Using generalized additive models to reduce residual confounding
Bibliographic record
Abstract
Traditionally, confounding by continuous variables is controlled by including a linear or categorical term in a regression model. Residual confounding occurs when the effect of the confounder on the outcome is mis-modelled. A continuous representation of a covariate was previously shown to result in a less biased estimate of the adjusted exposure effect than categorization provided the functional form of the covariate-outcome relationship is correctly specified. However, this is rarely known. In contrast to parametric regression, generalized additive models (GAM) fit a smooth dose-response curve to the data, without requiring a priori knowledge of the functional form. We used simulations to compare parametric multiple logistic regression vs its non-parametric GAM extension in their ability to control for a continuous confounder. We also investigated several issues related to the implementation of GAM in this context, including: (i) selecting the degrees of freedom; and (ii) alternative criteria for inclusion/exclusion of the potential confounder and for choosing between parametric and non-parametric representation of its effect. The impact of the shape and strength of the confounder-disease association, sample size, and the correlation between the confounder and exposure were investigated. Simulations showed that when the confounder has a non-linear association with the outcome, compared to a parametric representation, GAM modelling (i) reduced the mean squared error for the adjusted exposure effect; (ii) avoided inflation of the type I error for testing the exposure effect. When the true confounder-outcome relationship was linear, GAM performed as well as the parametric logistic regression. When modelling a continuous exposure non-parametrically, in the presence of a continuous confounder, our results suggest that assuming a linear effect of the confounder and focussing on the non-linearity of the exposure-outcome relationship leads to spurious findings of non-linearity: joint non-linear modelling is necessary. Overall, our results suggest that the use of GAM to reduce residual confounding offers several improvements over conventional parametric modelling.
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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 | 0.019 | 0.053 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 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".