Causal inference with a quantitative exposure.
The current statistical literature on causal inference is mostly concerned with binary or categorical exposures, even though exposures of a quantitative nature are frequently encountered in epidemiologic research. In this article, we review the available methods for estimating the dose-response curve for a quantitative exposure, which include ordinary regression based on an outcome regression model, inverse propensity weighting and stratification based on a propensity function model, and an augmented inverse propensity weighting method that is doubly robust with respect to the two models. We note that an outcome regression model often imposes an implicit constraint on the dose-response curve, and propose a flexible modeling strategy that avoids constraining the dose-response curve. We also propose two new methods: a weighted regression method that combines ordinary regression with inverse propensity weighting and a stratified regression method that combines ordinary regression with stratification. The proposed methods are similar to the augmented inverse propensity weighting method in the sense of double robustness, but easier to implement and more generally applicable. The methods are illustrated with an obstetric example and compared in simulation studies.
Division of Biostatistics, Office of Surveillance and Biometrics, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland, USA zhiwei_zhang@yahoo.com zhiwei.zhang@fda.hhs.gov.
Zhiwei
Z
Zhang
Division of Biostatistics, Office of Surveillance and Biometrics, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland, USA.
Jie
J
Zhou
Division of Biostatistics, Office of Surveillance and Biometrics, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland, USA.
Weihua
W
Cao
MOE and Shanghai Key Laboratory of Children's Environmental Health, Xinhua Hospital, Shanghai Jiaotong University School of Medicine, Shanghai, P.R. China.
Jun
J
Zhang
D000465:Algorithms; D056808:Biostatistics; D001724:Birth Weight; D015992:Body Mass Index; D015984:Causality; D003198:Computer Simulation; D004305:Dose-Response Relationship, Drug; D005260:Female; D006801:Humans; D007231:Infant, Newborn; D015233:Models, Statistical; D011247:Pregnancy; D012044:Regression Analysis