Does my patient have SARS-CoV-2 infection? A reminder of clinical probability formulas
Bibliographic record
Abstract
Around the world, people are wondering, ‘Do I have SARS-CoV-2?’. Determining a person’s probability of illness is central to the practice and teaching of evidence-based medicine (EBM). Probabilities can be calculated through mathematical formulas, but studies find that many clinicians have difficulty with the calculations.1–4 For many conditions in medicine, clinicians can rely on experience and/or established algorithms. However, with SARS-CoV-2 infection, clinicians lack experience and, given the rapidly changing prevalence of the illness, algorithms are difficult to establish. In this manuscript, we use the example of SARS-CoV-2 as an educational reminder of how clinicians can roughly gauge the probability of illness in different contexts and to highlight some conceptual issues in the estimates needed for the formulas. Broadly speaking, the diagnostic process involves a sequence of estimating the probability of an illness and then adjusting this estimate with each new piece of information. Clinicians are generally taught to calculate the probability of illness given new information through either the use of Bayes probability theorem or the use of a 2×2 contingency table. Mathematically, Bayes theorem and the 2×2 table are the same calculation. The 2×2 table calculation appears less complex than Bayes theorem, because it converts conditional probabilities into numbers that are entered into the cells of the table.2 ### Bayes probability theorem In writing formulas, the term ‘given’ is symbolised as a straight vertical line. Letting ‘P’=probability, ‘A’=SARS-CoV-2 and ‘B’=new information, Bayes probability theorem is: P(A I B)=[P(A) × P(B I A)] / P(B).5 Imagine that B, the new information, is the symptom of a cough. Then the probability of SARS-CoV-2 for a patient given the presence of cough, P(A I B), is equal to the probability of SARS-CoV-2 in the patient’s community, P(A), multiplied by the probability of cough given that the patient has SARS-CoV-2, P(B I A), …
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How this classification was reachedexpand
Direct model labels (unvalidated)
Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.
| Model arm | Categories | Study design | Confidence |
|---|---|---|---|
| gemma | no category Domain: not available · Genre: Commentary About the Canadian research system: no · About a Canadian topic: no | Not applicable | low |
| gpt | no category Domain: not available · Genre: Commentary About the Canadian research system: no · About a Canadian topic: no | Not applicable | high |
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 | 0.004 | 0.413 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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, unvalidatedLabeled directly by 2 models reading the full record.
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".