Leave ‘em Alone – Why Continuous Variables Should Be Analyzed as Such
Bibliographic record
Abstract
found that models with a categorized exposure variable removed only 67% of the confounding controlled when the continuous version was used. Categorizing continuous variables may not only miss the message, it can also get it wrong. Under some circumstances, categorizing continuous variables can give biased results. In a simulation study, Taylor and Yu [6] found that categorizing one continuous variable can artificially make another variable appear associated with the outcome. Selvin [4] showed that the cutpoint chosen during the categorization of continuous variables significantly changed the calculated odds ratio. Royston et al. [2] found that the significant association of the ‘S phase fraction’ with cancer outcomes repeatedly came and went depending on which cutpoint was used to define ‘abnormal’. Ragland [7] showed similar findings with prevalence ratios of hypertension. Information loss and bias from categorizing continuous variables explain why statisticians frequently warn us to leave continuous variables alone [2, 8] . It appears that this advice was lost to investigators – ourselves included – who have developed risk stratification schemes for patients with atrial fibrillation (AF). Quantifying stroke risk in AF is essential for patient management: high-risk patients require oral anticoagulants while low-risk patients (who stand to have a minimal absolute benefit from treatment) can avoid such a therapy. Patient age is significantly associated with stroke Continuous variables – be they outcomes, exposures or covariates – are common in clinical studies. They are frequently modified into categorical variables during their analysis. Pocock et. al. [1] found that 84% of epidemiological articles from leading journals categorized continuous variables. Such a categorization could be done for several reasons [2] . It is commonly perceived that categorization makes it easier to report and interpret final results (‘X doubles the risk of Y’ vs. ‘The risk of Y doubles when X increases by 10 units’). Researchers may be uncomfortable assuming a linear relationship between a continuous variable and the outcome but are unfamiliar with methods of handling non-linearity. Researchers and analysts may have less experience in dealing with continuous variables and prefer to make them behave like the more familiar categorical ones. Finally, it is also possible that physicians and epidemiologists, who frequently categorize continuous measures during their routine life (hypertensive or not, dyslipidemic or not, etc.), instinctually transplant this training from the clinic or field to their analysis. However, categorizing continuous variables can cause problems. The first is information loss. Zhao and Kolonel [3] found that analyses with categorized continuous variables required greater than 40% more patients for the same power as that achieved using continuous variables. Selvin [4] derives a formula to calculate the efficiency loss due to categorizing a continuous variable. Becher et al. [5] Received: February 9, 2008 Accepted: February 9, 2008 Published online: April 17, 2008
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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 | 0.067 | 0.336 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.007 | 0.010 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.004 | 0.009 |
| Insufficient payload (model declined to judge) | 0.083 | 0.022 |
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".