Causal effect on a target population: A sensitivity analysis to handle missing covariates
Randomized controlled trials (RCTs) are often considered the gold standard for estimating causal effect, but they may lack external validity when the population eligible to the RCT is substantially different from the target population. Having at hand a sample of the target population of interest all...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-11-01
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| Series: | Journal of Causal Inference |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jci-2021-0059 |
| _version_ | 1811320169652289536 |
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| author | Colnet Bénédicte Josse Julie Varoquaux Gaël Scornet Erwan |
| author_facet | Colnet Bénédicte Josse Julie Varoquaux Gaël Scornet Erwan |
| author_sort | Colnet Bénédicte |
| collection | DOAJ |
| description | Randomized controlled trials (RCTs) are often considered the gold standard for estimating causal effect, but they may lack external validity when the population eligible to the RCT is substantially different from the target population. Having at hand a sample of the target population of interest allows us to generalize the causal effect. Identifying the treatment effect in the target population requires covariates to capture all treatment effect modifiers that are shifted between the two sets. Standard estimators then use either weighting (IPSW), outcome modeling (G-formula), or combine the two in doubly robust approaches (AIPSW). However, such covariates are often not available in both sets. In this article, after proving L1{L}^{1}-consistency of these three estimators, we compute the expected bias induced by a missing covariate, assuming a Gaussian distribution, a continuous outcome, and a semi-parametric model. Under this setting, we perform a sensitivity analysis for each missing covariate pattern and compute the sign of the expected bias. We also show that there is no gain in linearly imputing a partially unobserved covariate. Finally, we study the substitution of a missing covariate by a proxy. We illustrate all these results on simulations, as well as semi-synthetic benchmarks using data from the Tennessee student/teacher achievement ratio (STAR), and a real-world example from critical care medicine. |
| first_indexed | 2024-04-13T12:55:27Z |
| format | Article |
| id | doaj.art-0f9459d60c954d618b6f35f39ac277c8 |
| institution | Directory Open Access Journal |
| issn | 2193-3685 |
| language | English |
| last_indexed | 2024-04-13T12:55:27Z |
| publishDate | 2022-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Causal Inference |
| spelling | doaj.art-0f9459d60c954d618b6f35f39ac277c82022-12-22T02:46:05ZengDe GruyterJournal of Causal Inference2193-36852022-11-0110137241410.1515/jci-2021-0059Causal effect on a target population: A sensitivity analysis to handle missing covariatesColnet Bénédicte0Josse Julie1Varoquaux Gaël2Scornet Erwan3Soda Project-team, Premedical Project-team, INRIA, and Centre de Mathémathiques Appliquées, Institut Polytechnique de Paris, Palaiseau, FrancePremedical Project Team, INRIA Sophia-Antipolis, Montpellier, FranceSoda Project-team, INRIA Saclay, FranceCentre de Mathémathiques Appliquées, UMR 7641, École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, FranceRandomized controlled trials (RCTs) are often considered the gold standard for estimating causal effect, but they may lack external validity when the population eligible to the RCT is substantially different from the target population. Having at hand a sample of the target population of interest allows us to generalize the causal effect. Identifying the treatment effect in the target population requires covariates to capture all treatment effect modifiers that are shifted between the two sets. Standard estimators then use either weighting (IPSW), outcome modeling (G-formula), or combine the two in doubly robust approaches (AIPSW). However, such covariates are often not available in both sets. In this article, after proving L1{L}^{1}-consistency of these three estimators, we compute the expected bias induced by a missing covariate, assuming a Gaussian distribution, a continuous outcome, and a semi-parametric model. Under this setting, we perform a sensitivity analysis for each missing covariate pattern and compute the sign of the expected bias. We also show that there is no gain in linearly imputing a partially unobserved covariate. Finally, we study the substitution of a missing covariate by a proxy. We illustrate all these results on simulations, as well as semi-synthetic benchmarks using data from the Tennessee student/teacher achievement ratio (STAR), and a real-world example from critical care medicine.https://doi.org/10.1515/jci-2021-0059average treatment effectdistributional shiftexternal validitygeneralizabilitytransportabilityprimary 62f1293c4162g35secondary 62p1062p25 |
| spellingShingle | Colnet Bénédicte Josse Julie Varoquaux Gaël Scornet Erwan Causal effect on a target population: A sensitivity analysis to handle missing covariates Journal of Causal Inference average treatment effect distributional shift external validity generalizability transportability primary 62f12 93c41 62g35 secondary 62p10 62p25 |
| title | Causal effect on a target population: A sensitivity analysis to handle missing covariates |
| title_full | Causal effect on a target population: A sensitivity analysis to handle missing covariates |
| title_fullStr | Causal effect on a target population: A sensitivity analysis to handle missing covariates |
| title_full_unstemmed | Causal effect on a target population: A sensitivity analysis to handle missing covariates |
| title_short | Causal effect on a target population: A sensitivity analysis to handle missing covariates |
| title_sort | causal effect on a target population a sensitivity analysis to handle missing covariates |
| topic | average treatment effect distributional shift external validity generalizability transportability primary 62f12 93c41 62g35 secondary 62p10 62p25 |
| url | https://doi.org/10.1515/jci-2021-0059 |
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