Regression-With-Residuals Estimation of Marginal Effects: A Method of Adjusting for Treatment-Induced Confounders That may also be Effect Modifiers
Bibliographic record
Abstract
Summary When making causal inferences, treatment-induced confounders complicate analyses of time-varying treatment effects. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between the treatment and the outcome, leading to bias. Although several methods for estimating marginal effects avoid these complications, including inverse probability of treatment weighted estimation of marginal structural models as well as g- and regression-with-residuals estimation of highly constrained structural nested mean models, each suffers from a set of non-trivial limitations, among them an inability to accommodate effect modification. In this study, we adapt the method of regression with residuals to estimate marginal effects with a set of moderately constrained structural nested mean models that easily accommodate several types of treatment-by-confounder interaction. With this approach, the confounders at each time point are first residualized with respect to the observed past, which involves centring them at their estimated means given prior treatments and confounders. The outcome is then regressed on all prior variables, including a set of treatment-by-confounder interaction terms, with these residuals substituted for the untransformed confounders both as ‘main effects’ and as part of any interaction terms. Through a series of simulation experiments and empirical examples, we show that this approach outperforms other methods for estimating the marginal effects of time-varying treatments.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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".