Effect modification and non-collapsibility together may lead to conflicting treatment decisions: A review of marginal and conditional estimands and recommendations for decision-making
Bibliographic record
Abstract
Effect modification occurs when a covariate alters the relative effectiveness of treatment compared to control. It is widely understood that, when effect modification is present, treatment recommendations may vary by population and by subgroups within the population. Population-adjustment methods are increasingly used to adjust for differences in effect modifiers between study populations and to produce population-adjusted estimates in a relevant target population for decision-making. It is also widely understood that marginal and conditional estimands for non-collapsible effect measures, such as odds ratios or hazard ratios, do not in general coincide even without effect modification. However, the consequences of both non-collapsibility and effect modification together are little-discussed in the literature.In this article, we set out the definitions of conditional and marginal estimands, illustrate their properties when effect modification is present, and discuss the implications for decision-making. In particular, we show that effect modification can result in conflicting treatment rankings between conditional and marginal estimates. This is because conditional and marginal estimands correspond to different decision questions that are no longer aligned when effect modification is present. For time-to-event outcomes, the presence of covariates implies that marginal hazard ratios are time-varying, and effect modification can cause marginal hazard curves to cross. We conclude with practical recommendations for decision-making in the presence of effect modification, based on pragmatic comparisons of both conditional and marginal estimates in the decision target population. Currently, multilevel network meta-regression is the only population-adjustment method capable of producing both conditional and marginal estimates, in any decision target population.
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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 | 0.092 | 0.216 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.008 | 0.011 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.006 | 0.002 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".