Estimation of Controlled Direct Effects
Abstract
Summary: When regression models adjust for mediators on the causal path from exposure to outcome, the regression coefficient of exposure is commonly viewed as a measure of the direct exposure effect. This interpretation can be misleading, even with a randomly assigned exposure. This is because adjustment for post-exposure measurements introduces bias whenever their association with the outcome is confounded by more than just the exposure. By the same token, adjustment for such confounders stays problematic when these are themselves affected by the exposure. Robins accommodated this by introducing linear structural nested direct effect models with direct effect parameters that can be estimated by using inverse probability weighting by a conditional distribution of the mediator. The resulting estimators are consistent, but inefficient, and can be extremely unstable when the mediator is absolutely continuous. We develop direct effect estimators which are not only more efficient but also consistent under a less demanding model for a conditional expectation of the outcome. We find that the one estimator which avoids inverse probability weighting altogether performs best. This estimator is intuitive, computationally straightforward and, as demonstrated by simulation, competes extremely well with ordinary least squares estimators in settings where standard regression is valid.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Causality: Models, Reasoning, and Inference
Pearl, J. (2009) · doi:10.1017/cbo9780511803161 · Cited by 11,653 · see citing works
CAUSALITY: MODELS, REASONING AND INFERENCE
Hitchcock, C., & Pearl, J. (2001) · The Philosophical Review · doi:10.2307/3182612 · Cited by 4,824 · see citing works
Causality: models, reasoning, and inference
(2000) · Choice Reviews Online · doi:10.5860/choice.38-1494a · Cited by 2,969 · see citing works
Robins, J. (1986) · Mathematical Modelling · doi:10.1016/0270-0255(86)90088-6 · Cited by 2,451 · see citing works
Identifiability and exchangeability for direct and indirect effects
Robins, J. M., & Greenland, S. (1992) · Epidemiology · doi:10.1097/00001648-199203000-00013 · Cited by 1,793 · see citing works
Principal Stratification in Causal Inference
Frangakis, C., & Rubin, D. B. (2002) · Biometrics · doi:10.1111/j.0006-341x.2002.00021.x · Cited by 1,496 · see citing works
Pearl, J. (2022) · ACM eBooks · doi:10.1145/3501714.3501736 · Cited by 1,039 · see citing works
Unified Methods for Censored Longitudinal Data and Causality
van der Laan, M. J., & Robins, J. M. (2003) · Springer series in statistics · doi:10.1007/978-0-387-21700-0 · Cited by 972 · see citing works
The Consquences of Adjustment for a Concomitant Variable That Has Been Affected by the Treatment
Rosenbaum, P. R. (1984) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2981697 · Cited by 849 · see citing works
Bickel, P. J., Hammel, E. A., & O'Connell, J. W. (1975) · Science · doi:10.1126/science.187.4175.398 · Cited by 659 · see citing works
Fallibility in estimating direct effects
Cole, S. R., & Hernán, M. A. (2002) · International Journal of Epidemiology · doi:10.1093/ije/31.1.163 · Cited by 548 · see citing works
Correcting for non-compliance in randomized trials using structural nested mean models
Robins, J. M. (1994) · Communication in Statistics- Theory and Methods · doi:10.1080/03610929408831393 · Cited by 534 · see citing works
Estimating Exposure Effects by Modelling the Expectation of Exposure Conditional on Confounders
Robins, J. M., Mark, S. D., & Newey, W. K. (1992) · Biometrics · doi:10.2307/2532304 · Cited by 384 · see citing works
Estimation of Direct Causal Effects
Petersen, M. L., Sinisi, S. E., & van der Laan, M. J. (2006) · Epidemiology · doi:10.1097/01.ede.0000208475.99429.2d · Cited by 362 · see citing works
Computation, Causation, and Discovery
(1999) · AAAI Press eBooks · doi:10.7551/mitpress/2006.001.0001 · Cited by 355 · see citing works
Robins, J. M., Sued, M., Lei-Gomez, Q., Rotnitzky, A. G., Ciencias, F., & Naturales, E. (2010) · Cited by 346 · see citing works
Direct and Indirect Causal Effects via Potential Outcomes*
Rubin, D. B. (2004) · Scandinavian Journal of Statistics · doi:10.1111/j.1467-9469.2004.02-123.x · Cited by 324 · see citing works
Robins, J. M., Sued, M., Lei-Gomez, Q., & Rotnitzky, A. G. (2007) · Statistical Science · doi:10.1214/07-sts227d · Cited by 314 · see citing works
A Distributional Approach for Causal Inference Using Propensity Scores
Tan, Z. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000023 · Cited by 232 · see citing works
Causal Mediation Analyses with Rank Preserving Models
Have, T. R. T., Joffe, M. M., Lynch, K. G., Brown, G. K., Maisto, S. A., & Beck, A. T. (2007) · Biometrics · doi:10.1111/j.1541-0420.2007.00766.x · Cited by 157 · see citing works
Direct and Indirect Effects of Sequential TreatmentsPreprint
Didelez, V., Dawid, A. P., & Geneletti, S. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1206.6840 · Cited by 108 · see citing works
van der Laan, M. J., & Petersen, M. L. (2008) · The International Journal of Biostatistics · doi:10.2202/1557-4679.1064 · Cited by 100 · see citing works
Sutter, P. D., Delbaere, I., Gerris, J., et al. (2006) · Human Reproduction · doi:10.1093/humrep/del247 · Cited by 90 · see citing works
Counterfactual Links to the Proportion of Treatment Effect Explained by a Surrogate Marker
Taylor, J. M. G., Wang, Y., & Thiébaut, R. (2005) · Biometrics · doi:10.1111/j.1541-0420.2005.00380.x · Cited by 78 · see citing works
Preterm birth in twins after subfertility treatment: population based cohort study
Verstraelen, H., Goetgeluk, S., Derom, C. A., Vansteelandt, S., Derom, R., Goetghebeur, E. J. T., & Temmerman, M. (2005) · BMJ · doi:10.1136/bmj.38625.685706.ae · Cited by 71 · see citing works
Self-citationWang, Y., Petersen, M. L., Bangsberg, D. R., et al. (2006) · Collection of Biostatistics Research Archive · Cited by 54 · see citing works
A perspective on surrogate endpoints in controlled clinical trials
Molenberghs, G., Burzykowski, T., Alonso, A., et al. (2004) · Statistical Methods in Medical Research · doi:10.1191/0962280204sm362ra · Cited by 53 · see citing works
Should we adjust for gestational age when analysing birth weights? The use of z-scores revisited
Delbaere, I., Vansteelandt, S., Bacquer, D. D., Verstraelen, H., Gerris, J., Sutter, P. D., & Temmerman, M. (2007) · Human Reproduction · doi:10.1093/humrep/dem151 · Cited by 45 · see citing works
Self-citationRobins, J. M., Rotnitzky, A. G., & Vansteelandt, S. (2007) · Biometrics · doi:10.1111/j.1541-0420.2007.00847_2.x · Cited by 25 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Mediation Analysis: A Practitioner's Guide
VanderWeele, T. J. (2016) · Annual Review of Public Health · doi:10.1146/annurev-publhealth-032315-021402 · Cited by 1,985 · see citing works
Odds Ratios for Mediation Analysis for a Dichotomous Outcome
VanderWeele, T. J., & Vansteelandt, S. (2010) · American Journal of Epidemiology · doi:10.1093/aje/kwq332 · Cited by 809 · see citing works
Self-citationBurgess, S., Daniel, R. M., Butterworth, A. S., Thompson, S. G., & the EPIC-InterAct Consortium (2015) · International Journal of Epidemiology · doi:10.1093/ije/dyu176 · Cited by 543 · see citing works
Bias Formulas for Sensitivity Analysis for Direct and Indirect Effects
VanderWeele, T. J. (2010) · Epidemiology · doi:10.1097/ede.0b013e3181df191c · Cited by 435 · see citing works
Emsley, R., Dunn, G., & White, I. R. (2010) · Statistical Methods in Medical Research · doi:10.1177/0962280209105014 · Cited by 356 · see citing works
Estimating Direct Effects in Cohort and Case–Control Studies
Vansteelandt, S. (2009) · Epidemiology · doi:10.1097/ede.0b013e3181b6f4c9 · Cited by 159 · see citing works
Self-citationBias-reduced doubly robust estimation
Vermeulen, K., & Vansteelandt, S. (2015) · Journal of the American Statistical Association · doi:10.1080/01621459.2014.958155 · Cited by 130 · see citing works
Self-citationTchetgen Tchetgen, E. J., & VanderWeele, T. J. (2014) · Epidemiology · doi:10.1097/ede.0000000000000054 · Cited by 93 · see citing works
- Authors
- Goetgeluk, S., Vansteelandt, S., & Goetghebeur, E.
- Affiliations
- Ghent University (BE)
- Harvard University (US)
- Corresponding author
- Vansteelandt, Stijn
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2008-09-16
- Volume
- 70
- Issue
- 5
- Pages
- 1049-1066
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W1964213733
- Cited by
- 104
- References
- 29
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 3 · 2023: 3 · 2022: 5 · 2021: 6 · 2020: 8 · 2019: 4 · 2018: 5 · 2017: 10 · 2016: 5 · 2015: 7 · 2014: 9 · 2013: 7 · 2012: 8
- FWCI
- 5.98
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion)
- Collection of Biostatistics Research Archive (submittedVersion)
- Funders
- Interuniversity Attraction Pole research network (P06/03)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- controlled direct effect, mediation analysis, inverse probability weighting, efficient estimators, causal inference
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
