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Doubly Robust Additive Hazards Models to Estimate Effects of a Continuous Exposure on Survival

Wang, Yana,b; Lee, Mihyea; Liu, Pengfeic; Shi, Liuhuaa; Yu, Zhid; Abu Awad, Yaraa; Zanobetti, Antonellaa; Schwartz, Joel D.a

doi: 10.1097/EDE.0000000000000742
Air Pollution

Background: The effect of an exposure on survival can be biased when the regression model is misspecified. Hazard difference is easier to use in risk assessment than hazard ratio and has a clearer interpretation in the assessment of effect modifications.

Methods: We proposed two doubly robust additive hazards models to estimate the causal hazard difference of a continuous exposure on survival. The first model is an inverse probability-weighted additive hazards regression. The second model is an extension of the doubly robust estimator for binary exposures by categorizing the continuous exposure. We compared these with the marginal structural model and outcome regression with correct and incorrect model specifications using simulations. We applied doubly robust additive hazard models to the estimation of hazard difference of long-term exposure to PM2.5 (particulate matter with an aerodynamic diameter less than or equal to 2.5 microns) on survival using a large cohort of 13 million older adults residing in seven states of the Southeastern United States.

Results: We showed that the proposed approaches are doubly robust. We found that each 1 μg m−3 increase in annual PM2.5 exposure was associated with a causal hazard difference in mortality of 8.0 × 10−4 (95% confidence interval 7.4 × 10−4, 8.7 × 10−4), which was modified by age, medical history, socioeconomic status, and urbanicity. The overall hazard difference translates to approximately 5.5 (5.1, 6.0) thousand deaths per year in the study population.

Conclusions: The proposed approaches improve the robustness of the additive hazards model and produce a novel additive causal estimate of PM2.5 on survival and several additive effect modifications, including social inequality.

Supplemental Digital Content is available in the text.

aDepartment of Environmental Health, Harvard T.H. Chan School of Public Health, Boston, MA; bDepartment of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA; cHarvard John A. Paulson School of Engineering and Applied Sciences, Cambridge, MA; and dDivision of Rheumatology, Allergy and Immunology, Section of Clinical Sciences, Brigham and Women’s Hospital, Boston, MA.

Submitted 5 September 2016; accepted 17 August 2017.

The authors report no conflicts of interest.

Data and code availability: R and SAS code for doubly robust additive hazards model A is given in eAppendix. The simulation code is available upon request. The Medicare dataset was used under a data use agreement and cannot be shared.

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Correspondence: Joel D. Schwartz, Department of Environmental Health, Harvard T.H. Chan School of Public Health, 401 Park Drive, PO Box 15677, Boston, MA 02215. E-mail:

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