation, precision of phenotypic descriptions, disease prevalence, and the accuracy of bioinformatics pathogenicity prediction programs on the performance of genomic matchmaking.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".