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Research article
Todd MacKenzie
Dartmouth Medical School
Corresponding Author
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This work is licensed under a CC BY 4.0 License. Read Full License
Estimation that employs instrumental variables (IV) can reduce or eliminate bias due to confounding. In observational studies instruments result from natural experiments such as the effect of clinician preference or geographic distance on treatment selection. In randomized studies the randomization indicator is an instrument, especially if the study is blinded, e.g. no placebo effect. Estimation via instruments is a highly developed field for linear models but the use of instruments in time-to-event analysis is far from established. Various IV-based estimators of the hazard ratio (HR) from Cox's regression models have been proposed. We extend IV based estimation of Cox's models beyond proportionality of hazards, and address estimation of a log-linear time dependent hazard ratio and a piecewise constant HR. We estimate the marginal time-dependent hazard ratio unlike other approaches that estimate the hazard ratio conditional on the omitted covariates. Due to the non-collapsibility of the Cox's models these two estimands are not identical. We report the results of simulations that includes the use of copulas to generate potential times-to-event that have a given marginal structural time dependent hazard ratio but are dependent on omitted covariates. We demonstrate the method to estimate the time dependent hazard ratio for two vascular interventions.
Keywords
Causal inference, Censoring, Semi-parametric model, Marginal model
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This is a preprint. It has not completed peer review.
Research article
Todd MacKenzie
Dartmouth Medical School
Corresponding Author
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
History
CURRENT STATUS: Posted
Version 1
Posted 22 Nov, 2019
No community comments so far
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Health Economics & Outcomes Research
License:
This work is licensed under a CC BY 4.0 License. Read Full License
Estimation that employs instrumental variables (IV) can reduce or eliminate bias due to confounding. In observational studies instruments result from natural experiments such as the effect of clinician preference or geographic distance on treatment selection. In randomized studies the randomization indicator is an instrument, especially if the study is blinded, e.g. no placebo effect. Estimation via instruments is a highly developed field for linear models but the use of instruments in time-to-event analysis is far from established. Various IV-based estimators of the hazard ratio (HR) from Cox's regression models have been proposed. We extend IV based estimation of Cox's models beyond proportionality of hazards, and address estimation of a log-linear time dependent hazard ratio and a piecewise constant HR. We estimate the marginal time-dependent hazard ratio unlike other approaches that estimate the hazard ratio conditional on the omitted covariates. Due to the non-collapsibility of the Cox's models these two estimands are not identical. We report the results of simulations that includes the use of copulas to generate potential times-to-event that have a given marginal structural time dependent hazard ratio but are dependent on omitted covariates. We demonstrate the method to estimate the time dependent hazard ratio for two vascular interventions.
This preprint is available for download as a PDF.
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